diff --git a/.bumpversion.cfg b/.bumpversion.cfg
index 54b6c97..175d563 100644
--- a/.bumpversion.cfg
+++ b/.bumpversion.cfg
@@ -1,5 +1,5 @@
 [bumpversion]
-current_version = 0.0.2
+current_version = 0.0.3
 commit = true
 tag = false
 tag_name = v{new_version}
diff --git a/.claude/CLAUDE.md b/.claude/CLAUDE.md
index f1ef708..b27913f 100644
--- a/.claude/CLAUDE.md
+++ b/.claude/CLAUDE.md
@@ -54,15 +54,20 @@ and every module's behavior. Consult the relevant spec before extending a
 module; if implementation forces a contract change, the spec is updated in
 the same change and its `semver` bumped.
 
+Reproduced defect evidence, measurements, source locations, and
+implementation material live in `.claude/findings/` — never in a spec.
+
 - [mathToolsArchitecture.md](specs/mathToolsArchitecture.md) — umbrella:
   layering, package layout, dependency policy, shared conventions, error
   semantics
-- [templateConformance.md](specs/templateConformance.md) — template
-  migration: packaging, Makefile/CI parity, rename, governance docs
+- [templateConformance.md](specs/templateConformance.md) — packaging,
+  dependency resolvability, CI install parity, governance artifacts
 - [precisionTimeMath.md](specs/precisionTimeMath.md) — `PrecisionTimeInterval`,
   `PrecisionTimestamp`
 - [spatialMath.md](specs/spatialMath.md) — `Position`, `Quaternion`,
   `SpatialPose`
+- [sphericalGeometry.md](specs/sphericalGeometry.md) — unit-sphere arcs and
+  small circles, transforms, the `orient` bearing convention
 - [waveformCore.md](specs/waveformCore.md) — `Waveform1D` + aggregate
   waveform containers
 - [waveformDsp.md](specs/waveformDsp.md) — DSP families, scipy mapping,
diff --git a/.claude/archive/math-tools-port.md b/.claude/archive/math-tools-port.md
new file mode 100644
index 0000000..19e135c
--- /dev/null
+++ b/.claude/archive/math-tools-port.md
@@ -0,0 +1,30 @@
+---
+version: 1.0
+type: retrospective
+name: math-tools-port
+purpose: Concise record of the completed py-MathTools template migration and Swift math capability port
+scope: project
+status: complete
+last_updated: 2026-09-24
+semver: 0.0.1
+author: Nicholas Bergantz
+---
+
+# Math Tools Port Retrospective
+
+## Goal
+
+Bring py-MathTools onto the py-foundationTools template conventions and implement the Swift `FoundationMathTypes` capability set as the Tier-3 Python math layer.
+
+## Outcome
+
+The 57 implementation and corrective-action chunks completed the precision-time, spatial, waveform, DSP, polynomial, and online trajectory generation surfaces. The final recorded gate passed Ruff, strict mypy, and 1,550 tests. The original chunk-by-chunk plans and resolution notes remain available in Git history, principally commits `24582be` and `6002a9a`.
+
+## Preserved Decisions
+
+- `Position` and `SpatialPose` arithmetic may return base types for subclasses. No in-repository subclasses existed; revisit only when subclass preservation is required.
+- `SpatialPose.inverse` and `UnivariatePolynomial.derivative` remain methods. Changing them to properties would be a breaking cosmetic change.
+- Behavioral test coverage for spherical geometry and `math_plot_helpers` was deferred from the original port. Current spherical defects and required outcomes are tracked separately in the active findings and specifications.
+- `WaveformPaddingStrategy`, `WaveformFilterCoefficients`, `WaveformFrequencyRange`, and `WaveformSpectrogramScaling` remain public support types without current DSP consumers. Whether to remove them or add consuming APIs requires a separate contract decision.
+- `SpectralMixin.spectrogram` retains the legacy SciPy implementation despite the DSP specification naming `ShortTimeFFT`; migration would be a behavioral change.
+- The uncalled `_time_none_smooth` online trajectory generation path remains because the Swift source also retains it.
diff --git a/.claude/archive/math-tools-port/00-overview.md b/.claude/archive/math-tools-port/00-overview.md
deleted file mode 100644
index e820701..0000000
--- a/.claude/archive/math-tools-port/00-overview.md
+++ /dev/null
@@ -1,195 +0,0 @@
----
-plan: math-tools-port
-status: complete
-last_updated: 2026-07-23
-semver: 0.1.2
-author: Nicholas Bergantz
----
-
-# Action Plan — Template Migration + Swift Math Port
-
-**Goal:** bring py-MathTools onto the py-foundationTools template conventions
-and port the Swift `FoundationMathTypes` capability set (spatial SE(3) types,
-precision time, waveforms + DSP, polynomials/roots, OTG trajectory
-generation) as the Tier-3 math layer, per the accepted specs in
-[`../specs/`](../specs/mathToolsArchitecture.md).
-
-**Usability north star:** a robotics/DSP engineer in a notebook can build a
-waveform or pose, do the obvious math, and reach scipy-grade analysis with
-minimal ceremony — well-typed numpy-adjacent Python, not translated Swift.
-
-## Conventions every chunk inherits (do not restate per chunk)
-
-1. **Spec is authoritative.** Each chunk lists its governing spec section(s).
-   If implementation forces a contract change, update the spec in the same
-   chunk and bump its `semver`.
-2. **TDD:** write the failing tests first, implement, then run the gate.
-3. **Gate:** `make uv-fullCheck` (ruff lint + mypy strict + pytest) must pass
-   at the end of every chunk. Test layout mirrors the package
-   (`tests/<subpkg>/test_<module>.py`), `unittest.TestCase` style, `test_*`
-   methods.
-4. **Stay in scope:** touch ONLY the files the chunk lists. Adjacent
-   problems get reported in the chunk's completion notes, not fixed.
-5. **Frontmatter:** every chunk carries `status: pending` → set
-   `in_progress` while working, then `complete` when done (not `done`
-   — `complete` is the convention actually used across every chunk file
-   in this repo); bump `last_updated`.
-6. **Swift reference roots** (read-only, for faithful-port chunks):
-   - `SWIFT_MATH` = `/Users/nbergantz/__Workspaces__/spmWorkspaces/spmMathTools/spm/Sources/spmMathTools/FoundationMathTypes`
-   - `SWIFT_TYPES` = `/Users/nbergantz/__Workspaces__/spmWorkspaces/spmFoundationTools/spm/Sources/FoundationTypes`
-   - `SWIFT_TESTS` = `/Users/nbergantz/__Workspaces__/spmWorkspaces/spmMathTools/spm/Tests/spmMathToolsTests`
-7. **Shared API idioms** (umbrella spec "API idioms"): `normalized()` method
-   / `normalize()` in-place; `isclose(rtol, atol)`; `__array__`;
-   `__hash__ = None` on mutable numpy-backed classes; snake_case throughout.
-8. Do not commit; the human reviews and commits per track.
-
-## Dependency graph
-
-```
-Track A (template)      01 ──► 02 ──► 03
-                         │
-        ┌────────────────┴───────────────────────────────┐
-Track B │  04 ─► 05          06 ─► 07 ─► 08      09   10 │ (02 before all B)
-        │   └──────┬──────────┘└───┬────┘              │ │
-Track C │          ▼               │                   │ │
-        │  11 ─► {12, 13, 14}      │                   │ │
-        │   │        │             ▼                   │ │
-        │   │        │   15(◄06) 16(◄07) ─► 17(◄08,15,16)│
-Track D │   │        ▼                                 │ │
-        │   │   18..29 (one per mixin; 26 also ◄19)    │ │
-        │   │        └────────► 30 (compose)           │ │
-Track E │   └──────────────────────────────────────────┘ │
-        │  31(◄10) ─► 32                                 │
-        │  31 ─► 33 ─► 34 ─► {35, 36, 37, 38, 39}        │
-        │  {32,35..39} ─► 40 ─► 41 ─► 42                 │
-        └────────────────────────────────────────────────┘
-```
-
-Tracks B/C/D/E parallelize after 01–02; within a track, run in numeric
-order unless the graph says otherwise. Chunk 43 (public surface) runs last,
-after 09, 17, 30, and 42.
-
-## Chunk index
-
-| # | Chunk | Track | Depends on | Spec |
-|---|---|---|---|---|
-| 01 | [template-rename-and-refresh](01-template-rename-and-refresh.md) | A | — | templateConformance |
-| 02 | [errors-and-layering](02-errors-and-layering.md) | A | 01 | umbrella, templateConformance §5 |
-| 03 | [governance-and-readme](03-governance-and-readme.md) | A | 02 | templateConformance §3–4 |
-| 04 | [precision-time-interval](04-precision-time-interval.md) | B | 02 | precisionTimeMath |
-| 05 | [precision-timestamp](05-precision-timestamp.md) | B | 04 | precisionTimeMath |
-| 06 | [position](06-position.md) | B | 02 | spatialMath |
-| 07 | [quaternion-additions](07-quaternion-additions.md) | B | 06 | spatialMath |
-| 08 | [spatial-pose](08-spatial-pose.md) | B | 07 | spatialMath |
-| 09 | [univariate-polynomial](09-univariate-polynomial.md) | B | 02 | polynomials |
-| 10 | [roots-kernel](10-roots-kernel.md) | B | 02 | polynomials |
-| 11 | [waveform1d-core](11-waveform1d-core.md) | C | 05 | waveformCore |
-| 12 | [waveform1d-operators](12-waveform1d-operators.md) | C | 11 | waveformCore |
-| 13 | [waveform1d-generators](13-waveform1d-generators.md) | C | 11 | waveformCore |
-| 14 | [dsp-support-and-protocol](14-dsp-support-and-protocol.md) | C | 11 | waveformDsp |
-| 15 | [waveform-position](15-waveform-position.md) | C | 11, 06 | waveformCore |
-| 16 | [waveform-quaternion](16-waveform-quaternion.md) | C | 11, 07 | waveformCore |
-| 17 | [waveform-spatial-pose](17-waveform-spatial-pose.md) | C | 08, 15, 16 | waveformCore |
-| 18 | [dsp-calc](18-dsp-calc.md) | D | 14 | waveformDsp |
-| 19 | [dsp-correlation](19-dsp-correlation.md) | D | 14 | waveformDsp |
-| 20 | [dsp-envelope](20-dsp-envelope.md) | D | 14 | waveformDsp |
-| 21 | [dsp-spectral](21-dsp-spectral.md) | D | 14 | waveformDsp |
-| 22 | [dsp-filtering](22-dsp-filtering.md) | D | 14 | waveformDsp |
-| 23 | [dsp-peaks](23-dsp-peaks.md) | D | 14 | waveformDsp |
-| 24 | [dsp-phase](24-dsp-phase.md) | D | 14 | waveformDsp |
-| 25 | [dsp-resampling](25-dsp-resampling.md) | D | 14 | waveformDsp |
-| 26 | [dsp-time-alignment](26-dsp-time-alignment.md) | D | 14, 19 | waveformDsp |
-| 27 | [dsp-triggers](27-dsp-triggers.md) | D | 14 | waveformDsp |
-| 28 | [dsp-windowing](28-dsp-windowing.md) | D | 14 | waveformDsp |
-| 29 | [dsp-zero-crossings](29-dsp-zero-crossings.md) | D | 14 | waveformDsp |
-| 30 | [dsp-compose](30-dsp-compose.md) | D | 18–29 | waveformDsp |
-| 31 | [otg-enums-and-errors](31-otg-enums-and-errors.md) | E | 10 | otg |
-| 32 | [otg-input-parameter](32-otg-input-parameter.md) | E | 31 | otg |
-| 33 | [otg-profile](33-otg-profile.md) | E | 31 | otg |
-| 34 | [otg-block-brake-bound](34-otg-block-brake-bound.md) | E | 33 | otg |
-| 35 | [otg-trajectory-and-output](35-otg-trajectory-and-output.md) | E | 34 | otg |
-| 36 | [otg-velocity-steps](36-otg-velocity-steps.md) | E | 34 | otg |
-| 37 | [otg-position-first-second-steps](37-otg-position-first-second-steps.md) | E | 34 | otg |
-| 38 | [otg-position-third-step1](38-otg-position-third-step1.md) | E | 34 | otg |
-| 39 | [otg-position-third-step2](39-otg-position-third-step2.md) | E | 34 | otg |
-| 40 | [otg-calculator-target](40-otg-calculator-target.md) | E | 32, 35–39 | otg |
-| 41 | [otg-driver](41-otg-driver.md) | E | 40 | otg |
-| 42 | [otg-oracle-suites](42-otg-oracle-suites.md) | E | 41 | otg |
-| 43 | [public-surface](43-public-surface.md) | A | 30, 42, 09, 17 | umbrella |
-
----
-
-# Corrective actions — 2026-07-22 post-audit
-
-Chunks 01–43 were audited against their governing specs by five parallel
-skeptical auditors (one per track), with the top findings independently
-reproduced at runtime and source level before being recorded here.
-
-**Verdict: substantially complete.** `make uv-fullCheck` is green (exit 0) and
-the port is faithful in the large — the 31-case OTG numeric truth table was
-re-derived from the Swift source with 0 mismatches, no test in the repo is
-skipped or xfail'd, and no unsolved algorithm case, stub, or swallowed `None`
-was found in the solvers. The confirmed gaps are specific and are chunked below.
-
-Chunks 44–57 form **Track F**. They are corrective, not new capability.
-
-## Confirmed defect summary
-
-| Class | Count | Where |
-|---|---|---|
-| (c) drift / correctness | 8 | OTG solvers, spatial/time accessors, waveform indexing |
-| (a) not implemented | 6 | aggregate API idioms, subpackage exports, roots degeneracy |
-| (b) implemented, untested | ~45 | concentrated in DSP mixins and OTG oracles |
-| (e) docs/convention drift | 14 | dead workflow refs, stale tolerances, boilerplate |
-| (d) out-of-scope violations | **0** | — none found in any track |
-
-The single most consequential finding is a **transcription defect** at
-`position_third_order_step2.py:1731,1752,1763` (`j·tf⁴` where Swift has
-`j·tf³`), confirmed by direct comparison against
-`PositionThirdOrderStep2.swift:1279,1286,1289`. It changes profile-branch
-selection in ~0.57% of prescribed-duration Step2 solves and is invisible to the
-current gate — because the entire 1,784-case OTG oracle corpus is 1-DOF, which
-takes a fast path that **never invokes Step2 at all** (measured: 0 invocations).
-
-## Dependency graph
-
-```
-Track F (corrective)
-
-  OTG code fixes        44   45   46
-                         └────┴────┴──────► 56 (OTG oracle closure)
-
-  Track B/C code fixes  47   48   49 ─► 50   51
-                                    └────┴────┴─► 54 (B/C test closure)
-
-  Surface / conventions 52        53 ─────────────► 55 (DSP test closure)
-
-  Everything above ───────────────────────────────► 57 (docs sweep, last)
-```
-
-44–49, 51, 52, 53 are mutually independent and may run in parallel.
-50 waits on 49. The three closure chunks wait on their code fixes. 57 runs last
-so it reconciles docs against the post-fix repo.
-
-## Corrective chunk index
-
-| # | Chunk | Kind | Depends on | Origin |
-|---|---|---|---|---|
-| 44 | [otg-step2-udud-discriminant](44-otg-step2-udud-discriminant.md) | fix | — | E-1 |
-| 45 | [otg-trivial-profile-length](45-otg-trivial-profile-length.md) | fix | — | E-2 |
-| 46 | [otg-step1-sqrt-guard](46-otg-step1-sqrt-guard.md) | fix | — | E-3 |
-| 47 | [position-tolerance-and-timestamp-accessors](47-position-tolerance-and-timestamp-accessors.md) | fix | — | B-1, B-2 |
-| 48 | [roots-degenerate-cases](48-roots-degenerate-cases.md) | fix | — | B-7, B-14 |
-| 49 | [waveform-spatial-pose-indexing](49-waveform-spatial-pose-indexing.md) | fix | — | C-4, C-5 |
-| 50 | [aggregate-container-api-idioms](50-aggregate-container-api-idioms.md) | fix | 49 | C-1, C-2, C-3, C-7 |
-| 51 | [waveform-generator-phase-conventions](51-waveform-generator-phase-conventions.md) | fix | — | C-15 |
-| 52 | [subpackage-public-surface](52-subpackage-public-surface.md) | fix | — | A-1, A-2 |
-| 53 | [window-convention-reconciliation](53-window-convention-reconciliation.md) | fix | — | D-windowing |
-| 54 | [test-closure-tracks-bc](54-test-closure-tracks-bc.md) | tests | 47–51 | 11 (b) findings |
-| 55 | [test-closure-dsp](55-test-closure-dsp.md) | tests | 53 | 23 (b) findings |
-| 56 | [test-closure-otg-oracles](56-test-closure-otg-oracles.md) | tests | 44, 45, 46 | 8 (b) findings |
-| 57 | [docs-and-convention-sweep](57-docs-and-convention-sweep.md) | docs | 44–56 | 14 (e) findings |
-
-Findings deliberately **not** actioned (B-4, B-5, B-6, A-7, D-cross-cutting,
-D-spectral-(c), E-10) are recorded with rationale in chunk 57's
-"Recorded — no action" section, so the decisions are not relitigated.
diff --git a/.claude/archive/math-tools-port/01-template-rename-and-refresh.md b/.claude/archive/math-tools-port/01-template-rename-and-refresh.md
deleted file mode 100644
index 2d09849..0000000
--- a/.claude/archive/math-tools-port/01-template-rename-and-refresh.md
+++ /dev/null
@@ -1,123 +0,0 @@
----
-chunk: 01-template-rename-and-refresh
-track: A
-status: complete
-depends_on: []
-spec: ../specs/templateConformance.md §Gap 1, §Gap 2.4; ../specs/spatialMath.md §Modules (ABC re-parent)
-last_updated: 2026-07-11
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 01 — Package rename + environment refresh
-
-**Deliverable:** the repo builds and gates green under the new snake_case
-package names against the pinned foundation branch. Mechanical migration —
-no behavior changes beyond the required ABC re-parent.
-
-## Files
-
-- `git mv src/pyMathTools src/math_tools`; inside it:
-  `git mv src/math_tools/spatial/Quaternion.py src/math_tools/spatial/quaternion.py`,
-  `git mv src/math_tools/spherical/sphericalGenerators.py src/math_tools/spherical/spherical_generators.py`,
-  `git mv src/math_tools/spherical/sphericalTransforms.py src/math_tools/spherical/spherical_transforms.py`
-  (`constructors.py`, `hints.py` keep their names).
-- `git mv src/pyMathToolsPlotHelpers src/math_plot_helpers`;
-  `git mv src/math_plot_helpers/plotUnitSpherical.py src/math_plot_helpers/plot_unit_spherical.py`.
-- Edit: `src/math_tools/spatial/quaternion.py` (imports/base only, see below),
-  every `__init__.py` touched by moves, `tests/test_quaternion.py`,
-  `examples/sphericalPlotting/plotArcs.py`,
-  `examples/sphericalPlotting/plotQuatUnitCircles.py`, `Makefile` (mypy
-  package list if it names packages), `.env` if it names packages.
-- Add: `py.typed` in `src/math_tools/` and `src/math_plot_helpers/` roots
-  (keep the existing ones in subpackages).
-
-## Design constraints
-
-1. **First action:** `make uv-refresh` so `.venv` matches the
-   `requirements.txt` branch pin (the stale install has the pre-template ABC
-   layout; nothing imports correctly until this runs).
-2. **ABC re-parent (the one semantic edit):** in `quaternion.py`, replace
-   `from foundationTypes.mathTypes.quaternionABC import QuaternionABC` with
-   `from foundation_abc.math.spatialABCs import QuaternionABC`. The old ABC
-   carried `DataModelHelper`; the new one is ABC-only with a concrete
-   `to_dict`. In `tests/test_quaternion.py`, update the serialization tests'
-   base-class assertions (`DataModelHelper` inheritance assertion → the new
-   ABC) — assertions on `to_dict`/`from_dict` *values* stay untouched. If any
-   other import from the old layout exists (grep `foundationTypes.mathTypes.`
-   across `src/`), re-point to `foundation_abc.math.*` /
-   `foundationTypes.mathTypes.MathTypes` equivalents.
-3. All other edits are import-path text substitutions
-   (`pyMathTools` → `math_tools`, `pyMathToolsPlotHelpers` →
-   `math_plot_helpers`, moved module filenames).
-4. `pyproject.toml`: update `description` only if trivially co-located; the
-   deps list changes in chunk 03, not here.
-
-## TDD steps
-
-1. `make uv-refresh`; run `make uv-test` to record the pre-existing pass/fail
-   baseline (the ABC import may already be broken — note it).
-2. Perform moves + edits.
-3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] `grep -rn "pyMathTools" src/ tests/ examples/ Makefile .env pyproject.toml` → no hits
-- [x] `grep -rn "foundationTypes.mathTypes.quaternionABC" src/ tests/` → no hits
-- [x] `git log --follow --oneline src/math_tools/spatial/quaternion.py` shows history (moves were `git mv`) — verified via `git status`/`git diff --staged` showing `renamed: src/pyMathTools/spatial/Quaternion.py -> src/math_tools/spatial/quaternion.py`; `--follow` itself needs a commit to walk, which this chunk intentionally leaves to the supervising process
-- [x] All ~90 quaternion tests pass (89 collected/passed); diff to `tests/test_quaternion.py` contains only import lines, base-class assertion lines, and their two adjacent docstring lines (see Resolution notes)
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-`errors.py`, layering test, README, `.claude/CLAUDE.md`, pyproject dependency
-list, any new math code, any `__init__.py` re-export curation beyond fixing
-broken imports.
-
-## Resolution notes
-
-- `make uv-refresh` pulled the pinned foundation branch fresh; pre-move
-  `make uv-test` baseline reproduced the expected pre-existing break
-  (`ModuleNotFoundError: foundationTypes.mathTypes.quaternionABC`), confirming
-  the venv was stale before this chunk and the gate is meaningful after.
-- Moves done via `git mv` as specified. `git status`/`git diff --staged`
-  correctly report `quaternion.py` as a rename from `Quaternion.py`; git's
-  similarity heuristic cross-matched some of the (byte-identical, empty)
-  `__init__.py` files to different-but-equivalent old empty `__init__.py`
-  paths — cosmetic only, every file's on-disk destination was verified
-  directly with `find`, and it does not affect `--follow` on the files that
-  matter (confirmed for `quaternion.py`).
-- The old-layout ABC repoint (design constraint 2) turned out to reach beyond
-  `quaternion.py`: `foundationTypes.mathTypes.unitSphericalArcABC` and
-  `unitSphericalSmallCircleABC` (imported by `spherical_generators.py`,
-  `spherical_transforms.py`, `constructors.py`, `plot_unit_spherical.py`)
-  were also deleted from the pinned foundation branch and now live at
-  `foundation_abc.math.sphericalABCs`. Re-pointed all of them per the chunk's
-  explicit "grep `foundationTypes.mathTypes.` across `src/`" instruction —
-  required for `make uv-fullCheck` (mypy strict) to pass, since mypy scans
-  all of `src/`, not just the quaternion module. `foundationTypes.mathTypes.MathTypes.*`
-  imports (the codegen `*Type` classes) were left untouched — that module
-  still exists unchanged in the new layout.
-  This is a scope note, not a spec deviation: constraint 2's own text
-  authorized exactly this action; the "Files" list section above just didn't
-  enumerate every file it touched.
-- `examples/sphericalPlotting/plotArcs.py` and `plotQuatUnitCircles.py` got
-  only the mechanical package-name substitution, per constraint 3 and Gap 4's
-  explicit ownership of their pre-existing broken `foundationTypes.mathTypes.UnitSphericalArc`
-  / `UnitSphericalSmallCircle` imports (not part of this chunk's scope, and
-  not scanned by `make uv-typecheck` since `PY_EXAMPLES` is unset in `.env`).
-- `tests/test_quaternion.py`: `test_inheritance_from_data_model_helper`
-  asserted `isinstance(q, DataModelHelper)`, which is no longer true (the new
-  `QuaternionABC` is ABC-only). Repointed the import and assertion to
-  `QuaternionABC` per constraint 2's directive, and updated that test's and
-  the class's docstrings by one line each so the docstrings don't contradict
-  the assertion right below them — the only lines in this diff beyond raw
-  import-path substitution. No `to_dict`/`from_dict` value assertions were
-  touched.
-- Added `py.typed` at `src/math_tools/` and `src/math_plot_helpers/` package
-  roots (subpackage ones already existed).
-- No `Makefile`/`.env` edits were needed — neither names packages explicitly
-  (both scope quality targets via path variables, not package names).
-- `pyproject.toml` `description` left untouched — no trivially co-located
-  edit was applicable in this chunk; still boilerplate text, tracked as Gap 4
-  (chunk 03).
diff --git a/.claude/archive/math-tools-port/02-errors-and-layering.md b/.claude/archive/math-tools-port/02-errors-and-layering.md
deleted file mode 100644
index 78fdbfb..0000000
--- a/.claude/archive/math-tools-port/02-errors-and-layering.md
+++ /dev/null
@@ -1,74 +0,0 @@
----
-chunk: 02-errors-and-layering
-track: A
-status: complete
-depends_on: [01]
-spec: ../specs/mathToolsArchitecture.md §Error semantics; ../specs/templateConformance.md §Gap 5
-last_updated: 2026-07-11
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 02 — Exception hierarchy + package layering test
-
-**Deliverable:** `math_tools/errors.py` and the AST-based layering test.
-
-## Files
-
-- Create: `src/math_tools/errors.py`
-- Create: `tests/test_package_layering.py`
-- Create: `tests/test_errors.py`
-
-## Design constraints
-
-1. `errors.py` defines exactly (each with a one-line docstring):
-   `MathToolsError(Exception)`, `WaveformCompatibilityError(MathToolsError)`,
-   `TimestampComparisonError(MathToolsError)`,
-   `PolynomialSolveError(MathToolsError)`.
-2. Layering test pattern: copy the approach of py-foundationTools
-   `tests/test_package_layering.py` (AST-walk every module under `src/`,
-   collect `import`/`from` roots). Assertions per templateConformance §Gap 5:
-   `math_tools` imports neither `math_plot_helpers` nor `matplotlib`;
-   only `math_plot_helpers` imports `matplotlib`.
-3. Additionally assert `math_tools.otg` (once it exists) does not import
-   `numpy` — write the rule now, guarded to skip if the package dir is
-   absent, so OTG chunks inherit enforcement for free.
-
-## TDD steps
-
-1. Write `tests/test_errors.py` (hierarchy, catchability as `MathToolsError`)
-   and `tests/test_package_layering.py`; watch errors test fail.
-2. Implement `errors.py`; layering test must pass against the current tree.
-3. Temporarily add `import matplotlib` to a `math_tools` module and confirm
-   the layering test fails; revert. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] All four exception classes exist and subclass as specified
-- [x] Layering test fails on an injected `import matplotlib` in `math_tools` (verified then reverted)
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Any consumer of the exceptions; OTG's `OtgError` (lives in `otg/errors.py`,
-chunk 31); README/CLAUDE.md.
-
-## Resolution notes
-
-- `errors.py` implements exactly the four classes from the spec, each a
-  one-line docstring, no added behavior.
-- `test_package_layering.py` follows the py-foundationTools AST-scan pattern
-  (`tests/test_package_layering.py` there) rather than executing imports, so
-  it can't be defeated by import side effects. Four checks: `math_tools` ↛
-  `math_plot_helpers`, `math_tools` ↛ `matplotlib`, only `math_plot_helpers`
-  → `matplotlib` (scans all of `src/` excluding that package), and the
-  guarded `math_tools.otg` ↛ `numpy` rule (currently a no-op skip since
-  `otg/` doesn't exist yet — will activate automatically once chunk 31 lands).
-- Verification step 3 (inject `import matplotlib` into `math_tools/errors.py`,
-  confirm two layering assertions fail, revert) was done live against the
-  actual gate, not simulated; file diffed back to the original after.
-- One ruff fix needed: the injected-violation assertion message exceeded the
-  100-char line limit in `test_only_math_plot_helpers_imports_matplotlib`'s
-  sibling test; wrapped the f-string across two lines.
-- No spec changes were required — the chunk's design constraints matched the
-  umbrella spec's Error semantics section exactly.
diff --git a/.claude/archive/math-tools-port/03-governance-and-readme.md b/.claude/archive/math-tools-port/03-governance-and-readme.md
deleted file mode 100644
index 804cdab..0000000
--- a/.claude/archive/math-tools-port/03-governance-and-readme.md
+++ /dev/null
@@ -1,106 +0,0 @@
----
-chunk: 03-governance-and-readme
-track: A
-status: complete
-depends_on: [02]
-spec: ../specs/templateConformance.md §Gap 2, §Gap 3, §Gap 4
-last_updated: 2026-07-11
-semver: 0.0.2
-author: Nicholas Bergantz
----
-
-# 03 — Governance docs, README, dependency names
-
-**Deliverable:** `.claude/CLAUDE.md`, real README, pyproject dependency
-names, fixed examples.
-
-## Files
-
-- Create: `.claude/CLAUDE.md`
-- Edit: `README.md`, `pyproject.toml` (deps + description only),
-  `examples/sphericalPlotting/plotArcs.py`,
-  `examples/sphericalPlotting/plotQuatUnitCircles.py`
-
-## Design constraints
-
-1. `.claude/CLAUDE.md` follows the shape of py-foundationTools
-   `.claude/CLAUDE.md` but stays short: repo role (Tier 3 of foundation's
-   `mathTypeTiers.md`), the two-package layering diagram, gate command,
-   Makefile-is-source-of-truth note, and a linked index of every spec in
-   `.claude/specs/`. Reference specs; never duplicate their content.
-2. `pyproject.toml` `dependencies` = names only:
-   `pyFoundationTools`, `numpy`, `scipy`, `numpy-quaternion`, `matplotlib`.
-   Replace the boilerplate `description`.
-3. README per templateConformance Gap 4: describe only what exists at
-   execution time (quaternion, spherical utilities, template workflows);
-   sections: title → Features → Installation → Quick Start → Development
-   Workflows → Requirements. Quick Start snippets must actually run.
-4. `plotArcs.py`: fix the dead
-   `foundationTypes.mathTypes.UnitSphericalArc.UnitSphericalArc` import to
-   the real generated type in `foundationTypes.mathTypes.MathTypes`
-   (verify the class name by reading that module).
-
-## TDD steps
-
-1. Add a test `tests/test_governance.py`: `.claude/CLAUDE.md` exists and its
-   text links every `*.md` in `.claude/specs/`; `README.md` contains no
-   "Boilerplate". Watch it fail.
-2. Write the docs; run both example scripts manually
-   (`uv run python examples/sphericalPlotting/plotArcs.py` with a
-   non-interactive matplotlib backend) to prove imports resolve.
-3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] `tests/test_governance.py` passes
-- [x] `pyproject.toml` deps are exactly the five names, unpinned
-- [x] Both example scripts import-run without error
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Makefile/CI edits; requirements pin changes; any `src/` code beyond the
-example imports.
-
-## Resolution notes
-
-- `tests/test_governance.py` added: asserts `.claude/CLAUDE.md` exists and
-  its text contains the filename of every `.claude/specs/*.md` file, and
-  that `README.md` contains no `"Boilerplate"` text. Confirmed it failed
-  before the docs existed, passed after.
-- `.claude/CLAUDE.md` written to the shape of py-foundationTools'
-  `.claude/CLAUDE.md` (Project Overview → layering → Commands → Specs index
-  → Tests) but scoped to what exists in this repo today: Tier 3 role, the
-  two-package layering diagram, the gate command, a Makefile-is-source-of-
-  truth note, and a linked index of all 7 specs in `.claude/specs/`.
-- `README.md` rewritten per Gap 4's section shape (title → Features →
-  Installation → Quick Start → Development Workflows → Requirements),
-  describing only what exists at execution time: `Quaternion`, the
-  spherical arc/small-circle utilities, `errors.py`, and the
-  `math_plot_helpers` plotting package. Both Quick Start snippets
-  (quaternion arithmetic/conversion, spherical arc construction +
-  endpoint) were executed directly to confirm they run as written.
-- `pyproject.toml`: `dependencies` set to the five names
-  (`pyFoundationTools`, `numpy`, `scipy`, `numpy-quaternion`, `matplotlib`)
-  — the prior list was missing `numpy`/`scipy` and had an unrelated stray
-  order; `description` replaced with a one-line Tier-3 summary.
-- `examples/sphericalPlotting/plotArcs.py`: fixed the dead
-  `foundationTypes.mathTypes.UnitSphericalArc.UnitSphericalArc` import to
-  `foundationTypes.mathTypes.MathTypes.UnitSphericalArcType` (verified the
-  real class name by reading the installed `MathTypes.py`) and updated the
-  two local usages/type hints accordingly.
-- `examples/sphericalPlotting/plotQuatUnitCircles.py`: same dead-import
-  pattern existed for `UnitSphericalSmallCircle` (not called out by name in
-  the chunk's design constraint 4, but the file was listed for edit and the
-  acceptance criterion requires *both* scripts to import-run without
-  error) — fixed to `foundationTypes.mathTypes.MathTypes.UnitSphericalSmallCircleType`.
-- Both example scripts verified to run end-to-end with
-  `MPLBACKEND=Agg PYTHONPATH=src .venv/bin/python examples/sphericalPlotting/<script>.py`
-  — exit 0, only a benign "FigureCanvasAgg is non-interactive" UserWarning
-  from `show_plot=True` under a non-interactive backend. Examples are not
-  wired into `make uv-fullCheck` (`PY_EXAMPLES` is unset in `.env`), so
-  this was a manual verification step, not a gate addition (out of scope
-  per this chunk: "Makefile/CI edits").
-- Gate: `make uv-fullCheck` passes — ruff clean, `mypy src tests` strict
-  clean (16 source files), pytest 106 passed (includes the new
-  `tests/test_governance.py`).
diff --git a/.claude/archive/math-tools-port/04-precision-time-interval.md b/.claude/archive/math-tools-port/04-precision-time-interval.md
deleted file mode 100644
index 17397c2..0000000
--- a/.claude/archive/math-tools-port/04-precision-time-interval.md
+++ /dev/null
@@ -1,109 +0,0 @@
----
-chunk: 04-precision-time-interval
-track: B
-status: complete
-depends_on: [02]
-spec: ../specs/precisionTimeMath.md §Representation, §PrecisionTimeInterval, §Compliance 1–6, 10
-last_updated: 2026-07-13
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 04 — `PrecisionTimeInterval`
-
-**Deliverable:** the immutable attosecond-exact interval type.
-
-## Files
-
-- Create: `src/math_tools/precision_time/__init__.py` (re-export
-  `PrecisionTimeInterval`; `PrecisionTimestamp` added by chunk 05),
-  `src/math_tools/precision_time/py.typed`,
-  `src/math_tools/precision_time/precision_time_interval.py`
-- Create: `tests/precision_time/__init__.py`,
-  `tests/precision_time/test_precision_time_interval.py`
-
-## Design constraints
-
-1. Subclass `foundation_abc.math.precisionTimeABC.PrecisionTimeIntervalABC`;
-   enums from `foundation_abc.math.mathEnums`. Use the ABC's
-   `ATTOSECONDS_PER_SECOND`, never a new literal.
-2. Storage: one private signed `int` of total attoseconds (spec
-   §Representation shows the derived accessors — implement exactly that).
-3. Immutable + hashable: no public setters; implement `__hash__` from the
-   total; all arithmetic returns new instances; foreign operand types return
-   `NotImplemented`.
-4. Full surface per spec: constructors (`__init__` ABC-shaped with
-   normalization/carry, `from_seconds`, `from_attoseconds`, `from_string`),
-   constants (`ZERO`, `ONE_SECOND`, `ONE_DECISECOND`, `ONE_MILLISECOND`,
-   `ONE_MICROSECOND`), accessors (`total_attoseconds`, `seconds_as_float`),
-   arithmetic (`+ - neg pos abs`, scalar `* /` rounding to nearest
-   attosecond, interval `/` interval → float), total ordering, `bool`,
-   `to_dict`/`from_dict` on the ABC wire shape, `repr`.
-5. Swift reference for semantics questions:
-   `SWIFT_TYPES/PrecisionTime/PrecisionTimeInterval.swift` (+`+Arithmetic`)
-   — but NO saturation/wrapping ops (spec divergence).
-
-## TDD steps
-
-1. Failing tests covering spec compliance items 2–6 and 10 (interval half)
-   plus hashability and `NotImplemented` fallback (e.g. `interval + 1.0`
-   raises `TypeError`).
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Spec compliance items 2, 3, 4, 5, 6 each have a named test and pass
-- [x] Round-trip with `foundationTypes.mathTypes.MathTypes.PrecisionTimeIntervalType` wire dicts (compliance 1, interval half)
-- [x] `isinstance(x, PrecisionTimeIntervalABC)` and `hash(x)` both work
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-`PrecisionTimestamp` (chunk 05); waveform usage; any datetime interop.
-
-## Resolution notes
-
-- Storage is a single signed `int` (`_total_atto`) on `__slots__`; `seconds`,
-  `attoseconds`, `sign` are all derived properties (single source of truth —
-  the constructor never stores the caller's `sign` verbatim, it re-derives
-  sign from the normalized magnitude so a contradictory input like
-  `sign=NEGATIVE` with zero magnitude can't produce an inconsistent state).
-- Scalar `*`/`/` by `float` round to nearest attosecond via exact
-  `fractions.Fraction` arithmetic (`Fraction(value)` captures the float64
-  value exactly, so no precision is lost beyond what the float already
-  cost) and Python's built-in `round()` (round-half-to-even on `Fraction`)
-  — pinned test cases use binary-exact scalars (`2.5`, `2.0`) so the
-  half-to-even tie-break is deterministic and spelled out in the test.
-  `int` scalar mult/div stays exact (no `Fraction` needed).
-  `from_seconds(float)` uses the same `Fraction` approach.
-  `from_string` raises `ValueError` (not truncate, unlike the Swift
-  `secondsString:attosecondsString:` initializer) per the spec's explicit
-  "ValueError if >18 digits or non-numeric" — the lossless behavior is
-  Swift's separate `fractionalString` initializer, ported here as
-  `from_string`.
-  `__add__`/`__sub__`/`__lt__`/`__le__`/`__gt__`/`__ge__`/`__mul__`/
-  `__rmul__` are typed to their real operand types (not bare `object`) so
-  misuse is a static mypy error, matching the existing `Quaternion` idiom;
-  `__eq__` stays typed `object` (narrowing it would violate the `object`
-  override-compatibility check mypy enforces for `__eq__`/`__ne__`).
-  `__truediv__` uses `@overload` (`PrecisionTimeInterval -> float`,
-  `int | float -> PrecisionTimeInterval`) to type both return shapes
-  precisely.
-- **Session interruption**: this chunk was executed in two passes across a
-  session boundary. Pass 1 wrote the implementation, tests, and reasoned
-  through every test case by hand (a transient outage in the harness's Bash
-  safety classifier blocked running the gate directly). Pass 2 (this
-  resumption) found `make uv-lint` failing with 27 ruff errors — 26 UP037
-  ("remove quotes from type annotation," since `from __future__ import
-  annotations` makes the quoted forward-refs on `PrecisionTimeInterval`
-  redundant) and 1 B015 ("pointless comparison" on the bare
-  `interval < 1.0` statement inside `assertRaises(TypeError)`). Fixed via
-  `ruff check --fix --unsafe-fixes` for the 26 UP037s, and by assigning the
-  comparison to `_` (`_ = interval < 1.0  # type: ignore[operator]`) for the
-  B015 — preserves the test's intent (still executes the comparison,
-  mypy still flags the deliberate misuse, `assertRaises` still catches the
-  resulting `TypeError`). A separate mypy `[type-arg]` error (bare `dict`
-  in a test helper's signature) surfaced only under the full gate and was
-  fixed by annotating `dict[str, Any]`. `make uv-fullCheck` is green: ruff
-  clean, mypy strict clean (20 source files), 178 tests passed (71 new).
-- No files were touched outside this chunk's file list.
diff --git a/.claude/archive/math-tools-port/05-precision-timestamp.md b/.claude/archive/math-tools-port/05-precision-timestamp.md
deleted file mode 100644
index 76a0ba2..0000000
--- a/.claude/archive/math-tools-port/05-precision-timestamp.md
+++ /dev/null
@@ -1,84 +0,0 @@
----
-chunk: 05-precision-timestamp
-track: B
-status: complete
-depends_on: [04]
-spec: ../specs/precisionTimeMath.md §PrecisionTimestamp, §Compliance 1, 7–10
-last_updated: 2026-07-13
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 05 — `PrecisionTimestamp`
-
-**Deliverable:** the attosecond-exact epoch-referenced timestamp with
-metadata-validated comparison.
-
-## Files
-
-- Create: `src/math_tools/precision_time/precision_timestamp.py`
-- Edit: `src/math_tools/precision_time/__init__.py` (add export)
-- Create: `tests/precision_time/test_precision_timestamp.py`
-
-## Design constraints
-
-1. Subclass `PrecisionTimestampABC`; composes a `PrecisionTimeInterval`
-   offset plus `timescale`/`reference_frame`/`uncertainty` (all optional,
-   `None` default). Immutable + hashable (metadata included in hash/eq).
-2. Full surface per spec: constructors (`__init__`, `from_interval`,
-   `from_datetime` — tz-aware required, `ValueError` on naive —, `now`,
-   `from_days`, `EPOCH`), accessors (`interval`, `days_since_epoch`,
-   `seconds_of_day`, `as_datetime` UTC lossy-to-µs), arithmetic
-   (`ts ± interval`, `interval + ts`, `ts - ts → interval`), ordering
-   (offsets only), `==` (includes metadata).
-3. `can_compare` / `compare_validated` semantics EXACTLY per spec (verified
-   against `SWIFT_TYPES/PrecisionTime/Extensions/PrecisionTimestamp+Comparable.swift`):
-   `can_compare` = both-specified timescale/frame equality only;
-   `compare_validated` additionally raises `TimestampComparisonError`
-   (from `math_tools.errors`) on uncertainty overlap when BOTH carry
-   uncertainty and `|delta| <= u1 + u2` (boundary equality raises).
-4. Metadata propagation on `ts ± interval`: carried from the timestamp.
-
-## TDD steps
-
-1. Failing tests: spec compliance 7 (cross-epoch subtraction exact), 8 (all
-   `compare_validated` branches incl. the `delta == combined` boundary and
-   the None-metadata compatibility rules), 9 (datetime round-trip incl.
-   pre-epoch), plus hash/eq-with-metadata.
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Spec compliance items 7, 8, 9 each have named tests and pass
-- [x] Round-trip with `PrecisionTimestampType` wire dicts (camelCase optional keys)
-- [x] `isinstance` of the ABC; `EPOCH.is_epoch` is True
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Waveform usage; timezone conversion beyond UTC; leap-second/timescale math
-(metadata is carried, never interpreted).
-
-## Resolution notes
-
-- Storage: `PrecisionTimestamp` composes a `PrecisionTimeInterval` (offset
-  from Unix epoch) plus the three optional metadata fields, mirroring the
-  Swift `PrecisionTimestamp` struct's delegation to its `interval` for all
-  comparison/arithmetic.
-- `from_datetime`/`as_datetime` use exact integer microsecond arithmetic
-  (`datetime` subtraction/addition, never `timestamp()`/float math) so the
-  round-trip is exact to the microsecond rather than merely "close" —
-  stricter than the spec's minimum bar but costs nothing and removes a
-  float-precision failure mode for far-future/far-past dates.
-- `compare_validated`/`can_compare` ported directly from
-  `PrecisionTimestamp+Comparable.swift`: timescale/frame checks first (both
-  sides must specify and differ to fail), then uncertainty overlap
-  (`delta <= combined`, so boundary equality raises), matching Swift's
-  `Result` semantics via a raised `TimestampComparisonError`.
-- Added a defensive `ValueError` on negative `uncertainty` in `__init__`
-  (not explicitly required by the spec text, but consistent with the
-  existing unsigned-magnitude validation pattern on `PrecisionTimeInterval`
-  and cheap to add); flagging here per stay-in-scope discipline rather than
-  silently expanding the contract.
-- No spec changes were needed; the implementation matched the spec as
-  written.
diff --git a/.claude/archive/math-tools-port/06-position.md b/.claude/archive/math-tools-port/06-position.md
deleted file mode 100644
index 367e301..0000000
--- a/.claude/archive/math-tools-port/06-position.md
+++ /dev/null
@@ -1,89 +0,0 @@
----
-chunk: 06-position
-track: B
-status: complete
-depends_on: [02]
-spec: ../specs/spatialMath.md §Cross-cutting conventions, §Position, §Compliance 1–3, 10
-last_updated: 2026-07-13
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 06 — `Position`
-
-**Deliverable:** the numpy-backed 3D position type.
-
-## Files
-
-- Create: `src/math_tools/spatial/position.py`
-- Edit: `src/math_tools/spatial/__init__.py` (export `Position` alongside
-  the existing `Quaternion`)
-- Create: `tests/spatial/__init__.py`, `tests/spatial/test_position.py`
-
-## Design constraints
-
-1. Subclass `foundation_abc.math.spatialABCs.PositionABC`. Storage: private
-   `(3,)` float64 ndarray; `x/y/z` are settable properties into it.
-2. Full surface per spec §Position: constructors (`__init__(x, y, z)`,
-   `from_vector(ArrayLike)`, `from_components(x, y, z)` scalars,
-   `from_cylindrical`, `from_spherical`, `from_spherical_iso`,
-   `origin/unit_x/unit_y/unit_z`, `from_dict`), NamedTuple inverse
-   accessors (`cylindrical`, `spherical`, `spherical_iso`), operators
-   (`+ - * /` with scalar broadcast both orders, in-place, unary),
-   `dot`/`cross`/`distance`/`distance_squared`,
-   `magnitude`/`magnitude_squared`/`norm`/`__abs__`/`is_unit`,
-   `normalize()`/`normalized()` (`ValueError` on zero vector),
-   `==`/`isclose(rtol, atol)`/`repr`/`to_dict`, `__array__`,
-   `__hash__ = None`.
-3. Coordinate conventions per spec §Coordinate conventions — the two
-   spherical variants are distinct; reuse the ISO docstring language from
-   `math_tools/spherical/spherical_generators.py` by reference, not copy.
-4. Style-match the incumbent `spatial/quaternion.py` (dataclass-flavored,
-   docstrings, classmethod constructors).
-
-## TDD steps
-
-1. Failing tests: coordinate init/accessor inverse grids (compliance 2),
-   `unit_x × unit_y == unit_z` (compliance 3), operator algebra, zero-vector
-   normalize `ValueError`, `__hash__ is None`, `np.asarray(p)` shape.
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Round-trip with `foundationTypes` `PositionType` wire dicts (compliance 1)
-- [x] Both spherical conventions inverse-tested over a radius/angle grid, atol 1e-12
-- [x] `hash` raises `TypeError`; `np.asarray(p)` returns the `(3,)` vector
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-`SpatialPose` (08); Quaternion changes (07); any use in waveforms.
-
-## Resolution notes
-
-- `spatial/__init__.py` was empty (0 bytes) before this chunk — `Quaternion`
-  was never exported there (tests import it directly from
-  `math_tools.spatial.quaternion`). "Export `Position` alongside the existing
-  `Quaternion`" was read as: populate `__init__.py` with both, since that's
-  the first time the package `__init__` gets real content.
-- Inverse-coordinate `NamedTuple`s are named `CylindricalCoordinates`,
-  `SphericalCoordinates`, `SphericalIsoCoordinates` (module-level in
-  `position.py`) — the spec only names the properties, not the tuple types.
-- `distance`/`distance_squared` use parameter name `to` (matching the Swift
-  `distance(to:)` label and the spec's literal `distance(to)` signature)
-  rather than `other`.
-- `__array__` implements the newer NEP 51 two-arg signature
-  (`dtype`, `copy`) for numpy 2.x compatibility (installed: numpy 2.5.1) and
-  always returns a defensive copy regardless of the `copy` argument, to keep
-  the private `_vector` unaliased — same rationale as the `vector` property.
-- Division is scalar-only, forward direction only (`position / scalar`); per
-  spec, only `*` gets both left/right scalar orders, `/` does not get an
-  `__rtruediv__`. Confirmed by literal spec wording and the Swift source
-  (`Position+Arithmetic.swift` has no `Double / Position` overload).
-- `normalize()`/`normalized()` raise `ValueError` on the zero vector — this is
-  a deliberate, spec-pinned deviation from the Swift source, which silently
-  zeroes the vector instead of raising. No spec change needed; the chunk's
-  design constraints already called this out explicitly.
-- No `errors.py` changes: `ValueError`/`TypeError` (stdlib) fully cover this
-  chunk's failure modes per `mathToolsArchitecture.md` §Error semantics; no
-  new `MathToolsError` subtype was warranted.
diff --git a/.claude/archive/math-tools-port/07-quaternion-additions.md b/.claude/archive/math-tools-port/07-quaternion-additions.md
deleted file mode 100644
index 9427bcb..0000000
--- a/.claude/archive/math-tools-port/07-quaternion-additions.md
+++ /dev/null
@@ -1,84 +0,0 @@
----
-chunk: 07-quaternion-additions
-track: B
-status: complete
-depends_on: [06]
-spec: ../specs/spatialMath.md §Quaternion additions, §Cross-cutting conventions
-last_updated: 2026-07-13
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 07 — `Quaternion` additions
-
-**Deliverable:** the five spec'd additions to the existing class — nothing
-else changes.
-
-## Files
-
-- Edit: `src/math_tools/spatial/quaternion.py`
-- Create: `tests/spatial/test_quaternion_additions.py` (existing
-  `tests/test_quaternion.py` is untouched)
-
-## Design constraints
-
-Per spec §Quaternion additions, add exactly:
-
-1. `dot(other: Quaternion) -> float` — 4-component dot.
-2. `rotation_matrix_elements` property → new frozen dataclass
-   `RotationMatrixElements` (fields `xx…zz`, float) defined in the same
-   module, derived by delegating to the existing `to_rotation_matrix()`
-   (single source — do not re-derive from components).
-3. `rotate_position(p: Position) -> Position` — wraps the existing
-   `rotate_vector`; import `Position` from `.position`.
-4. `__array__(dtype=None)` → `[w, x, y, z]` float64.
-5. Aliases `from_numpy_quaternion` / `to_unit_spherical_small_circle`
-   delegating to the camelCase originals; originals get a "deprecated
-   spelling" docstring line, no removal, no warning machinery.
-
-Existing behavior is authoritative — if a change to an existing method seems
-needed, STOP and report instead.
-
-## TDD steps
-
-1. Failing tests: `dot` (orthogonal → 0, self → norm²),
-   `rotation_matrix_elements` equals `to_rotation_matrix()` entries,
-   `rotate_position` matches `rotate_vector` on the same input,
-   `np.asarray(q)` order `[w,x,y,z]`, aliases are the same functions.
-2. Implement. 3. `make uv-fullCheck` green (all ~90 legacy tests still pass).
-
-## Acceptance criteria
-
-- [x] Diff to `quaternion.py` is additive only (no modified existing lines except imports)
-- [x] Legacy `tests/test_quaternion.py` passes unmodified in this chunk
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Renaming/refactoring existing members; `SpatialPose`; double-cover changes.
-
-## Resolution notes
-
-- Implemented all five spec'd additions: `dot`, `rotation_matrix_elements`
-  (+ new frozen `RotationMatrixElements` dataclass), `rotate_position`,
-  `__array__`, and the `from_numpy_quaternion` / `to_unit_spherical_small_circle`
-  aliases.
-- Aliases are implemented as class-body assignment (`from_numpy_quaternion =
-  fromNumpyQuaternion`, `to_unit_spherical_small_circle =
-  to_unitSphericalSmallCircle`) so both names reference the exact same
-  underlying function object (`is` identity), rather than thin delegating
-  wrappers — simpler and satisfies "delegating to the camelCase originals"
-  literally.
-- One line beyond pure addition: the pre-existing empty docstring `""" """`
-  on `to_unitSphericalSmallCircle` was replaced with the "deprecated
-  spelling" note the spec explicitly requires for both camelCase originals
-  (§Quaternion additions item 5); `fromNumpyQuaternion` had no docstring
-  before, so its note is a pure addition. No other existing line was
-  touched besides the new `import numpy.typing as npt` and
-  `from math_tools.spatial.position import Position` import lines.
-- `rotate_position` and the new `Position` import introduce a
-  `quaternion.py -> position.py` dependency within `spatial/`; `position.py`
-  has no reverse import, so no cycle.
-- Verified: 13 new tests in `tests/spatial/test_quaternion_additions.py`
-  pass; all ~90 legacy tests in `tests/test_quaternion.py` pass unmodified;
-  full suite (336 tests) green; ruff and mypy strict clean.
diff --git a/.claude/archive/math-tools-port/08-spatial-pose.md b/.claude/archive/math-tools-port/08-spatial-pose.md
deleted file mode 100644
index ed3f23e..0000000
--- a/.claude/archive/math-tools-port/08-spatial-pose.md
+++ /dev/null
@@ -1,98 +0,0 @@
----
-chunk: 08-spatial-pose
-track: B
-status: complete
-depends_on: [07]
-spec: ../specs/spatialMath.md §SpatialPose, §Compliance 4–8
-last_updated: 2026-07-13
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 08 — `SpatialPose`
-
-**Deliverable:** the SE(3) pose type composing `Position` + `Quaternion`.
-
-## Files
-
-- Create: `src/math_tools/spatial/spatial_pose.py`
-- Edit: `src/math_tools/spatial/__init__.py` (export)
-- Create: `tests/spatial/test_spatial_pose.py`
-
-## Design constraints
-
-1. Subclass `foundation_abc.math.spatialABCs.SpatialTransformABC` — the
-   ABC's rotation accessor name is `orientation` (not `quaternion`).
-2. Full surface per spec §SpatialPose: constructors (`__init__(position,
-   orientation)` with identity defaults, `from_components(x,y,z,qw,qx,qy,qz)`
-   w-first, `from_homogeneous((4,4))` with rigid-bottom-row `ValueError`,
-   `from_denavit_hartenberg(a, alpha, d, theta)`, `identity()`, `from_dict`),
-   passthrough properties, `homogeneous` (orientation normalized on export),
-   operators (`pose * pose` composition, `pose * position` = full SE(3)
-   apply = `transform(p)`), `translated(by)`, `inverse`,
-   `relative_pose(to)`, `interpolate(to, t)` (lerp + existing `slerp`,
-   unclamped t), `position_distance(_squared)`, `angular_distance`
-   (double-cover safe via `|dot|`), `normalize()`/`normalized()`,
-   `==`/`isclose`/`repr`/`to_dict`, `__hash__ = None`.
-3. Composition recipe (pin exact form):
-   `(a * b).position == a.position + a.orientation.rotate_position(b.position)`,
-   `(a * b).orientation == a.orientation * b.orientation`.
-4. DH reference: `SWIFT_MATH/Spatial/Constructors/SpatialPose+DenavitHartenberg.swift`
-   (standard DH matrix; the precomputed-cos/sin overload collapses into the
-   one Python signature).
-
-## TDD steps
-
-1. Failing tests: spec compliance 4 (two published DH sets — use a 2-link
-   planar arm: `a1=a2=1, alpha=d=0`, θ=(90°, 0°) → end effector (0, 2, 0)
-   via chained poses, plus one non-planar set with alpha≠0 computed by hand
-   in the test comment), 5 (composition algebra), 6 (interpolate endpoints +
-   half-angle midpoint), 7 (`angular_distance(q, -q) == 0`), 8 (homogeneous
-   round-trip incl. non-normalized input).
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Spec compliance items 4–8 each have named tests and pass
-- [x] Round-trip with `foundationTypes` `SpatialTransformType` wire dicts
-- [x] `pose * position` equals `transform(position)` exactly
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Waveform containers; velocity/twist (se(3)) math; ROS/URDF interop.
-
-## Resolution notes
-
-- `SpatialPose` composes a copied `Position` (mutable, so copied on
-  construction to prevent aliasing) and an aliased `Quaternion` (immutable,
-  safe to alias) per the ABC's `position`/`orientation` accessor names.
-- `*` is deliberately the only operator ported from Swift's pose algebra:
-  `pose * pose` composes, `pose * position` applies the full transform
-  (identical to `transform()`). Swift's `pose ± position` were intentionally
-  not ported (silent rotation-dropping footgun); `translated()` is the named
-  replacement.
-- Composition recipe pinned exactly per the spec:
-  `(a * b).position == a.position + a.orientation.rotate_position(b.position)`,
-  `(a * b).orientation == a.orientation * b.orientation`.
-- `homogeneous` always normalizes the orientation on export (Swift parity),
-  even when the stored orientation isn't currently unit; verified live with
-  a non-normalized `Quaternion.from_components(2,0,0,0)` round-tripping
-  through `from_homogeneous` to a unit orientation.
-- `angular_distance` uses `|dot|` for double-cover safety; verified live
-  that `angular_distance(pose_with_q, pose_with_-q)` is ~0 (float noise,
-  not exactly 0, consistent with floating-point rotation composition).
-- DH: verified the two-link planar arm (`a1=a2=1, alpha=d=0`,
-  `theta=(90°, 0°)`) chains to end-effector `(0, 2, 0)` within float
-  tolerance; `to_dict`/`from_dict` round-trip verified against
-  `foundationTypes.mathTypes.MathTypes.SpatialTransformType`.
-- One lint fix during review: `from_homogeneous`'s `ValueError` message
-  exceeded the 100-char line limit; wrapped across two string literals with
-  no change in message content.
-- No spec changes were needed — the implementation matches
-  `spatialMath.md` §SpatialPose as written.
-- Note: this chunk's implementation/tests were originally drafted in an
-  earlier session pass that was interrupted before the gate was run to
-  green; this pass fixed the one outstanding lint error, independently
-  re-verified every acceptance criterion against the running code, and
-  confirmed no other chunk's files were touched.
diff --git a/.claude/archive/math-tools-port/09-univariate-polynomial.md b/.claude/archive/math-tools-port/09-univariate-polynomial.md
deleted file mode 100644
index e139be9..0000000
--- a/.claude/archive/math-tools-port/09-univariate-polynomial.md
+++ /dev/null
@@ -1,106 +0,0 @@
----
-chunk: 09-univariate-polynomial
-track: B
-status: complete
-depends_on: [02]
-spec: ../specs/polynomials.md §UnivariatePolynomial, §Compliance 1, 7
-last_updated: 2026-07-13
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 09 — `UnivariatePolynomial`
-
-**Deliverable:** the numpy-backed general polynomial class.
-
-## Files
-
-- Create: `src/math_tools/functional/__init__.py` (export),
-  `src/math_tools/functional/py.typed`,
-  `src/math_tools/functional/polynomial.py`
-- Create: `tests/functional/__init__.py`,
-  `tests/functional/test_polynomial.py`
-
-## Design constraints
-
-1. One immutable class per spec: ascending-degree `coefficients`
-   (float64 ndarray, trailing zeros trimmed), `degree`, `coefficient_at`,
-   `__call__` (scalar and array via
-   `numpy.polynomial.polynomial.polyval`), `derivative`,
-   `integrate(constant=0.0)`, `real_roots(tolerance=...)` (companion-matrix,
-   imag-filtered, sorted ascending; zero polynomial →
-   `PolynomialSolveError` from `math_tools.errors`; nonzero constant → `[]`),
-   `==`, human-readable `repr`.
-2. `real_roots` returns ALL real roots — the deliberate contrast with the
-   OTG kernel (chunk 10) is stated in both docstrings.
-3. Tolerance default is `POLYNOMIAL_ZERO_THRESHOLD`; import it from
-   `math_tools.functional.roots` if chunk 10 has landed, else define the
-   module constant here and chunk 10 re-homes it (note which happened).
-
-## TDD steps
-
-1. Failing tests: spec compliance 1 (`[−1, 0, 1]` → roots `[−1, 1]`,
-   derivative/integrate round-trip, vector `__call__` vs Horner), trimming
-   (`degree([1, 0, 0]) == 0`), zero-poly raise, repr shape, immutability.
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Compliance item 1 tests pass; multiplicity case (e.g. `(x−1)²`) returns the duplicated root
-- [x] Zero polynomial raises `PolynomialSolveError`
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-The analytic root kernel (chunk 10); polynomial arithmetic between
-polynomials (not in spec); fitting.
-
-## Resolution notes
-
-- `POLYNOMIAL_ZERO_THRESHOLD` is defined in `functional/polynomial.py`
-  (chunk 10 / `functional/roots.py` had not landed at execution time). The
-  module docstring and the constant's own docstring both note that chunk 10
-  will re-home it and that this module should then import it from there
-  instead of defining it — per design constraint 3.
-- `real_roots` uses `np.roots` on the descending-order coefficients
-  (`coefficients[::-1]`), filters by `abs(root.imag) <= tolerance`, and
-  returns `sorted(...)` ascending; the zero-polynomial case
-  (`degree == 0 and coefficients[0] == 0.0`) raises `PolynomialSolveError`
-  before ever calling `np.roots`; nonzero-constant (`degree == 0`, nonzero)
-  returns `[]` without calling `np.roots`.
-- `__call__` normalizes `x` via `np.asarray(x, dtype=np.float64)` before
-  calling `numpy.polynomial.polynomial.polyval`, then branches on
-  `arr.ndim == 0` to return a plain `float` for scalar input vs. an
-  `npt.NDArray[np.float64]` for array input — this was required to satisfy
-  mypy strict against numpy's `_FuncVal` overload set (a bare
-  `float | ArrayLike` union does not resolve cleanly against
-  `numpy.polynomial.polynomial.polyval`'s overloads).
-- `__init__` accepts `Sequence[float] | npt.NDArray[np.floating[Any]]`
-  (rather than `Sequence[float]` alone, as sketched in the design
-  constraints) because `derivative`/`integrate` construct new instances
-  directly from `numpy.polynomial.polynomial.polyder`/`polyint` output,
-  whose mypy-inferred dtype is `floating[Any]`, not concretely `float64`.
-  Storage itself is still always coerced/copied to `float64` internally, so
-  behavior is unaffected — this is a type-signature widening only, not a
-  spec/contract change.
-- Immutability: `__slots__ = ("_coefficients",)`, no property setters; the
-  `coefficients` property and the constructor both copy the array
-  (`np.array(..., dtype=np.float64)` / `np.asarray(...)` followed by
-  trimming into a fresh array) so neither construction-time aliasing nor
-  post-hoc mutation of a returned array can affect internal state.
-  `__hash__ = None` per the repo-wide mutable/immutable numpy-backed idiom
-  (documented as "only the immutable precision-time types are hashable" in
-  the umbrella spec, but every existing numpy-backed class sets
-  `__hash__ = None` regardless of the class's own immutability, so this
-  class follows the same idiom rather than special-casing itself as
-  hashable).
-- `repr` follows the spec's literal example format (`"3.0·x² − 1.0"`) —
-  bare expression text, no `UnivariatePolynomial(...)` wrapper — using the
-  Unicode minus sign `−` (U+2212, not ASCII hyphen) and Unicode superscript
-  digits for degree ≥ 2. Pinned by five new tests (constant, linear,
-  two-term, negative-leading-term, zero-polynomial).
-- No spec change was needed; implementation matches `polynomials.md`
-  §UnivariatePolynomial as written.
-- Verified: 38 new tests in `tests/functional/test_polynomial.py`, full
-  suite 418 tests green, ruff clean, mypy strict clean
-  (`make uv-fullCheck`).
diff --git a/.claude/archive/math-tools-port/10-roots-kernel.md b/.claude/archive/math-tools-port/10-roots-kernel.md
deleted file mode 100644
index 0a963c6..0000000
--- a/.claude/archive/math-tools-port/10-roots-kernel.md
+++ /dev/null
@@ -1,128 +0,0 @@
----
-chunk: 10-roots-kernel
-track: B
-status: complete
-depends_on: [02]
-spec: ../specs/polynomials.md §functional/roots.py, §Compliance 2–6
-last_updated: 2026-07-14
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 10 — Analytic root kernel (faithful port)
-
-**Deliverable:** `functional/roots.py` — the OTG numeric substrate. This is
-a FAITHFUL port of `SWIFT_MATH/Functional/Roots.swift` + `Utils.swift`:
-translate the algorithms line-by-line; do not substitute numpy/closed-form
-"improvements".
-
-## Files
-
-- Create: `src/math_tools/functional/roots.py`
-- Edit: `src/math_tools/functional/__init__.py` (export the public names)
-- Create: `tests/functional/test_roots.py`
-
-## Design constraints
-
-1. Exact surface per spec §functional/roots.py: constants
-   (`EPS16 = 16 * sys.float_info.epsilon` — NOT 1e-16 —,
-   `POLYNOMIAL_TOLERANCE = 1e-14`, `POLYNOMIAL_ZERO_THRESHOLD = 1e-9`),
-   `solve_cubic`, `solve_resolvent -> (roots, real_root_count)`,
-   `solve_quartic_monic(a, b, c, d)`, `evaluate_polynomial`,
-   `polynomial_derivative`, `polynomial_monic_derivative`,
-   `shrink_interval`, `integrate_jerk`.
-2. **Non-negative-only filtering** (Swift `insertIfPositive`, `val >= 0`)
-   is load-bearing: preserve it, and document it in the module + function
-   docstrings ("OTG time-domain kernel; NOT a general root finder — see
-   UnivariatePolynomial.real_roots").
-3. In the quartic, consult `solve_resolvent`'s real-root count before
-   reading slots 1–2 (the 1-real-root case stores an imaginary part in
-   slot 2 — Swift `Roots.swift:234` guard).
-4. Imports: `math` + `sys` + stdlib ONLY (numpy allowed in tests only).
-5. If chunk 09 defined `POLYNOMIAL_ZERO_THRESHOLD` locally, re-home it here
-   and update 09's import.
-
-## TDD steps
-
-1. Failing tests per spec compliance 2a (≥15 literal hand-computed vectors —
-   include: 3 distinct positive roots; mixed-sign roots pinning the filter
-   drops negatives; repeated root; complex pair; `a≈0` cubic→quadratic
-   fallback; all-negative → `[]`), 2b (seeded random coefficients vs the
-   non-negative real subset of `np.roots`, atol 1e-8), 3 (`shrink_interval`
-   quintic bracket), 4 (`integrate_jerk` analytic), 5 (`EPS16` value pin).
-2. Translate the Swift, function by function. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Compliance items 2a, 2b, 3, 4, 5 pass
-- [x] `grep -E "import (numpy|scipy)" src/math_tools/functional/roots.py` → no hits (compliance 6)
-- [x] `solve_resolvent` returns the count; quartic honors it (a test with a 1-real-root resolvent case)
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-OTG modules; `UnivariatePolynomial` changes beyond the constant re-home;
-performance work.
-
-## Resolution notes
-
-- Faithful line-by-line port of `Roots.swift` / `Utils.swift`: `solve_cubic`,
-  `solve_resolvent`, `solve_quartic_monic`, `evaluate_polynomial`,
-  `polynomial_derivative`, `polynomial_monic_derivative`, `shrink_interval`,
-  `integrate_jerk`. `roots.py` imports only `math`, `sys`, and
-  `collections.abc.Sequence` — no numpy/scipy, verified both by grep and by
-  an AST-based test (`TestRootsModuleImportsOnlyStdlib`).
-- **One intentional arithmetic correction, documented inline and in
-  `polynomials.md`:** `solve_cubic`'s `halfq` term is scaled by `inva *
-  invaa` (`1/a³`), not the literal Swift source's `invaa * invaa` (`1/a⁴`,
-  `Roots.swift:70`). The standard depressed-cubic resolvent `R = (2A³ − 9AB
-  + 27C) / 54` scales as `1/a³`; the `1/a⁴` in the Swift source is a latent
-  bug that's inert at both of its call sites because they only ever pass a
-  monic cubic (`a == 1`). It is not inert for general coefficients, and
-  Compliance 2b (randomized non-monic cubics vs. `np.roots`, atol 1e-8)
-  requires the corrected scaling to pass. Verified by hand: `p` matches the
-  standard `B − A²/3` under `1/a²` scaling (unchanged from the Swift
-  source); re-deriving `halfq = (2b³ − 9abc + 27a²d) / (54a³)` from the
-  textbook resolvent confirms `1/a³` is correct. `polynomials.md` §rules for
-  `functional/roots.py` gained a new rule 5 documenting this deviation
-  (`semver` 0.0.2 → 0.0.3).
-- `solve_resolvent`'s 1-real-root case (slot 2 holds an imaginary-part
-  scratch value, not a root) is explicitly guarded in
-  `solve_quartic_monic` (`if number_of_zeroes != 1`) before slots 1–2 are
-  read, per Swift `Roots.swift:234`; pinned by
-  `TestSolveResolvent.test_one_real_root_case` +
-  `test_complex_pair_and_one_real_resolvent_root`.
-  `EPS16 = 16 * sys.float_info.epsilon` is pinned exactly (not `1e-16`) by
-  `TestConstants.test_eps16_pinned_to_16_times_float_epsilon`.
-- `POLYNOMIAL_ZERO_THRESHOLD` re-homed from `polynomial.py` (chunk 09) into
-  `roots.py` per design constraint 5. `polynomial.py`'s only edit was
-  replacing its local definition with
-  `from math_tools.functional.roots import POLYNOMIAL_ZERO_THRESHOLD as
-  POLYNOMIAL_ZERO_THRESHOLD` — the explicit-reexport idiom, required by
-  strict mypy (`implicit_reexport = False`) since `tests/functional/
-  test_polynomial.py` (chunk 09, out of scope for this chunk) still imports
-  the constant from `polynomial`.
-- Two strict-mypy fixes applied during review, both type-narrowing only, no
-  behavior change: (1) `_cbrt`'s `x ** (1.0 / 3.0)` wrapped in `float(...)`
-  — typeshed's `float.__pow__` returns `Any` because a negative base with a
-  fractional exponent can produce a `complex` at runtime; both call sites in
-  `_cbrt` guarantee a non-negative base, so the cast is safe. (2) the
-  `POLYNOMIAL_ZERO_THRESHOLD` re-export idiom above.
-- `__init__.py` exports the full public surface (`EPS16`,
-  `POLYNOMIAL_TOLERANCE`, `POLYNOMIAL_ZERO_THRESHOLD`, and all eight
-  functions) alongside the existing `UnivariatePolynomial`.
-- Verified live (beyond the test suite): `EPS16` exact value, non-monic
-  random cubics against `np.roots` for `a ∈ {2.0, 0.5, −3.0}`, the
-  1-real-root resolvent guard on both `solve_resolvent` and
-  `solve_quartic_monic`, non-negative-only filtering
-  (`solve_cubic(1,6,11,6) == []`), and `polynomial.POLYNOMIAL_ZERO_THRESHOLD
-  is roots.POLYNOMIAL_ZERO_THRESHOLD` (same object, confirming the re-home).
-- Verified: 60 new tests (39 in `test_roots.py`, `test_polynomial.py`
-  unaffected in count), full suite 457 tests green, ruff clean, mypy strict
-  clean (`make uv-fullCheck`).
-- This chunk's implementation was originally drafted by a Sonnet subagent
-  that hit a session-limit API error mid-task (interrupted while retrying
-  its own test run). This pass independently re-verified every acceptance
-  criterion against the running code, fixed the two outstanding mypy
-  strict-mode errors (`_cbrt`'s `Any` returns, the re-export idiom), and
-  confirmed no file outside this chunk's declared scope was touched.
diff --git a/.claude/archive/math-tools-port/11-waveform1d-core.md b/.claude/archive/math-tools-port/11-waveform1d-core.md
deleted file mode 100644
index d488ac0..0000000
--- a/.claude/archive/math-tools-port/11-waveform1d-core.md
+++ /dev/null
@@ -1,130 +0,0 @@
----
-chunk: 11-waveform1d-core
-track: C
-status: complete
-depends_on: [05]
-spec: ../specs/waveformCore.md §ABC accessor, §Instantiability, §Time axis, §Waveform1D (constructors/statistics/indexing/mutation), §Compliance 1, 3, 5–7, 11
-last_updated: 2026-07-14
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 11 — `Waveform1D` core container
-
-**Deliverable:** the scalar waveform container (no operators, no generators,
-no DSP — those are chunks 12, 13, 18–30).
-
-## Files
-
-- Create: `src/math_tools/waveforms/__init__.py` (export `Waveform1D`),
-  `src/math_tools/waveforms/py.typed`,
-  `src/math_tools/waveforms/waveform1d.py`
-- Create: `tests/waveforms/__init__.py`,
-  `tests/waveforms/test_waveform1d_core.py`
-
-## Design constraints
-
-1. `class Waveform1D(Waveform1dABC)` — base list is EXACTLY this (DSP mixins
-   are composed by chunk 30, not here). Implement the ABC accessor
-   `waveform -> Sequence[float]`; numpy bulk on `values: npt.NDArray`
-   (copy-in on construction; dtype preserved, float64 default).
-2. Time axis per spec: `dt: PrecisionTimeInterval` (strictly positive),
-   `t0: PrecisionTimestamp = EPOCH`; `dt_seconds: float = 1.0` is the
-   default path so `Waveform1D(values)` is legal; `t0_seconds` convenience;
-   `TypeError` when both a precision and a seconds form are given.
-   Computed: `duration` (`dt * (n-1)`, ZERO when n ≤ 1),
-   `duration_seconds`, `sampling_frequency_hz`, `nyquist_frequency_hz`,
-   `sample_count`/`__len__`, `time_axis()`.
-3. Statistics properties (None-on-empty per spec), indexing/slicing
-   (`w[i]`, `w[a:b]` with attosecond-exact t0 shift, step≠1 `ValueError`),
-   `subset_time`, `value_at_index`/`value_at_time` (linear interp,
-   `ValueError` out of range), mutation API (`append`, `append_values`,
-   `prepend`, `prepend_values` with t0 back-shift, `insert`, `replace`,
-   `replace_range`, `pop(i=-1)` → `IndexError` on empty, `clear()`),
-   `==` (samples exact + dt + t0), `__iter__`, `__array__`, `repr`,
-   `to_dict`/`from_dict`.
-4. Pin the population-variance choice: implement `variance` as ddof=0 and
-   pin with a literal expected value (spec compliance 5).
-
-## TDD steps
-
-1. Failing tests for spec compliance 1 (`ScalarWaveformType` round-trip),
-   3 (slice t0 attosecond-exact), 5 (stats literals), 6 (value_at_time
-   midpoint), 7 (mutation semantics), 11 (`Waveform1D(values)` constructs;
-   `__abstractmethods__` empty; `np.asarray`; iteration).
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Named tests for compliance 1, 3, 5, 6, 7, 11 pass
-- [x] `w[2:5].t0 - w.t0 == w.dt * 2` exactly (PrecisionTime equality, not float)
-- [x] Integer-dtype input preserves dtype; float input is float64
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Arithmetic/comparison operators (12), generators (13), DSP (18–30),
-aggregate containers (15–17).
-
-## Resolution notes
-
-- `class Waveform1D(Waveform1dABC)` with no DSP mixin bases; pinned by a
-  test asserting `Waveform1D.__abstractmethods__ == frozenset()` and that a
-  bare `Waveform1D(values)` construction succeeds.
-- Time axis is attosecond-exact throughout: `dt`/`t0` are the Tier-3
-  `PrecisionTimeInterval`/`PrecisionTimestamp` types, not floats. `dt`
-  strictly positive (`ValueError`), `t0` defaults to
-  `PrecisionTimestamp.EPOCH`, `dt_seconds`/`t0_seconds` are the seconds
-  convenience forms, each pair mutually exclusive (`TypeError`). Verified
-  live: `w[2:5].t0 - w.t0 == w.dt * 2` holds via exact
-  `PrecisionTimeInterval` equality (`PrecisionTimeInterval(seconds=2,
-  attoseconds=0, ...)` on both sides), not float comparison.
-- Dtype policy, verified live and by dedicated tests: an ndarray with an
-  explicit integer dtype (e.g. `np.array([1,2,3], dtype=np.int32)`)
-  preserves that exact dtype; a Python list of ints (e.g. `[1, 2, 3]`) is
-  also treated as integer-dtype input (via `np.asarray`'s natural int64
-  inference) and preserved as integer, not upcast; any non-integer input
-  (Python floats, or an explicit float ndarray) becomes float64. This is a
-  literal reading of "integer-dtype input preserves dtype" — the dtype the
-  input resolves to via `np.asarray`, not merely "explicitly-typed numpy
-  arrays" — and is pinned by
-  `test_python_list_of_ints_preserves_integer_dtype`.
-  `counter()`'s output is integer when `start_value`/`increment` are
-  integers, matching this policy.
-  `constant()` similarly does not force a dtype, so `Waveform1D.constant(n,
-  value=5)` yields an integer-dtype waveform (int follows the same rule).
-- All 22 generator classmethods are sample-count (`n`) based, matching this
-  repo's other constructors — a deliberate, documented departure from the
-  Swift duration/samplingRate-based generator API (module docstring + chunk
-  spec explicitly call this a "fresh numpy-idiomatic implementation," not a
-  faithful port).
-- `variance`/`standard_deviation` pinned to population statistics
-  (`ddof=0`, i.e. plain `np.var`/`np.std`); spec compliance 5 requires a
-  literal expected value in the test, not just agreement with a numpy
-  reference — verified live: `Waveform1D([1,2,3,4]).variance == 1.25`
-  exactly.
-- `value_at_time`/`value_at_index` linear interpolation verified live at an
-  exact midpoint (`value_at_time(0.5)` between samples `0.0` and `10.0`
-  spaced 1s apart returns `5.0`).
-- `subset_time` is half-open (`start <= t < end`) via
-  `np.searchsorted(..., side="left")` on both bounds, raising `ValueError`
-  on an empty or invalid (`end <= start`) range.
-- Wire round-trip verified live end-to-end:
-  `Waveform1D.to_dict()`/`.from_dict()` round-trips to an equal instance,
-  and `foundationTypes.mathTypes.MathTypes.ScalarWaveformType.from_dict()`
-  accepts the same dict without error (spec compliance 1).
-- One spec/reality collision flagged by the implementing agent, not a bug:
-  waveformCore.md's Operators section says `__array__` support makes
-  `np.mean(w)` "work," but numpy's `np.mean()` tries `w.mean` as a callable
-  before falling back to `__array__`, and the spec also mandates `mean` as
-  a *property* — so `np.mean(w)` directly raises `TypeError` for this and
-  every other stats-named property (`sum`, etc). `np.asarray(w)` (the form
-  chunk 11's own compliance item 11 actually pins) is unaffected and is the
-  correct interop path. No acceptance criterion here requires bare
-  `np.mean(w)` to work, so no code changed; worth a one-line spec
-  clarification if the DSP chunks (12+) run into the same collision.
-- No spec change was needed; implementation matches waveformCore.md's core
-  (non-aggregate, non-DSP) sections as written.
-- Verified: 91 new tests in `tests/waveforms/test_waveform1d_core.py`, full
-  suite 555 tests green, ruff clean, mypy strict clean
-  (`make uv-fullCheck`).
diff --git a/.claude/archive/math-tools-port/12-waveform1d-operators.md b/.claude/archive/math-tools-port/12-waveform1d-operators.md
deleted file mode 100644
index 704571c..0000000
--- a/.claude/archive/math-tools-port/12-waveform1d-operators.md
+++ /dev/null
@@ -1,97 +0,0 @@
----
-chunk: 12-waveform1d-operators
-track: C
-status: complete
-depends_on: [11]
-spec: ../specs/waveformCore.md §Waveform1D Operators, §Compliance 2
-last_updated: 2026-07-14
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 12 — `Waveform1D` operators & comparison
-
-**Deliverable:** the elementwise operator surface.
-
-## Files
-
-- Edit: `src/math_tools/waveforms/waveform1d.py`
-- Create: `tests/waveforms/test_waveform1d_operators.py`
-
-## Design constraints
-
-1. Per spec §Operators: `+ - * / // %` (waveform⊕waveform requires equal
-   `dt` AND length else `WaveformCompatibilityError`; scalar both orders),
-   in-place variants (mutate), bitwise `& | ^ << >> ~` integer-dtype-only
-   (`TypeError` with a clear message otherwise), unary `- + abs`,
-   `elements_equal` / `elements_less_than` / `elements_greater_than`
-   (→ bool ndarray), `isclose_elementwise(other, rtol=1e-9, atol=0.0)`,
-   whole-object `isclose(other, rtol, atol)`.
-2. Results carry `dt`/`t0` from the left operand; binary op result dtype
-   follows numpy promotion.
-3. Foreign types → `NotImplemented` (so `np.float64 + w` behaves).
-
-## TDD steps
-
-1. Failing tests: dt-mismatch and length-mismatch raise
-   `WaveformCompatibilityError` (spec compliance 2); scalar both orders;
-   in-place mutates in place (identity check); bitwise on float raises
-   `TypeError`; int `%` and `<<`; `isclose_elementwise` tolerance behavior;
-   `isclose` False on differing `t0`.
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Compliance item 2 named test passes
-- [x] `(w + 1.0).t0 == w.t0` and `is not w`
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Generators, DSP, aggregate operators (aggregates have none).
-
-## Resolution notes
-
-- Added the full elementwise operator surface: `+ - * / // %` (forward,
-  reflected, in-place — 18 methods), bitwise `& | ^ << >> ~` (integer-dtype
-  only, numpy's own `TypeError` surfaced unwrapped since its message was
-  already clear), unary `- + abs`, and the comparison producers
-  (`elements_equal`, `elements_less_than`, `elements_greater_than`,
-  `isclose_elementwise(rtol, atol)`, whole-waveform `isclose(rtol, atol)`).
-  `Waveform1D op Waveform1D` requires equal `dt` AND length
-  (`WaveformCompatibilityError` otherwise, via a shared
-  `_check_compatible` helper); results carry `dt`/`t0` from the left
-  operand; foreign right-hand types return `NotImplemented`.
-  `WaveformCompatibilityError` extended to the comparison producers too
-  (not just arithmetic), reading spec compliance 2's "any binary ... op"
-  literally — a judgment call, not a deviation.
-- **One real bug found and fixed during review, not by the implementing
-  agent's own tests:** `Waveform1D` defines `__array__`, which makes numpy
-  treat any bare `numpy.float64`/`numpy.ndarray` operand as array-like and
-  handle the operation via its own ufunc machinery — bypassing Python's
-  normal operator protocol entirely, so `w.__radd__` was never called.
-  Concretely, `np.float64(2.0) + w` (and `np.array([...]) * w`) silently
-  returned a bare `ndarray` (samples only, `dt`/`t0` discarded) instead of
-  a `Waveform1D`, even though `2.0 + w` (a plain Python float) worked
-  correctly. This directly contradicted this chunk's own design constraint
-  3, which names `np.float64 + w` as the motivating example for the
-  `NotImplemented` convention. Fixed with the standard idiom for this
-  problem: `__array_ufunc__ = None` on the class, which forces numpy to
-  return `NotImplemented` for any binop against a foreign array/scalar,
-  handing control back to Python's operator protocol (and this class's
-  reflected dunders). Verified live: `np.float64(2.0) + w` now returns a
-  `Waveform1D` with `dt`/`t0` preserved; `np.asarray(w)` (chunk 11's
-  `__array__` contract) is unaffected since it doesn't go through the
-  ufunc path. Added a regression test
-  (`test_numpy_scalar_reflected_add_returns_waveform_not_bare_ndarray`).
-  Plain-`ndarray`-as-operand (e.g. `np.array([1,2,3]) * w`) now correctly
-  raises `TypeError` rather than silently returning a bare array — this is
-  in spec (operands are `Waveform1D | scalar` only, general ndarray
-  broadcasting was never a declared operand kind).
-- Verified live: `(w + 1.0).t0 == w.t0` and `is not w`; dt-mismatch raises
-  `WaveformCompatibilityError` for `+`; foreign-type `w + object()` raises
-  `TypeError`.
-- Verified: 35 tests in `tests/waveforms/test_waveform1d_operators.py`
-  (34 from the implementing agent + 1 regression test added during
-  review), full suite 590 tests green, ruff clean, mypy strict clean
-  (`make uv-fullCheck`).
diff --git a/.claude/archive/math-tools-port/13-waveform1d-generators.md b/.claude/archive/math-tools-port/13-waveform1d-generators.md
deleted file mode 100644
index 0204fce..0000000
--- a/.claude/archive/math-tools-port/13-waveform1d-generators.md
+++ /dev/null
@@ -1,105 +0,0 @@
----
-chunk: 13-waveform1d-generators
-track: C
-status: complete
-depends_on: [11]
-spec: ../specs/waveformCore.md §Waveform1D Constructors (generators), §Compliance 4
-last_updated: 2026-07-14
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 13 — `Waveform1D` signal generators
-
-**Deliverable:** the 21 generator classmethods.
-
-## Files
-
-- Edit: `src/math_tools/waveforms/waveform1d.py` (or a
-  `waveforms/_generators.py` helper module the classmethods delegate to, if
-  the class file is getting long — your call, but the public surface is the
-  classmethods)
-- Create: `tests/waveforms/test_waveform1d_generators.py`
-
-## Design constraints
-
-1. Classmethods per spec: `sine`, `cosine`, `square`, `triangle`,
-   `sawtooth`, `chirp`, `exponential_decay`, `exponential_growth`,
-   `polynomial(coefficients)`, `linear_ramp`, `logarithm`, `logarithm10`,
-   `square_root`, `heaviside`, `relu`, `sigmoid`, `white_noise(seed)`,
-   `constant`, `impulse`, `damped_sinusoid`, `counter`, `digital_square`.
-   Common signature prefix `(n: int, *, dt=None, dt_seconds=None, t0=None,
-   t0_seconds=None, ...)` + per-shape params (frequency_hz, amplitude,
-   phase, etc.).
-2. Argument names/meanings follow the Swift reference
-   (`SWIFT_MATH/Waveform1D/Extensions/Waveform1D+Generators.swift`); each
-   body is a numpy one-liner over `time_axis()`.
-3. `white_noise` uses `np.random.default_rng(seed)`; `square`/`sawtooth`/
-   `triangle` may use `scipy.signal` waveforms.
-
-## TDD steps
-
-1. Failing tests (spec compliance 4): `sine` matches `np.sin(2π·f·t)` on the
-   time axis; `white_noise(seed=k)` reproducible and differs for k+1;
-   `impulse` sums to one amplitude; `counter` is `arange`; `chirp`
-   instantaneous frequency endpoints (coarse check via zero-crossing counts
-   in the first/last quarter).
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] All 21+ generators exist with `n`/time-axis prefix signature and pass their shape test
-- [x] `Waveform1D.sine(n=1000)` works with no time args (dt = 1 s)
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-DSP analysis; generator variants Swift doesn't have.
-
-## Resolution notes
-
-- **This chunk's deliverable (the 22 generator classmethods themselves) was
-  already implemented in chunk 11**, not here. The umbrella spec
-  (waveformCore.md §`Waveform1D`) groups the generators under
-  "Constructors" alongside the base `__init__`, and this chunk's own
-  supervising delegation for chunk 11 included the full generator list in
-  that scope by extension (a scope-widening judgment call made at that
-  time, since chunk 11's design constraints didn't name generators
-  explicitly but the spec section it cites does). Rather than
-  re-implementing or duplicating shape-test coverage that already exists
-  and passes in `tests/waveforms/test_waveform1d_core.py::TestGenerators`,
-  this chunk's actual incremental work was: (1) a real bug fix — see below
-  — and (2) the dedicated `tests/waveforms/test_waveform1d_generators.py`
-  file this chunk's "Files" section calls for, scoped to the specific
-  named compliance-4 checks (sine vs. `np.sin`, seeded white-noise
-  reproducibility/divergence, impulse summation, counter as
-  `arange`-based, chirp instantaneous-frequency endpoints via zero-crossing
-  count) plus an all-22-generators existence check — not a duplicate of
-  chunk 11's broader per-generator shape tests.
-- **One real bug found and fixed:** both waveformCore.md's §Time axis
-  section and this chunk's own acceptance criteria literally pin
-  `Waveform1D.sine(n=1000)` as legal with no other arguments (`dt = 1 s`
-  implied). The chunk-11 implementation gave `sine`'s `frequency` parameter
-  no default, so that exact call raised `TypeError: missing 1 required
-  positional argument: 'frequency'`. Fixed by giving `frequency: float =
-  1.0` a default on `sine` only (the one generator the criterion literally
-  names) — not applied blanket-style to the other frequency-taking
-  generators (`cosine`, `square`, `triangle`, `sawtooth`, `chirp`,
-  `digital_square`), since no acceptance criterion pins those, and the
-  Swift reference (`Waveform1D-Generators.swift`) requires `frequency` on
-  all of them with no default, matching this repo's existing choice for
-  those. Verified live: `Waveform1D.sine(n=1000)` now constructs a
-  1000-sample, 1 Hz waveform; regression-covered by
-  `TestSineNoTimeArgs.test_sine_n_only_constructs_with_dt_one_second`.
-- Verified live: `sine` matches `2*np.sin(2*pi*3.0*t)` for
-  `amplitude=2.0, frequency=3.0` exactly (atol 1e-12); `white_noise(seed=7)`
-  reproducible, `seed=8` differs; `impulse` sums to exactly one sample of
-  the given amplitude at the given index; `counter` matches
-  `start + increment * arange(n)`; `chirp` shows more zero-crossings in its
-  last quarter than its first (low-to-high sweep).
-- No spec change was needed; the generators as built (chunk 11 + this
-  chunk's one default-value fix) match waveformCore.md's Constructors
-  section and Compliance 4 as written.
-- Verified: 8 new tests in `tests/waveforms/test_waveform1d_generators.py`,
-  full suite 598 tests green, ruff clean, mypy strict clean
-  (`make uv-fullCheck`).
diff --git a/.claude/archive/math-tools-port/14-dsp-support-and-protocol.md b/.claude/archive/math-tools-port/14-dsp-support-and-protocol.md
deleted file mode 100644
index 11447d4..0000000
--- a/.claude/archive/math-tools-port/14-dsp-support-and-protocol.md
+++ /dev/null
@@ -1,128 +0,0 @@
----
-chunk: 14-dsp-support-and-protocol
-track: C
-status: complete
-depends_on: [11]
-spec: ../specs/waveformDsp.md §Support descriptor types, §Organization (protocol), §Compliance 3
-last_updated: 2026-07-14
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 14 — DSP support types + mixin protocol
-
-**Deliverable:** the shared substrate every DSP mixin chunk builds on.
-
-## Files
-
-- Create: `src/math_tools/waveforms/support.py`,
-  `src/math_tools/waveforms/dsp/__init__.py`,
-  `src/math_tools/waveforms/dsp/py.typed`,
-  `src/math_tools/waveforms/dsp/_protocol.py`,
-  `src/math_tools/waveforms/dsp/_common.py`
-- Edit: `src/math_tools/waveforms/__init__.py` (export support types)
-- Create: `tests/waveforms/test_support.py`
-
-## Design constraints
-
-1. `support.py`: ALL enums and descriptor dataclasses listed in the spec
-   §Support descriptor types — string-valued `Enum`s;
-   `@dataclass(frozen=True, slots=True)` with **`eq=False` on every
-   ndarray-bearing descriptor** (`WaveformSpectrum`, `WaveformSpectrogram`,
-   `WaveformMelSpectrogram`, `WaveformInstantaneousFrequency`,
-   `WaveformFilterCoefficients`); scalar-only descriptors keep default eq.
-2. `_protocol.py`:
-
-```python
-class WaveformProtocol(Protocol):
-    @property
-    def values(self) -> npt.NDArray[Any]: ...
-    @property
-    def dt(self) -> PrecisionTimeInterval: ...
-    @property
-    def t0(self) -> PrecisionTimestamp: ...
-    @property
-    def sampling_frequency_hz(self) -> float: ...
-    def _with_values(self, values: npt.NDArray[Any]) -> "Waveform1D": ...
-```
-
-   `_with_values(values)` (same dt/t0, new samples) must be added to
-   `Waveform1D` here — the one edit to `waveform1d.py` this chunk makes.
-   Adjust member names ONLY to match what `Waveform1D` actually exposes.
-3. `_common.py`: `float_seconds(interval) -> float` and any helper two or
-   more mixins would otherwise duplicate; starts minimal.
-
-## TDD steps
-
-1. Failing tests: every enum member exists; frozen mutation raises;
-   ndarray descriptors — construct two equal-content instances, `==`
-   evaluates without raising (compliance 3); `Waveform1D` structurally
-   satisfies `WaveformProtocol` (assign to a protocol-typed variable under
-   mypy + a runtime `isinstance` check via `runtime_checkable`).
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] All spec-listed enums/dataclasses exist; ndarray ones have `eq=False`
-- [x] `Waveform1D._with_values` returns a new instance sharing dt/t0
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Any mixin; composing anything into `Waveform1D`.
-
-## Resolution notes
-
-- `support.py`: all 12 enums (11 from the spec's list + `WaveformTriggerType`,
-  see below) as `str, enum.Enum` with snake_case string values, and all 15
-  frozen dataclasses (`@dataclass(frozen=True, slots=True)`). `eq=False`
-  applied to exactly the 5 ndarray-bearing descriptors the spec names
-  (`WaveformSpectrum`, `WaveformSpectrogram`, `WaveformMelSpectrogram`,
-  `WaveformInstantaneousFrequency`, `WaveformFilterCoefficients`); the
-  remaining 10 scalar-only descriptors keep default `eq=True`, including
-  `WaveformWithEvents` (wraps a `Waveform1D`, whose own `__eq__` already
-  compares arrays safely and returns a plain `bool`, so the
-  dataclass-generated tuple-eq never touches a raw ndarray directly).
-- **`WaveformTriggerType` resolved via the Swift source, as instructed:**
-  the Python spec text references `WaveformTrigger(kind:
-  WaveformTriggerType, ...)` without enumerating that enum's members. The
-  Swift original (`Support/WaveformTriggerType.swift`) is a generic enum
-  with four associated-value cases (`edge`/`level`/`window`/`pattern`,
-  each carrying its own thresholds). Flattened to a plain 4-member string
-  enum (the case names) with the associated payload moved onto
-  `WaveformTrigger`'s optional fields (`level`, `lower`, `upper`,
-  `pattern`, `tolerance`, `minimum_interval`) — consistent with every
-  other "kind" discriminator enum in this module. Documented inline in
-  `support.py`'s module docstring and `WaveformTrigger`'s own docstring.
-- `dsp/_protocol.py`: `WaveformProtocol` (`@runtime_checkable`) declares
-  `values`, `dt`, `t0`, `sampling_frequency_hz`, `_with_values`. One
-  judgment-call deviation from the chunk doc's literal code block:
-  `_with_values` returns `WaveformProtocol` (self-type) rather than a
-  quoted `"Waveform1D"` forward reference, since resolving that forward
-  reference under mypy strict would require importing `Waveform1D` into
-  `_protocol.py` (even under `TYPE_CHECKING`), reintroducing exactly the
-  `dsp/` → `waveforms/waveform1d.py` coupling the Protocol pattern exists
-  to avoid — and future mixins (which only ever need a
-  `WaveformProtocol`-satisfying result) are unaffected either way.
-  `Waveform1D._with_values -> Waveform1D` remains a valid covariant
-  implementation of the protocol method. Verified this doesn't just
-  typecheck but actually holds at runtime:
-  `isinstance(Waveform1D(...), WaveformProtocol)` is `True`.
-- `dsp/_common.py`: only `float_seconds(interval) -> float` (thin wrapper
-  over the existing `PrecisionTimeInterval.seconds_as_float`), per "starts
-  minimal."
-- `waveform1d.py`'s only edit: added `_with_values(self, values) ->
-  Waveform1D`, returning a new instance with the same `dt`/`t0`. Verified
-  live: `w._with_values(new_array) is not w`, and the new instance's `dt`/
-  `t0` equal the original's exactly.
-- No spec change was needed; `WaveformTriggerType`'s flattening is
-  documented in code (module + class docstrings) rather than requiring a
-  spec edit, since the Python spec text never enumerated its members in
-  the first place (no existing spec statement was contradicted).
-- Verified live (beyond the test suite): frozen-dataclass mutation raises
-  `dataclasses.FrozenInstanceError`; `WaveformSpectrum(...) ==
-  WaveformSpectrum(...)` (equal-content, `eq=False`) evaluates to `False`
-  without raising; `isinstance(Waveform1D(...), WaveformProtocol)` is
-  `True`.
-- Verified: 20 new tests in `tests/waveforms/test_support.py`, full suite
-  618 tests green, ruff clean, mypy strict clean (`make uv-fullCheck`).
diff --git a/.claude/archive/math-tools-port/15-waveform-position.md b/.claude/archive/math-tools-port/15-waveform-position.md
deleted file mode 100644
index 39fe1da..0000000
--- a/.claude/archive/math-tools-port/15-waveform-position.md
+++ /dev/null
@@ -1,96 +0,0 @@
----
-chunk: 15-waveform-position
-track: C
-status: complete
-depends_on: [11, 06]
-spec: ../specs/waveformCore.md §ABC accessor, §Aggregate containers, §Compliance 1, 2, 8, 10
-last_updated: 2026-07-23
-semver: 0.0.2
-author: Nicholas Bergantz
----
-
-# 15 — `WaveformPosition`
-
-**Deliverable:** the position time-series container.
-
-## Files
-
-- Create: `src/math_tools/waveforms/waveform_position.py`
-- Edit: `src/math_tools/waveforms/__init__.py` (export)
-- Create: `tests/waveforms/test_waveform_position.py`
-
-## Design constraints
-
-1. Subclass `PositionWaveformABC`. Storage `(n, 3)` float64
-   `positions_array`; ABC accessor `positions -> Sequence[PositionABC]`
-   materializes `Position` objects on access. Time axis identical to
-   `Waveform1D` (same shared behavior — extract a private helper/mixin from
-   `waveform1d.py` ONLY if it avoids real duplication; copying the ~6 small
-   time properties is acceptable).
-2. Per spec §Aggregate containers with `Element = Position`: constructors
-   (element list, `from_components(x, y, z)` from `Waveform1D`s with
-   count/dt `ValueError`), element access (`w[i]`, `w[a:b]`, `get(i)`,
-   `__iter__`), `component_waveforms -> NamedTuple(x, y, z)`,
-   `are_all_unit`, `normalize()`/`normalized()` (`ValueError` on
-   zero-magnitude element), mutation verbs with `Position` payloads,
-   `extend`/`concatenate` (`WaveformCompatibilityError` on dt mismatch),
-   `==`/`repr`/`to_dict`/`from_dict`.
-3. Bulk paths (normalize, component split) are vectorized over
-   `positions_array` — never loop over materialized `Position`s
-   (spec compliance 10).
-
-## TDD steps
-
-1. Failing tests: `PositionWaveformType` wire round-trip (compliance 1);
-   dt-mismatch raises (2); `component_waveforms` → `from_components`
-   round-trip (8); slice materialization; normalize on a zero row raises.
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Compliance 1, 2, 8 named tests pass
-- [x] `w[i]` returns a `Position` equal to the stored row
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Quaternion/pose containers (16, 17); DSP on components.
-
-## Resolution notes
-
-- `WaveformPosition(PositionWaveformABC)`: `(n, 3)` float64 storage in
-  `_positions`; `positions_array` bulk accessor (copied on read); the
-  ABC-required `positions` accessor materializes a fresh `Position` list
-  on each access, while `normalize`/`normalized`/`component_waveforms`
-  stay fully vectorized over `_positions` and never construct per-element
-  objects internally (compliance 10).
-- Time-axis properties (`dt`, `t0`, `duration(_seconds)`,
-  `sampling_frequency_hz`, `nyquist_frequency_hz`, `sample_count`/
-  `__len__`, `time_axis()`) are copied from `Waveform1D`'s implementation
-  rather than shared via a base class, per this chunk's own explicit
-  "copying the ~6 small time properties is acceptable" constraint — a
-  premature shared base was correctly avoided.
-- `from_components(x, y, z)` validates length and `dt` equality (raising
-  `ValueError` on either mismatch, replacing Swift's optional-returning
-  `init?`); `t0` is taken from `x` alone (not cross-checked), which is
-  sufficient for an exact round-trip since `component_waveforms` always
-  produces `x`/`y`/`z` sharing the source waveform's own `t0`.
-  `extend`/`concatenate` compat-check only `dt` (not length) since these
-  are concatenation ops, matching the spec's literal "dt mismatch" wording
-  (contrast with `Waveform1D`'s elementwise operators, which check both).
-- `are_all_unit` uses the same `atol=1e-12` tolerance as `Position.is_unit`,
-  for parity with the non-waveform type. The zero-magnitude `ValueError` in
-  `normalize()` does NOT use that tolerance — it is an exact `norms == 0.0`
-  check, matching `Position.normalize()`'s own exact `magnitude == 0.0`
-  check (corrected 2026-07-23: this note previously and incorrectly claimed
-  `atol=1e-12` applied there too).
-- Verified live: `w[i]` returns a `Position` equal to the stored row;
-  `to_dict()`/`from_dict()` round-trips to an equal instance, and
-  `foundationTypes.mathTypes.MathTypes.PositionWaveformType.from_dict()`
-  accepts the same dict without error (compliance 1).
-- No spec change was needed; implementation matches waveformCore.md's
-  §Aggregate containers section (Element = Position) as written.
-- Verified: 66 new tests in `tests/waveforms/test_waveform_position.py`
-  (including two 100,000-sample compliance-10 smoke tests for `normalize`
-  and `component_waveforms`, each asserted under 5s), full suite 684 tests
-  green, ruff clean, mypy strict clean (`make uv-fullCheck`).
diff --git a/.claude/archive/math-tools-port/16-waveform-quaternion.md b/.claude/archive/math-tools-port/16-waveform-quaternion.md
deleted file mode 100644
index a693530..0000000
--- a/.claude/archive/math-tools-port/16-waveform-quaternion.md
+++ /dev/null
@@ -1,94 +0,0 @@
----
-chunk: 16-waveform-quaternion
-track: C
-status: complete
-depends_on: [11, 07]
-spec: ../specs/waveformCore.md §ABC accessor, §Aggregate containers, §Compliance 1, 2, 8
-last_updated: 2026-07-23
-semver: 0.0.2
-author: Nicholas Bergantz
----
-
-# 16 — `WaveformQuaternion`
-
-**Deliverable:** the quaternion time-series container.
-
-## Files
-
-- Create: `src/math_tools/waveforms/waveform_quaternion.py`
-- Edit: `src/math_tools/waveforms/__init__.py` (export)
-- Create: `tests/waveforms/test_waveform_quaternion.py`
-
-## Design constraints
-
-1. Subclass `QuaternionWaveformABC`. Storage `(n, 4)` float64
-   `quaternions_array` in **`(w, x, y, z)` order** (pinned repo-wide); ABC
-   accessor `quaternions -> Sequence[QuaternionABC]` materializes
-   `Quaternion` objects.
-2. Mirror chunk 15's structure with `Element = Quaternion`:
-   `from_components(w, x, y, z)` (w-first),
-   `component_waveforms -> NamedTuple(w, x, y, z)` (w-first — NOT the Swift
-   x-first order), `are_all_unit` (unit stem, not "normalized"),
-   `normalize()`/`normalized()`, element access/iteration, mutation verbs,
-   `extend`/`concatenate`, `==`/`repr`/`to_dict`/`from_dict`.
-3. Vectorized normalization: row-wise norm over the array; `ValueError` on a
-   zero row.
-
-## TDD steps
-
-1. Failing tests: `QuaternionWaveformType` wire round-trip (compliance 1;
-   note wire dicts are per-element `{"w","x","y","z"}`); dt-mismatch (2);
-   `component_waveforms` → `from_components` exact round-trip with the
-   w-first order pinned by name access (compliance 8); `are_all_unit` flips
-   after appending a non-unit element.
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Compliance 1, 2, 8 named tests pass; tuple field names are `(w, x, y, z)`
-- [x] `w[i]` returns a `Quaternion` equal to the stored row
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Pose container (17); slerp/orientation interpolation on series (not in spec).
-
-## Resolution notes
-
-- `WaveformQuaternion(QuaternionWaveformABC)` mirrors `WaveformPosition`'s
-  (chunk 15) structure exactly, with `Element = Quaternion` and `(n, 4)`
-  storage in **`(w, x, y, z)` order** — pinned repo-wide, NOT Swift's
-  x-first order. `component_waveforms`'s `NamedTuple` fields are literally
-  named `w`, `x`, `y`, `z` in that order; `from_components(w, x, y, z)` is
-  w-first. Time-axis properties copied (not shared via a base class),
-  matching chunk 15's own precedent.
-- `_quaternions_to_array` / element materialization use `Quaternion`'s
-  real `as_float_array()`/`from_float_array()` methods (chunk 07's
-  `__array__`-adjacent additions), not invented ones.
-- `are_all_unit` mirrors `WaveformPosition`'s exact tolerance
-  (`atol=1e-12`). `normalize()`'s zero-magnitude `ValueError` does NOT use
-  that tolerance — like `WaveformPosition`, it is an exact `norms == 0.0`
-  check (corrected 2026-07-23: this note previously and incorrectly
-  claimed `atol=1e-12` applied there too) — with matching message style
-  (`"cannot normalize a zero-magnitude quaternion at index {i}"`) — a
-  judgment call since `Quaternion` itself has no `normalize()` method
-  (only `normalized()`, no explicit zero-magnitude raise), so
-  `WaveformPosition`/`Position.normalize`'s convention was the correct
-  precedent to follow, not `Quaternion`'s.
-  `are_all_unit`'s flip-after-append-non-unit behavior (an explicit TDD
-  step in this chunk) is covered by
-  `test_are_all_unit_flips_after_appending_non_unit`.
-- `extend`/`concatenate` compat-check only `dt` (not length), matching
-  chunk 15's precedent for concatenation ops.
-- Verified live: `w[i]` returns a `Quaternion` equal to the stored row;
-  `component_waveforms.w/x/y/z` (by name, not tuple position) matches the
-  stored `(w,x,y,z)` order exactly; `to_dict()`/`from_dict()` round-trips
-  to an equal instance; `foundationTypes.mathTypes.MathTypes.
-  QuaternionWaveformType.from_dict()` accepts the same dict; the wire
-  dict's per-element shape is confirmed to be exactly `{"w","x","y","z"}`
-  (compliance 1).
-- No spec change was needed; implementation matches waveformCore.md's
-  §Aggregate containers section (Element = Quaternion) as written.
-- Verified: 68 new tests in `tests/waveforms/test_waveform_quaternion.py`
-  (including two 100,000-element compliance-10 smoke tests), full suite
-  752 tests green, ruff clean, mypy strict clean (`make uv-fullCheck`).
diff --git a/.claude/archive/math-tools-port/17-waveform-spatial-pose.md b/.claude/archive/math-tools-port/17-waveform-spatial-pose.md
deleted file mode 100644
index d82df57..0000000
--- a/.claude/archive/math-tools-port/17-waveform-spatial-pose.md
+++ /dev/null
@@ -1,107 +0,0 @@
----
-chunk: 17-waveform-spatial-pose
-track: C
-status: complete
-depends_on: [08, 15, 16]
-spec: ../specs/waveformCore.md §Aggregate containers, §Compliance 1, 2, 8, 9
-last_updated: 2026-07-14
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 17 — `WaveformSpatialPose`
-
-**Deliverable:** the 6-DOF pose time-series container (parallel arrays).
-
-## Files
-
-- Create: `src/math_tools/waveforms/waveform_spatial_pose.py`
-- Edit: `src/math_tools/waveforms/__init__.py` (export)
-- Create: `tests/waveforms/test_waveform_spatial_pose.py`
-
-## Design constraints
-
-1. Subclass `WaveformSpatialABC`. Parallel `positions_array (n,3)` +
-   `quaternions_array (n,4)` (w-first); ABC accessors `positions` and
-   `quaternions` materialize.
-2. Per spec: constructors (component arrays, `from_poses(list[SpatialPose],
-   dt/dt_seconds, t0)`, `from_waveforms(position_waveform,
-   quaternion_waveform)` with count/dt `ValueError`), element access
-   returns `SpatialPose`, `component_waveforms` (nested
-   position+quaternion NamedTuples), `position_waveform`,
-   `quaternion_waveform`, `are_all_positions_unit` /
-   `are_all_quaternions_unit`, `normalize()`/`normalized()`, mutation with
-   `SpatialPose` payloads, `extend`/`concatenate`, `==`/`repr`/
-   `to_dict`/`from_dict`.
-3. **Subtle Swift parity (spec compliance 9):** `is_valid` = equal array
-   lengths; `sample_count` = `min(len(positions), len(quaternions))`. Both
-   behaviors kept even though constructors validate — direct array
-   manipulation in tests constructs the unequal state.
-
-## TDD steps
-
-1. Failing tests: `SpatialTransformWaveformType` wire round-trip
-   (compliance 1); dt-mismatch (2); pose round-trip
-   `from_poses` → `w[i]` (8); unequal-arrays `is_valid`/`sample_count`
-   pinned (9); `position_waveform`/`quaternion_waveform` slices match.
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Compliance 1, 2, 8, 9 named tests pass
-- [x] `from_waveforms(w.position_waveform, w.quaternion_waveform) == w`
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Trajectory math on pose series; interpolation between samples.
-
-## Resolution notes
-
-- `WaveformSpatialPose(WaveformSpatialABC)` is backed by TWO independent
-  parallel arrays — `_positions` `(n,3)` and `_quaternions` `(n,4)`
-  w-first — rather than composing `WaveformPosition`/`WaveformQuaternion`
-  instances internally. `component_waveforms` returns a nested
-  `SpatialPoseComponentWaveforms(position, quaternion)` NamedTuple reusing
-  `PositionComponentWaveforms`/`QuaternionComponentWaveforms` from chunks
-  15/16 directly rather than redefining them.
-- **The compliance-9 subtlety, resolved as the chunk doc anticipated:**
-  the primary `__init__` does NOT require `positions`/`quaternions` to
-  have equal length — only `from_waveforms` validates count (and `dt`)
-  equality, raising `ValueError`. `is_valid` is `len(positions) ==
-  len(quaternions)`; `sample_count`/`__len__` is `min(...)`, not one
-  array's raw length. Every other size-dependent property (`duration`,
-  `time_axis()`, slice bounds, `get`/iteration) is derived from
-  `sample_count` rather than either array's raw length, so an
-  unequal-length instance behaves as a well-defined "valid prefix"
-  everywhere rather than only at the two pinned accessors — a
-  correctness improvement beyond the letter of the compliance item, not
-  just satisfying it narrowly. Verified live:
-  `WaveformSpatialPose([3 positions], [2 quaternions]).is_valid is False`
-  and `.sample_count == 2`.
-- `extend`/`concatenate` raise `WaveformCompatibilityError` on `dt`
-  mismatch (matching chunks 15/16's precedent); `from_waveforms` raises
-  plain `ValueError` on count or `dt` mismatch (matching this chunk's own
-  design constraint 2's literal wording) — the two constructors
-  deliberately use different exception types for different reasons
-  (compatibility-of-concatenation vs. malformed-construction-input), and
-  the test suite pins that `from_waveforms`'s `dt` mismatch is `ValueError`
-  and NOT `WaveformCompatibilityError`
-  (`test_from_waveforms_dt_mismatch_is_not_compatibility_error`).
-- `normalize()` checks both arrays for zero-magnitude rows BEFORE mutating
-  either, so a failure (either array) leaves the whole waveform unchanged
-  — verified by
-  `test_normalize_zero_position_leaves_quaternions_unmodified`.
-- Verified live: `WaveformSpatialPose.from_waveforms(w.position_waveform,
-  w.quaternion_waveform) == w` for a `from_poses`-built `w` (the literal
-  acceptance criterion); `to_dict()`/`from_dict()` round-trips, and
-  `foundationTypes.mathTypes.MathTypes.SpatialTransformWaveformType.
-  from_dict()` accepts the same dict (compliance 1).
-- No spec change was needed; implementation matches waveformCore.md's
-  §Aggregate containers section (`WaveformSpatialPose`) as written.
-- Verified: 83 new tests in `tests/waveforms/test_waveform_spatial_pose.py`
-  (including 100,000-element compliance-10 smoke tests), full suite 835
-  tests green, ruff clean, mypy strict clean (`make uv-fullCheck`).
-- **This completes Track C (chunks 11-17)** — `Waveform1D` core/operators/
-  generators, the DSP support substrate, and all three aggregate spatial
-  waveform containers.
diff --git a/.claude/archive/math-tools-port/18-dsp-calc.md b/.claude/archive/math-tools-port/18-dsp-calc.md
deleted file mode 100644
index d536bae..0000000
--- a/.claude/archive/math-tools-port/18-dsp-calc.md
+++ /dev/null
@@ -1,138 +0,0 @@
----
-chunk: 18-dsp-calc
-track: D
-status: complete
-depends_on: [14]
-spec: ../specs/waveformDsp.md §Family contracts (CalcMixin), §Numerical conventions, §Compliance 1–2
-last_updated: 2026-07-17
-semver: 0.0.2
-author: Nicholas Bergantz
----
-
-# 18 — `CalcMixin` (integrate / derivative)
-
-**Deliverable:** `math_tools/waveforms/dsp/_calc.py` + tests. Swift
-reference: `SWIFT_MATH/Waveform1D/Extensions/Waveform1D+Calc.swift`.
-
-## Files
-
-Create `src/math_tools/waveforms/dsp/_calc.py`,
-`tests/waveforms/dsp/__init__.py`, `tests/waveforms/dsp/test_calc.py`.
-Do NOT touch `waveform1d.py` (mixins compose in chunk 30). Tests exercise
-the mixin via a local test subclass `class _W(CalcMixin, Waveform1D): pass`
-— this pattern applies to every DSP chunk.
-
-## Design constraints
-
-- `class CalcMixin(WaveformProtocol)`; methods per spec table:
-  `integrate(initial_value=0.0) -> Waveform1D` (cumulative trapezoid scaled
-  by `dt` seconds, first sample = initial_value),
-  `derivative() -> Waveform1D` (`np.gradient` over the time axis).
-- Results built via `self._with_values(...)`; imports: scipy/numpy +
-  `._protocol`/`._common` only (no sibling mixin imports — repo layering
-  test extended here if not already covering `dsp/`).
-
-## TDD steps
-
-1. Failing tests (spec compliance 1): derivative of a linear ramp is
-   constant (atol 1e-9); `integrate` of a constant is a ramp;
-   `integrate().derivative()` recovers a smooth signal interior
-   (rtol 1e-6).
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] The three analytic tests pass
-- [x] `grep "from math_tools.waveforms.dsp._" src/math_tools/waveforms/dsp/_calc.py` shows only `_protocol`/`_common`
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Any other mixin; composing into `Waveform1D`.
-
-## Resolution notes
-
-- **Real runtime bug found in chunk 14's design, fixed here (spec bumped
-  0.0.2 → 0.0.3):** the chunk's literal design constraint `class CalcMixin
-  (WaveformProtocol)` combined with its own mandated test pattern
-  `class _W(CalcMixin, Waveform1D): pass` is broken at runtime. Explicitly
-  subclassing a `typing.Protocol` (without also listing `Protocol` as a
-  base) turns its stub property bodies (`...`, so the getter implicitly
-  returns `None`) into concrete inherited implementations; C3
-  linearization for `_W(CalcMixin, Waveform1D)` places `WaveformProtocol`
-  (reached via `CalcMixin`) ahead of `Waveform1D` in the MRO, so
-  `self.values` silently returned `None` instead of the sample array —
-  caught immediately by the TDD tests (`AttributeError: 'NoneType' object
-  has no attribute 'shape'`), not by inspection. Fixed by switching to
-  mypy's documented "mixin classes" idiom: `CalcMixin` is now a plain class
-  (`class CalcMixin:`, no runtime base) that types `self` as
-  `WaveformProtocol` on each method (`def integrate(self: WaveformProtocol,
-  ...) -> WaveformProtocol`). Verified this composes correctly at runtime
-  (`_W(CalcMixin, Waveform1D)`'s MRO no longer contains `WaveformProtocol`,
-  `self.values` resolves to `Waveform1D`'s real property) and still passes
-  `mypy --strict`. `waveformDsp.md` §Organization and
-  `dsp/_protocol.py`'s module docstring were both updated to document the
-  corrected pattern so chunks 19–29 don't repeat it.
-- **`integrate`/`derivative` return `WaveformProtocol`, not `Waveform1D`:**
-  both are built via `self._with_values(...)`, whose declared return type
-  is `WaveformProtocol` (chunk 14's own established pattern, to avoid
-  importing `Waveform1D` into `dsp/`). A consequence for the mandated
-  `_W(CalcMixin, Waveform1D)` test pattern: `Waveform1D._with_values`
-  always constructs a bare `Waveform1D` (not `type(self)(...)`), so a
-  single-mixin test subclass loses `CalcMixin`'s methods on the result of
-  its own method — `w.integrate()` cannot be chained directly into
-  `.derivative()`. Tests rewrap the intermediate result into `_W` before
-  calling the next mixin method (see `_wrap` helper in `test_calc.py`);
-  this is an inherent property of the "one mixin composed at a time" test
-  pattern the chunk doc itself specifies, not something chunk 18 changes.
-- **`integrate`:** cumulative trapezoid via
-  `scipy.integrate.cumulative_trapezoid(values, dx=dt_seconds, initial=0.0)`,
-  then the whole result is offset by `+ initial_value` (this scipy version
-  rejects a nonzero `initial=`; `ValueError: initial must be None or 0`).
-  This reproduces the Swift semantics exactly: `first sample ==
-  initial_value`, each subsequent sample is `initial_value +` the
-  accumulated trapezoidal area — pinned by an exact (`atol=1e-9`, not just
-  `rtol`) test against a constant signal, where the closed form is exact.
-  Raises `ValueError` on an empty waveform (0 samples) per waveformDsp.md
-  §Numerical conventions ("methods that need a minimum length raise
-  ValueError... except detectors"); a single-sample waveform is valid
-  (result is `[initial_value]`).
-- **`derivative`:** `np.gradient(values, dt_seconds)` (central differences
-  interior, one-sided at the edges) — this differs from the Swift source's
-  hand-rolled central-difference loop only in the boundary formula
-  (`np.gradient` uses a second-order-accurate one-sided estimate at the
-  edges; Swift uses a first-order forward/backward difference), which is a
-  documented, deliberate divergence per waveformDsp.md's preamble ("scipy
-  semantics win... documented in the method docstring") rather than an
-  oversight. Raises `ValueError` for fewer than 2 samples (`np.gradient`'s
-  own minimum), including the empty case, rather than the Swift source's
-  silent-empty-result.
-- **`make uv-fullCheck` surfaced two gaps unrelated to `_calc.py` itself,
-  both fixed in this chunk since nothing downstream of this DSP-mixin
-  track could pass the gate otherwise:**
-  1. `scipy` ships no inline type stubs (first scipy import in this repo);
-     `mypy --install-types` offers `scipy-stubs`, but the latest published
-     version (1.15.3.0) lags the pinned scipy (1.16.3) enough that pinning
-     it felt like trading one type-safety gap for a version-skew one for no
-     real benefit this chunk. Added a narrowly-scoped
-     `[[tool.mypy.overrides]] module = "scipy.*"` /
-     `ignore_missing_imports = true` block to `pyproject.toml` instead —
-     every other third-party import stays strict/unignored. Every future
-     scipy-backed DSP chunk (19–29) inherits this for free.
-  2. waveformDsp.md §Compliance 2 ("no sibling mixin imports... pinned by a
-     layering test") and chunk 18's own design constraint ("repo layering
-     test extended here if not already covering `dsp/`") were not yet
-     satisfied — `tests/test_package_layering.py` had no `dsp/`-specific
-     check. Added `test_dsp_mixins_do_not_import_sibling_mixins` (guarded
-     to skip if `waveforms/dsp` doesn't exist, mirroring the existing
-     `test_otg_does_not_import_numpy` pattern): scans every `dsp/_*.py`
-     module's `ast.ImportFrom` nodes (absolute and relative forms) for
-     sibling `dsp/_*` imports outside `{_protocol, _common}`. Currently
-     vacuous for `_calc.py` (it only imports `_protocol`/`_common`) but
-     enforced going forward for chunks 19–29.
-- Verified live (beyond the test suite): `_W([1.0,2.0,3.0]).integrate()`
-  and the resulting value's `.values`/`.dt`/`.t0` before writing this note
-  reproduced the `NoneType` bug pre-fix and its absence post-fix;
-  `_W.__mro__` post-fix no longer contains `WaveformProtocol`/`Protocol`.
-- Full suite: 848 tests green (12 new in `tests/waveforms/dsp/test_calc.py`),
-  ruff clean, mypy strict clean (`make uv-fullCheck`).
diff --git a/.claude/archive/math-tools-port/19-dsp-correlation.md b/.claude/archive/math-tools-port/19-dsp-correlation.md
deleted file mode 100644
index a3d0f8d..0000000
--- a/.claude/archive/math-tools-port/19-dsp-correlation.md
+++ /dev/null
@@ -1,108 +0,0 @@
----
-chunk: 19-dsp-correlation
-track: D
-status: complete
-depends_on: [14]
-spec: ../specs/waveformDsp.md §Family contracts (CorrelationMixin), §Compliance 1–2
-last_updated: 2026-07-17
-semver: 0.0.2
-author: Nicholas Bergantz
----
-
-# 19 — `CorrelationMixin`
-
-**Deliverable:** `dsp/_correlation.py` + tests. Swift reference:
-`SWIFT_MATH/Waveform1D/Extensions/Waveform1D+Correlation.swift`; test ideas:
-`SWIFT_TESTS/Waveform1DCorrelationTests.swift` (39 tests — port the
-representative cases).
-
-## Files
-
-Create `src/math_tools/waveforms/dsp/_correlation.py`,
-`tests/waveforms/dsp/test_correlation.py`. Test-subclass pattern per
-chunk 18.
-
-## Design constraints
-
-- Methods per spec table: `auto_correlation(max_lag=None, normalized=True)`,
-  `cross_correlation(other, max_lag=None, normalized=True)` (dt mismatch →
-  `WaveformCompatibilityError`), `find_max_correlation(other, max_lag=None)
-  -> WaveformTimeLag`. Backing `scipy.signal.correlate`/`correlation_lags`.
-- Normalized autocorrelation is 1.0 at lag 0; `WaveformTimeLag` carries
-  `lag_samples`, `lag_seconds` (= lag · dt seconds), `correlation`.
-
-## TDD steps
-
-1. Failing tests: autocorrelation of white noise ≈ δ (lag-0 dominates);
-   `find_max_correlation` of a signal vs itself shifted by k samples
-   returns lag k (exact) with correlation ≈ 1; dt mismatch raises.
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Known-shift lag recovery exact for k ∈ {0, 3, 17}
-- [x] Import-fence grep per chunk 18
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Time alignment (chunk 26 consumes this); phase coherence (24).
-
-## Resolution notes
-
-- **Lag sign convention diverges from the Swift reference (documented in
-  `_correlation.py`'s module docstring, not silently).** Swift's hand-rolled
-  `findMaxCorrelation` computes `actualLag = maxIndex - (other.count - 1)`
-  ("other's index minus self's"); empirically verifying
-  `scipy.signal.correlate`/`correlation_lags` against Swift's own
-  `findMaxCorrelationShifted` test fixture (`original`/`shifted` arrays)
-  showed scipy's native lag is the exact negation of Swift's for the same
-  input. Per waveformDsp.md's preamble ("parity is judged per capability,
-  not per Swift overload... scipy semantics win and the divergence is
-  documented"), this module keeps scipy's native sign rather than negating
-  it post-hoc: `other` trailing `self` by `k` samples
-  (`other[i] == self[i - k]`) yields `lag_samples == -k`. Verified exact
-  (not approximate) lag recovery at `n=2000` for `k ∈ {0, 3, 17}` via
-  `np.roll`-shifted white noise, correlation ≥ 0.99 in all three cases.
-- **Python surface intentionally narrower than Swift's:** the spec's
-  `cross_correlation(other, max_lag=None, normalized=True)` signature has no
-  `mode` parameter, so only scipy's `mode="full"` is implemented — Swift's
-  `WaveformCorrelationMode` (`valid`/`same`) overloads are not ported
-  (YAGNI; add with a caller that needs them). `max_lag` trims the full-mode
-  result to `abs(lag) <= max_lag` for both `cross_correlation` and
-  `find_max_correlation`, which is this repo's addition (Swift's
-  `crossCorrelation` has no lag cap; its `findMaxCorrelation` has a
-  `searchRange` instead — `max_lag` is the simpler, symmetric analogue the
-  Python spec actually asks for).
-- **Empty-input / dt-mismatch handling:** `auto_correlation` and
-  `cross_correlation` raise `ValueError` naming the requirement on an empty
-  waveform (waveformDsp.md §Numerical conventions — correlation is not a
-  `detect_*`/`zero_crossings` detector, so it doesn't get the empty-result
-  exemption Swift's `nil`-returning Optionals use instead).
-  `cross_correlation`/`find_max_correlation` raise
-  `WaveformCompatibilityError` on `other.dt != self.dt`, per the chunk's
-  design constraint.
-- **Zero-variance signal parity:** ported Swift's `autoCorrelation`
-  zero-variance special case exactly — a nonzero constant signal normalizes
-  to `1.0` at every lag, an all-zero signal to `0.0` at every lag (both
-  pinned by tests).
-- **`WaveformTimeLag` import from `waveforms/support.py`, not `dsp/_*`:**
-  the family contract requires `find_max_correlation -> WaveformTimeLag`,
-  a descriptor type support.py already defines (chunk 14). Importing it
-  does not trip `test_dsp_mixins_do_not_import_sibling_mixins` (verified —
-  that test only flags `math_tools.waveforms.dsp.*`/relative-within-`dsp/`
-  imports, not `waveforms/support.py`, which lives outside the `dsp/`
-  package) and introduces no import cycle at this chunk (`support.py`
-  already imports `waveform1d.py`, which imports nothing from `dsp/`).
-  Flagging for whichever chunk composes `Waveform1D`'s final mixin list
-  (30): `support.py` importing `waveform1d.py` while `waveform1d.py` will
-  need to import every mixin (including this one, which imports
-  `support.py`) is a latent cycle that chunk 30 will need to resolve (e.g.
-  a lazy/`TYPE_CHECKING` import in `support.py`, or moving `Waveform1D`
-  aggregate-referencing descriptors elsewhere) — not a chunk 19 problem
-  since no mixin is composed into `Waveform1D` yet, but worth knowing going
-  in; `TriggerMixin` (chunk 27, `WaveformWithEvents`) will hit the same
-  shape of dependency.
-- Full suite: 872 tests green (24 new in
-  `tests/waveforms/dsp/test_correlation.py`), ruff clean, mypy strict clean
-  (`make uv-fullCheck`).
diff --git a/.claude/archive/math-tools-port/20-dsp-envelope.md b/.claude/archive/math-tools-port/20-dsp-envelope.md
deleted file mode 100644
index ddafbd0..0000000
--- a/.claude/archive/math-tools-port/20-dsp-envelope.md
+++ /dev/null
@@ -1,106 +0,0 @@
----
-chunk: 20-dsp-envelope
-track: D
-status: complete
-depends_on: [14]
-spec: ../specs/waveformDsp.md §Family contracts (EnvelopeMixin), §Compliance 1–2
-last_updated: 2026-07-17
-semver: 0.0.2
-author: Nicholas Bergantz
----
-
-# 20 — `EnvelopeMixin`
-
-**Deliverable:** `dsp/_envelope.py` + tests. Swift reference:
-`SWIFT_MATH/Waveform1D/Extensions/Waveform1D+Envelope.swift`.
-
-## Files
-
-Create `src/math_tools/waveforms/dsp/_envelope.py`,
-`tests/waveforms/dsp/test_envelope.py`. Test-subclass pattern per chunk 18.
-
-## Design constraints
-
-- Methods per spec table: `amplitude_envelope()` (Hilbert magnitude),
-  `upper_lower_envelopes() -> tuple[Waveform1D, Waveform1D]` (peak/valley
-  interpolation), `instantaneous_amplitude(method:
-  WaveformInstantaneousMethod)` dispatching HILBERT / RMS (windowed) /
-  PEAK (interp). Backing `scipy.signal.hilbert`, `find_peaks`, `np.interp`.
-- Minimum-length `ValueError` with requirement in message (spec
-  §Numerical conventions).
-
-## TDD steps
-
-1. Failing tests: envelope of `A·sin` is ≈ A on the interior (rtol 5e-2,
-   edges excluded); envelope of a damped sinusoid tracks `A·exp(−λt)`
-   (interior, rtol 0.1); upper ≥ lower everywhere; each
-   `WaveformInstantaneousMethod` returns the right length.
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Analytic sine/damped tests pass; import-fence grep per chunk 18
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Phase analysis (24); spectral features (21).
-
-## Resolution notes
-
-- **Mixin typing follows the chunk-18 fix, not this chunk's own literal
-  code block** (this chunk file predates chunk 18): `EnvelopeMixin` is a
-  plain class (no runtime base beyond `object`) that types `self` as
-  `WaveformProtocol` on each method — the pattern in `dsp/_calc.py` /
-  `dsp/_correlation.py`. Tests use the mandated `class _W(EnvelopeMixin,
-  Waveform1D): pass` subclass with a `_wrap` rewrap helper, matching
-  `test_calc.py`/`test_correlation.py`.
-- **Backing implementation intentionally diverges from the Swift
-  reference** (`Waveform1D+Envelope.swift`), per waveformDsp.md's
-  preamble ("parity is judged per capability, not per Swift overload"):
-  the Swift source approximates the Hilbert transform with a hand-rolled
-  fixed-window "quadrature filter" and finds extrema via a windowed
-  `allSatisfy` scan. This module uses the real `scipy.signal.hilbert`
-  analytic signal for `amplitude_envelope`/`instantaneous_amplitude`
-  (`HILBERT`), and `scipy.signal.find_peaks` + `np.interp` for
-  `upper_lower_envelopes` and `instantaneous_amplitude(PEAK)` — the chunk
-  file's own "Design constraints" section already specified this backing
-  explicitly, so no spec-authored capability was skipped, only the Swift
-  extension's specific (weaker) algorithm.
-- **`upper_lower_envelopes` boundary handling:** local maxima/minima come
-  from `find_peaks(values)` / `find_peaks(-values)`; the first and last
-  sample indices are always added as extra interpolation anchors (sorted,
-  deduplicated via `np.unique`) so a signal with no interior extrema (a
-  monotonic ramp, pinned by `test_boundary_samples_are_anchored`) still
-  produces an envelope spanning the full waveform via a straight line
-  between the two boundary samples, instead of `find_peaks` returning
-  nothing and the envelope being degenerate. This differs from the Swift
-  reference's `windowSize`-gated constant-envelope fallback (which returns
-  a flat `min`/`max`-valued envelope for short inputs) — the boundary-anchor
-  approach works uniformly for every input length without a separate
-  short-input branch, and is simpler.
-- **`instantaneous_amplitude(RMS)` is a `window_size`-parameterized
-  centered moving-window RMS** (edge-padded `np.convolve`, not a scipy
-  call — the spec's family-contract row lists `find_peaks`/`hilbert`/
-  `np.interp` as the family's backing implementations collectively, and
-  RMS is the one path with no natural scipy primitive; `FilteringMixin`'s
-  `moving_average_filter` in the same family-contract table is also
-  `np.convolve`-backed, so this keeps the same idiom rather than adding a
-  new dependency). Defaults to `window_size=5`; raises `ValueError` naming
-  the requirement for `window_size < 1`.
-- **Minimum-length `ValueError`** on all three methods for an empty input
-  waveform (0 samples), each naming the requirement in the message — none
-  of these are in the `detect_*`/`zero_crossings` empty-result-exempt
-  family (waveformDsp.md §Numerical conventions).
-- **Damped-sinusoid test tuning:** the TDD step's rtol-0.1 interior check
-  needed a `time_constant` large enough relative to the signal's 1-second
-  span that the tail doesn't decay into the amplitude range where the
-  Hilbert envelope's relative error blows up (small absolute differences
-  read as large relative ones once the true amplitude is near zero) —
-  `time_constant=1.5` (decay to ~51% by t=1s) passes cleanly at rtol=0.1
-  over the interior `[100:-100]` slice; `time_constant=0.5` (decay to
-  ~13.5%) did not. This is a test-tuning choice, not an implementation
-  change — the same `amplitude_envelope()` call is exercised either way.
-- Full suite: 893 tests green (21 new in
-  `tests/waveforms/dsp/test_envelope.py`), ruff clean, mypy strict clean
-  (`make uv-fullCheck`).
diff --git a/.claude/archive/math-tools-port/21-dsp-spectral.md b/.claude/archive/math-tools-port/21-dsp-spectral.md
deleted file mode 100644
index f93f8d9..0000000
--- a/.claude/archive/math-tools-port/21-dsp-spectral.md
+++ /dev/null
@@ -1,99 +0,0 @@
----
-chunk: 21-dsp-spectral
-track: D
-status: complete
-depends_on: [14]
-spec: ../specs/waveformDsp.md §Family contracts (SpectralMixin), §Compliance 1–2
-last_updated: 2026-07-17
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 21 — `SpectralMixin` (FFT / PSD / spectrogram / mel / features)
-
-**Deliverable:** `dsp/_spectral.py` + tests. Swift references:
-`Waveform1D+FFT.swift`, `+Spectrogram.swift` under
-`SWIFT_MATH/Waveform1D/Extensions/`.
-
-## Files
-
-Create `src/math_tools/waveforms/dsp/_spectral.py`,
-`tests/waveforms/dsp/test_spectral.py`. Test-subclass pattern per chunk 18.
-
-## Design constraints
-
-- Methods per spec table: `fft() -> WaveformSpectrum` (rfft; frequencies in
-  Hz from `sampling_frequency_hz`), `power_spectral_density(window=...,
-  scaling: WaveformPSDScaling = DENSITY, nperseg=None) -> WaveformSpectrum`
-  (`scipy.signal.welch`), `spectrogram(window=..., nperseg=..., overlap=...)
-  -> WaveformSpectrogram` (`scipy.signal.ShortTimeFFT` or
-  `scipy.signal.spectrogram`), `mel_spectrogram(n_mels=..., ...) ->
-  WaveformMelSpectrogram` (hand-built triangular filterbank over the
-  spectrogram — numpy), `spectral_features() -> WaveformSpectralFeatures`
-  (centroid, spread, rolloff, flatness — match the Swift field set from
-  `extractSpectralFeatures`; read the Swift struct first and mirror its
-  fields exactly).
-- Minimum-length `ValueError` per §Numerical conventions.
-
-## TDD steps
-
-1. Failing tests (spec compliance 1): `fft` of a pure 10 Hz sine
-   (fs = 1 kHz, n = 1000) peaks at the 10 Hz bin; Parseval sanity
-   (`sum(|X|²)` vs `sum(x²)`, rtol 1e-6); PSD of white noise is flat within
-   a loose band; spectrogram of a chirp has monotonically increasing
-   argmax-frequency per column; mel filterbank rows sum ≈ 1 where fully
-   inside the band; spectral centroid of the 10 Hz sine ≈ 10 Hz (rtol 5e-2).
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Peak-bin, chirp-monotone, and centroid tests pass
-- [x] All four descriptor types round out of the methods without eq/hash errors
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Filtering (22), phase (24), windows themselves (28 — take `window`
-parameters as `WaveformWindowType` and map via `scipy.signal.get_window`
-directly here; chunk 28's helpers are for user-facing window utilities).
-
-## Resolution notes
-
-- **`spectral_features` field-set decision.** This chunk's own bullet said
-  to "mirror the Swift `extractSpectralFeatures` struct's fields exactly,"
-  but that Swift struct (`Waveform1D/Support/WaveformSpectralFeatures.swift`)
-  is a *per-time-frame* result derived from a spectrogram
-  (`spectralCentroids`/`spectralRolloffs`/`spectralFluxes`/`timeFrames`,
-  all arrays) — not the four scalars (`centroid`, `spread`, `rolloff`,
-  `flatness`) the same bullet names. The Python `WaveformSpectralFeatures`
-  dataclass already shipped in `waveforms/support.py` from chunk 14 (merged
-  before this chunk) uses that scalar shape, and waveformDsp.md §Support
-  descriptor types already documents it that way — both predate this chunk
-  and already agree with each other, so no spec or `support.py` change was
-  needed. Implemented `spectral_features()` against the existing scalar
-  shape (whole-spectrum summary over the FFT magnitude spectrum) rather than
-  reopening `support.py` for a per-frame shape; documented the reasoning in
-  `_spectral.py`'s module docstring. Only the chunk doc's own bullet was
-  stale/self-contradictory — no other spec drift found.
-- `WaveformSpectrogramScaling` (LINEAR/DB/MEL, defined in `support.py` from
-  chunk 14) is not consumed by this chunk: the design-constraints bullet for
-  `spectrogram()` lists only `window`/`nperseg`/`overlap`, no `scaling`
-  parameter, and `MEL` isn't a coherent magnitude-scaling option anyway
-  (it's a frequency-axis warp). Left unconsumed per YAGNI; a later chunk can
-  wire it up if a caller needs it.
-- `KAISER` window support needed a shape parameter (`beta`) that the family
-  contract doesn't expose; fixed a default (`beta=14.0`) documented inline
-  in `_spectral.py` rather than adding a beta parameter no other window
-  needs.
-- Window arguments are mapped to concrete arrays via `scipy.signal.get_window`
-  directly in `_spectral.py` (not through a shared `dsp/_common.py` helper),
-  per this chunk's own design-constraint text ("map ... directly here").
-- Mel filterbank rows are normalized to sum to ~1 by construction (each row
-  divided by its own weight sum) rather than the usual peak-height-1
-  triangle — satisfies the TDD step's "rows sum ≈ 1" requirement directly;
-  documented as a deliberate choice, not a Slaney-style bandwidth
-  normalization.
-- No deviation from the chunk 18 mixin-typing pattern was needed: this
-  chunk's own code was written fresh following `_calc.py`/`_correlation.py`/
-  `_envelope.py` (self-typed `self: WaveformProtocol`, no nominal Protocol
-  inheritance).
diff --git a/.claude/archive/math-tools-port/22-dsp-filtering.md b/.claude/archive/math-tools-port/22-dsp-filtering.md
deleted file mode 100644
index c757293..0000000
--- a/.claude/archive/math-tools-port/22-dsp-filtering.md
+++ /dev/null
@@ -1,127 +0,0 @@
----
-chunk: 22-dsp-filtering
-track: D
-status: complete
-depends_on: [14]
-spec: ../specs/waveformDsp.md §Family contracts (FilteringMixin), §Numerical conventions, §Compliance 1–2
-last_updated: 2026-07-17
-semver: 0.0.2
-author: Nicholas Bergantz
----
-
-# 22 — `FilteringMixin`
-
-**Deliverable:** `dsp/_filtering.py` + tests. Swift reference:
-`SWIFT_MATH/Waveform1D/Extensions/Waveform1D+Filtering.swift`.
-
-## Files
-
-Create `src/math_tools/waveforms/dsp/_filtering.py`,
-`tests/waveforms/dsp/test_filtering.py`. Test-subclass pattern per chunk 18.
-
-## Design constraints
-
-- Methods per spec table: `low_pass_filter(cutoff_hz, order=4)`,
-  `high_pass_filter(cutoff_hz, order=4)`, `band_pass_filter(low_hz,
-  high_hz, order=4)`, generic `filtered(filter_type: WaveformFilterType,
-  ...)` dispatching to the above (+ BAND_STOP), `moving_average_filter(
-  window_size)`, `exponential_filter(alpha)`,
-  `savitzky_golay_filter(window_length, polyorder, deriv=0)`,
-  `whittaker_henderson_filter(lam, order=2)` (sparse difference-matrix
-  solve via `scipy.sparse` + `spsolve`), `frequency_response(...) ->
-  WaveformSpectrum`.
-- Butterworth designs zero-phase via `filtfilt` (spec: zero-phase unless a
-  `causal=` flag). Cutoffs validated against Nyquist (`ValueError`).
-
-## Whittaker–Henderson recipe (the one clever bit)
-
-```python
-n = len(v); D = sparse.eye(n, format="csc")
-for _ in range(order): D = D[1:] - D[:-1]          # order-th difference matrix
-z = spsolve((sparse.eye(n) + lam * D.T @ D).tocsc(), v)
-```
-
-## TDD steps
-
-1. Failing tests (spec compliance 1): 5 Hz + 200 Hz mix (fs = 2 kHz) →
-   `low_pass_filter(50)` attenuates the 200 Hz component ≥ 40 dB while the
-   5 Hz amplitude survives (rtol 5e-2), measured via chunk-local rfft;
-   high-pass mirror; band-pass keeps only the in-band tone; moving average
-   of a constant is identity; savgol on a noiseless cubic reproduces it
-   (atol 1e-8); Whittaker–Henderson with `lam→0` ≈ identity and large `lam`
-   ≈ linear trend.
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] The ≥ 40 dB attenuation test and savgol-cubic test pass
-- [x] Nyquist-violation cutoff raises `ValueError`
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Resampling (25); windowing utilities (28).
-
-## Resolution notes
-
-- Followed the chunk-18 self-typed-mixin pattern throughout (`FilteringMixin`
-  is a plain class, no `WaveformProtocol` base); this chunk's own code
-  samples didn't show the broken nominal-inheritance pattern, so no
-  correction was needed there.
-- The chunk doc's design-constraints bullet gives `filtered(filter_type:
-  WaveformFilterType, ...)` with an elided `...`; resolved the omitted
-  signature as `filtered(filter_type, cutoff_hz=None, low_hz=None,
-  high_hz=None, order=4, causal=False)` — the union of the args the four
-  dispatched Butterworth families need, with per-branch `ValueError` when
-  the wrong ones are missing. `low_pass_filter`/`high_pass_filter`/
-  `band_pass_filter`/`filtered` all funnel through one private
-  `_butter_coefficients` design helper so validation and design parameters
-  can't drift between the dedicated methods and the dispatcher.
-  `frequency_response` reuses the same helper against `scipy.signal.freqz`.
-- `causal: bool = False` was added (not explicitly named in the chunk file,
-  but required by the spec's own line: "Butterworth designs zero-phase via
-  `filtfilt` unless a `causal=` flag" — §Numerical conventions). Zero-phase
-  `filtfilt` is the default; `causal=True` switches to a single
-  `scipy.signal.lfilter` pass.
-- Deviated from the Swift reference's silent-no-op-on-invalid-input
-  behavior (e.g. `guard windowSize > 0 ... else { return self }`): every
-  invalid parameter (bad `window_size`, `alpha` outside `(0, 1]`, bad
-  `savgol` window/polyorder/deriv combination, `order < 1`, Nyquist
-  violations, missing dispatch args) raises `ValueError` naming the
-  requirement instead, per waveformDsp.md §Numerical conventions (already
-  the convention every prior DSP mixin chunk follows) and the spec's
-  "parity is judged per capability, not per Swift overload" policy.
-- `moving_average_filter` implements a centered average whose window
-  shrinks (not zero-pads) at the edges — closest Python-idiomatic
-  equivalent of the Swift reference's clamped-index behavior — via a
-  vectorized cumulative-sum formulation (no explicit Python loop).
-- `exponential_filter` is a genuinely sequential recursion
-  (`y[i]` depends on `y[i-1]`); implemented as a plain Python loop since a
-  vectorized closed form would need `alpha*(1-alpha)**arange(n)` weights
-  convolved against `values`, which is a real de-vectorization win only at
-  large `n` and adds nontrivial complexity — correctness/clarity outrank
-  that here (tenets: Correctness/Clarity > Performance; no evidence this is
-  ever a bottleneck for typical waveform sizes).
-- `savitzky_golay_filter` passes `delta=dt_seconds` to
-  `scipy.signal.savgol_filter` only when `deriv > 0` (scipy scales
-  derivative estimates by `1/delta**deriv`; passing a real `delta` for
-  `deriv=0` is harmless but pointless) so the returned derivative carries
-  proper physical units — not explicit in the chunk file, inferred from
-  waveformDsp.md's general "scale by dt seconds" convention used by
-  `CalcMixin`.
-- `whittaker_henderson_filter` implements the chunk's own sparse
-  difference-matrix recipe verbatim (`D = D[1:] - D[:-1]` applied `order`
-  times, then `spsolve(I + lam * D^T @ D, v)`).
-- No spec changes were needed — implementation matched
-  `waveformDsp.md`'s family-contract row and numerical conventions as
-  written; only the elided `filtered(...)` signature and the `causal=`
-  parameter required interpretation, and both are already licensed by the
-  spec text itself (§Numerical conventions) rather than contradicting it.
-- Test coverage exceeds the two acceptance-box-named cases (40 dB
-  attenuation, savgol-cubic) to satisfy the repo-wide §Compliance 1 ("every
-  mixin method tested against an analytically known signal"): all 9 public
-  methods have dedicated tests, including the TDD step's high-pass mirror,
-  band-pass in-band-survival, moving-average identity, and
-  Whittaker-Henderson `lam→0`/`lam→∞` cases.
-- `dsp/__init__.py` and `waveform1d.py` were not touched (mixin composition
-  is chunk 30's job per waveformDsp.md's "Composition phasing").
diff --git a/.claude/archive/math-tools-port/23-dsp-peaks.md b/.claude/archive/math-tools-port/23-dsp-peaks.md
deleted file mode 100644
index 18999b4..0000000
--- a/.claude/archive/math-tools-port/23-dsp-peaks.md
+++ /dev/null
@@ -1,91 +0,0 @@
----
-chunk: 23-dsp-peaks
-track: D
-status: complete
-depends_on: [14]
-spec: ../specs/waveformDsp.md §Family contracts (PeakMixin), §Compliance 1–2
-last_updated: 2026-07-17
-semver: 0.0.2
-author: Nicholas Bergantz
----
-
-# 23 — `PeakMixin`
-
-**Deliverable:** `dsp/_peaks.py` + tests. Swift references:
-`SWIFT_MATH/Waveform1D/Extensions/Waveform1D+Peak.swift`;
-`SWIFT_TESTS/Waveform1DPeakTests.swift` (27 tests — port representative
-cases).
-
-## Files
-
-Create `src/math_tools/waveforms/dsp/_peaks.py`,
-`tests/waveforms/dsp/test_peaks.py`. Test-subclass pattern per chunk 18.
-
-## Design constraints
-
-- Methods per spec table: `detect_peaks(min_height=None, min_distance=None,
-  min_prominence=None) -> list[WaveformPeak]`, `detect_valleys(...)`
-  (negate + detect_peaks), `find_most_prominent_peaks(count,
-  min_distance=None) -> list[WaveformPeakWithProminence]`. Backing
-  `scipy.signal.find_peaks` / `peak_prominences`.
-- `WaveformPeak.time_seconds` = `index * dt` seconds; empty list on no-hit
-  (never raise for no peaks).
-
-## TDD steps
-
-1. Failing tests (spec compliance 1): `sine(n, f, fs)` yields exactly
-   `⌊n·f/fs⌋` peaks (choose n, f, fs so the count is unambiguous);
-   valleys mirror peaks under negation; prominence ordering on a two-tone
-   signal (big + small bumps) returns the big ones first; flat signal → [].
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Sine peak-count and prominence-order tests pass
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Trigger detection (27); zero crossings (29).
-
-## Resolution notes
-
-- Implemented `PeakMixin` (`detect_peaks`, `detect_valleys`,
-  `find_most_prominent_peaks`) exactly per the mixin table in
-  `waveformDsp.md` §Family contracts, backed by `scipy.signal.find_peaks` /
-  `peak_prominences`. No spec changes were needed — this chunk's design
-  constraints already matched the spec verbatim (no divergence to
-  reconcile).
-- Followed the chunk-18 typing fix (self-typed `WaveformProtocol`, no
-  nominal `Protocol` inheritance) throughout; `_peaks.py` imports only
-  `scipy`/`numpy` plus `dsp/_protocol.py`, `dsp/_common.py`, and
-  `waveforms/support.py` (for `WaveformPeak`/`WaveformPeakWithProminence`),
-  so the pre-existing generic sibling-import layering test
-  (`tests/test_package_layering.py::test_dsp_mixins_do_not_import_sibling_mixins`)
-  covers it automatically — no new layering-test code required.
-- `detect_valleys` is implemented as an exact negate/detect_peaks/negate
-  round-trip through a shared module-level helper
-  (`_detect_peaks_in_array`), matching the "valleys mirror peaks under
-  negation" TDD requirement literally: `min_height`/`min_prominence` are
-  forwarded unchanged to the negated-signal search (so `min_height` bounds
-  the original `value` from *above*, not below — documented in the
-  docstring since this is a semantic choice the chunk left implicit).
-- `find_most_prominent_peaks` treated as part of the same detector family
-  as `detect_peaks`/`detect_valleys` for the empty-result convention
-  (returns `[]` for `count <= 0`, an empty waveform, or no interior peaks,
-  rather than raising `ValueError`) — the spec's §Numerical conventions
-  ValueError-vs-empty-list split is keyed off the `detect_*`/
-  `zero_crossings` name prefix, but `find_most_prominent_peaks` is built
-  directly on `detect_peaks`'s results and documented as the same family in
-  the mixin table, so the empty-list contract was extended to it for
-  consistency; flagging this as a judgment call in case a future chunk
-  wants it spec'd explicitly.
-- Swift `Waveform1D+Peak.swift`'s hand-rolled `threshold`/`prominence`/
-  `minDistance`/`edgePeaks` local-maxima scan was **not** ported
-  literally — the chunk's own "Design constraints" section already pins
-  the Python surface to `min_height`/`min_distance`/`min_prominence`
-  scipy-style kwargs, so `Waveform1DPeakTests.swift`'s 27 cases were used
-  only for behavioral inspiration (mirrored valleys, prominence ordering,
-  flat/empty edge cases), not transliterated.
-- Gate: `make uv-fullCheck` green — ruff clean, mypy strict clean (64
-  source files), 971 tests passed (18 new in `test_peaks.py`).
diff --git a/.claude/archive/math-tools-port/24-dsp-phase.md b/.claude/archive/math-tools-port/24-dsp-phase.md
deleted file mode 100644
index 65ecc60..0000000
--- a/.claude/archive/math-tools-port/24-dsp-phase.md
+++ /dev/null
@@ -1,94 +0,0 @@
----
-chunk: 24-dsp-phase
-track: D
-status: complete
-depends_on: [14]
-spec: ../specs/waveformDsp.md §Family contracts (PhaseMixin), §Compliance 1–2
-last_updated: 2026-07-17
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 24 — `PhaseMixin`
-
-**Deliverable:** `dsp/_phase.py` + tests. Swift reference:
-`SWIFT_MATH/Waveform1D/Extensions/Waveform1D+PhaseAnalysis.swift`.
-
-## Files
-
-Create `src/math_tools/waveforms/dsp/_phase.py`,
-`tests/waveforms/dsp/test_phase.py`. Test-subclass pattern per chunk 18.
-
-## Design constraints
-
-- Methods per spec table: `instantaneous_phase(unwrapped=True)` (Hilbert
-  angle), `unwrap_phase(threshold=π)` (`np.unwrap` on already-phase data),
-  `instantaneous_frequency() -> WaveformInstantaneousFrequency` (phase
-  gradient / 2π), `phase_difference(other)`, `phase_coherence(other,
-  window=...)`, `phase_synchronization_index(other) -> float` (PLV, in
-  [0, 1]), `group_delay(...)`. dt mismatch on binary methods →
-  `WaveformCompatibilityError`.
-
-## TDD steps
-
-1. Failing tests (spec compliance 1): unwrapped phase of a chirp is
-   monotone increasing; instantaneous frequency of a pure f-Hz sine ≈ f on
-   the interior (rtol 1e-2); PLV of a signal with itself == 1.0 and with an
-   independent seeded-noise signal < 0.3; `phase_difference` of `sin` vs
-   `cos` ≈ π/2 interior.
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Chirp-monotone and PLV tests pass
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Envelope (20); spectral (21).
-
-## Resolution notes
-
-- Backed `instantaneous_phase`/`phase_difference`/`phase_coherence`/
-  `phase_synchronization_index` with `scipy.signal.hilbert`'s analytic-signal
-  angle rather than the Swift reference's hand-rolled "quadrature filter"
-  finite-difference approximation — allowed explicitly by the spec's opening
-  note ("parity is judged per capability... scipy semantics win").
-- `phase_difference` wraps its result into `(-pi, pi]` via
-  `np.angle(np.exp(1j * diff))` rather than a raw subtraction, avoiding a
-  spurious near-±π discontinuity; verified against the sin-vs-cos ≈π/2
-  compliance test.
-- Binary methods (`phase_difference`, `phase_coherence`,
-  `phase_synchronization_index`) raise `WaveformCompatibilityError` on
-  **both** dt mismatch (per the chunk's explicit design constraint) and
-  sample-count mismatch — the latter isn't literally named in the chunk
-  text, but `errors.py`'s `WaveformCompatibilityError` docstring scopes it to
-  "dt/shape mismatch", and these are element-wise phase-difference ops that
-  are undefined across differing lengths.
-- `phase_coherence(other, window=...)`: the chunk's design-constraint bullet
-  gives only the two named parameters, so the implementation is a minimal
-  non-overlapping-window PLV (no `overlap` parameter, unlike the Swift
-  reference) — window size defaults to `min(256, max(1, n // 4))`, mirroring
-  the Swift default. Its result reuses `self`'s `dt`/`t0` as inherited
-  metadata (not physically accurate for the new, coarser sample spacing);
-  this follows the precedent already set by `CorrelationMixin.auto_correlation`
-  (chunk 19), which does the same for its differently-spaced lag output —
-  `WaveformProtocol._with_values` has no other way to construct a result.
-- `group_delay(...)`: the chunk's method-list bullet leaves the signature as
-  `group_delay(...)`, and the Swift reference itself never touches
-  `self.values` (it operates purely on caller-supplied `frequencies`/`phases`
-  arrays). Ported as a `@staticmethod` taking exactly those two arrays and
-  returning group delay in seconds (`-d(unwrap(phases))/d(frequencies) /
-  (2*pi)`, via `np.gradient` — replacing the Swift version's manual
-  central-difference-plus-duplicated-boundary loop with numpy's own
-  boundary handling, a capability-preserving scipy/numpy-idiomatic
-  simplification). No cross-mixin dependency on `SpectralMixin`/
-  `FilteringMixin` was introduced (both are out of scope for this chunk).
-- No spec changes were needed: `waveformDsp.md`'s `PhaseMixin` row and
-  `WaveformInstantaneousFrequency` descriptor (already in `support.py` since
-  chunk 14) matched the implementation as written.
-- Gate: `make uv-fullCheck` green — ruff clean, mypy strict clean (66 source
-  files), 999 tests passed (28 new in `tests/waveforms/dsp/test_phase.py`).
-  The pre-existing generic sibling-import layering test
-  (`tests/test_package_layering.py::test_dsp_mixins_do_not_import_sibling_mixins`)
-  covers `_phase.py` automatically — no test-file changes were needed there.
diff --git a/.claude/archive/math-tools-port/25-dsp-resampling.md b/.claude/archive/math-tools-port/25-dsp-resampling.md
deleted file mode 100644
index 3007139..0000000
--- a/.claude/archive/math-tools-port/25-dsp-resampling.md
+++ /dev/null
@@ -1,107 +0,0 @@
----
-chunk: 25-dsp-resampling
-track: D
-status: complete
-depends_on: [14]
-spec: ../specs/waveformDsp.md §Family contracts (ResamplingMixin), §Compliance 1–2
-last_updated: 2026-07-17
-semver: 0.0.2
-author: Nicholas Bergantz
----
-
-# 25 — `ResamplingMixin`
-
-**Deliverable:** `dsp/_resampling.py` + tests. Swift reference:
-`SWIFT_MATH/Waveform1D/Extensions/Waveform1D+Resampling.swift`.
-
-## Files
-
-Create `src/math_tools/waveforms/dsp/_resampling.py`,
-`tests/waveforms/dsp/test_resampling.py`. Test-subclass pattern per
-chunk 18.
-
-## Design constraints
-
-- Methods per spec table: `decimated(factor)` (`scipy.signal.decimate`),
-  `interpolated(factor, method: WaveformInterpolationMethod = LINEAR)`,
-  `resampled(target_frequency_hz)` (`scipy.signal.resample` /
-  `resample_poly`), `resampled_to_match(other)`,
-  `polyphase_resampled(up, down)` (`resample_poly`).
-- **dt bookkeeping is the tricky bit:** integer factor paths compute the new
-  `dt` exactly in PrecisionTime (`dt * factor` / `dt / factor` rounding to
-  nearest attosecond); `resampled(hz)` derives dt from the achieved rate.
-  New `t0` is unchanged.
-- `factor < 1` or non-int factor → `ValueError`.
-
-## TDD steps
-
-1. Failing tests (spec compliance 1): `interpolated(2).decimated(2)`
-   round-trips a smooth signal interior (rtol 1e-3); `decimated(4).dt ==
-   dt * 4` exactly (PrecisionTime equality); `resampled_to_match` yields
-   matching `dt` and length within ±1; polyphase 3:2 length check.
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Round-trip and exact-dt tests pass
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Time alignment (26); `value_at_time` (already in core).
-
-## Resolution notes
-
-- **Forced contract change: `WaveformProtocol` gained a second factory,
-  `_with_axis(values, dt) -> WaveformProtocol`.** Every mixin through chunk
-  24 builds its results via `_with_values(values)`, which carries `self`'s
-  `dt`/`t0` forward unchanged — sufficient because none of those families
-  ever change the sample spacing. `ResamplingMixin` is the first that does
-  (`decimated`/`interpolated`/`resampled`/`polyphase_resampled` all compute
-  a new `dt`), and the acceptance criterion "`decimated(4).dt == dt * 4`
-  exactly" is unsatisfiable through `_with_values` alone. Added `_with_axis`
-  to `dsp/_protocol.py`'s `WaveformProtocol` and implemented it on
-  `Waveform1D` (`waveforms/waveform1d.py`, alongside `_with_values`); `t0`
-  is not a parameter (every method here leaves `t0` unchanged, per the
-  design constraints). Per the 00-overview.md convention ("if implementation
-  forces a contract change, update the spec in the same chunk and bump its
-  semver"), `waveformDsp.md` §Organization documents the addition and its
-  semver was bumped 0.0.3 → 0.0.4. This is the only file touched outside
-  this chunk's own `Files` list.
-- **`decimated` uses `scipy.signal.decimate(..., ftype="fir")`, not the
-  default `ftype="iir"`.** The default Chebyshev-I IIR anti-alias filter's
-  ~0.05 dB passband ripple, doubled by zero-phase `sosfiltfilt`, produced
-  ~1.1% amplitude error even deep in the passband on a 5 Hz sine sampled at
-  1 kHz — enough to blow the `interpolated(2).decimated(2)` round-trip's
-  `rtol=1e-3` acceptance bound. The FIR variant (linear-phase, near-flat
-  passband) round-trips to ~1e-6 on the same signal and, as a side benefit,
-  tolerates much shorter inputs (its padding requirement scales with taps
-  rather than a fixed ~27-sample IIR minimum). `decimated(factor)`'s public
-  signature is unchanged — this is an internal default choice, not an
-  exposed parameter — so it stays within the spec's `decimated(factor)`
-  surface.
-- **`interpolated`'s four kernels:** `LINEAR`/`NEAREST` use `np.interp`-style
-  sample-index interpolation directly; `CUBIC` uses
-  `scipy.interpolate.CubicSpline`; `FOURIER` uses `scipy.signal.resample`.
-  All four produce `(n - 1) * factor + 1` samples (endpoints preserved),
-  matching the Swift reference's insert-between-samples scheme rather than
-  `scipy.signal.resample`'s periodic/`n * factor` convention.
-  `resampled`/`resampled_to_match`/`polyphase_resampled` are unaffected
-  (they always use FFT/polyphase resampling per the spec's Backing column).
-- **`resampled(target_frequency_hz)`** computes the achieved sample count as
-  `round(sample_count * target_frequency_hz / sampling_frequency_hz)` and
-  derives `dt` from that achieved count (`dt * sample_count /
-  achieved_count`) rather than `1 / target_frequency_hz` — matches the
-  design constraint ("`resampled(hz)` derives dt from the achieved rate")
-  and the `scipy.signal.resample` input/output-length/sample-rate
-  relationship. `resampled_to_match(other)` is a thin wrapper calling the
-  same helper with `other.sampling_frequency_hz`.
-- All TDD-step scenarios pass as written: `interpolated(2).decimated(2)`
-  round-trips a 2000-sample, 5 Hz sine's interior to `rtol=1e-3` (both
-  `LINEAR` and `CUBIC` kernels tested); `decimated(4).dt == dt * 4` exactly
-  (`PrecisionTimeInterval` equality); `resampled_to_match` yields matching
-  `dt` (6 decimal places) and length within ±1 of `other`'s; polyphase 3:2
-  length matches `ceil(n * 3 / 2)` against `scipy.signal.resample_poly`'s
-  actual output.
-- 30 new tests in `tests/waveforms/dsp/test_resampling.py`; full gate
-  (`make uv-fullCheck`) green at 1029 passed, ruff clean, mypy strict clean.
diff --git a/.claude/archive/math-tools-port/26-dsp-time-alignment.md b/.claude/archive/math-tools-port/26-dsp-time-alignment.md
deleted file mode 100644
index cea9b9a..0000000
--- a/.claude/archive/math-tools-port/26-dsp-time-alignment.md
+++ /dev/null
@@ -1,147 +0,0 @@
----
-chunk: 26-dsp-time-alignment
-track: D
-status: complete
-depends_on: [14, 19]
-spec: ../specs/waveformDsp.md §Family contracts (TimeAlignmentMixin), §Compliance 1–2
-last_updated: 2026-07-17
-semver: 0.0.2
-author: Nicholas Bergantz
----
-
-# 26 — `TimeAlignmentMixin`
-
-**Deliverable:** `dsp/_time_alignment.py` + tests. Swift reference:
-`SWIFT_MATH/Waveform1D/Extensions/Waveform1D+TimeAlignment.swift`.
-
-## Files
-
-Create `src/math_tools/waveforms/dsp/_time_alignment.py`,
-`tests/waveforms/dsp/test_time_alignment.py`. Test-subclass note: this
-mixin's CORRELATION method calls the correlation surface, so the test
-subclass composes both: `class _W(TimeAlignmentMixin, CorrelationMixin,
-Waveform1D)`.
-
-## Design constraints
-
-- Methods per spec table: `aligned(to, method: WaveformAlignmentMethod =
-  CORRELATION)` (shift by detected lag; START_TIME aligns `t0`s),
-  `time_lag(to, max_lag=None) -> WaveformTimeLag | None` (None when no
-  correlation peak qualifies), classmethod
-  `synchronize(waveforms) -> list[Waveform1D]` (common overlapping span),
-  `time_windows(window_duration, overlap=0.0) -> list[Waveform1D]`,
-  `time_segments(boundaries) -> list[Waveform1D]`.
-- Exception to the no-sibling-imports rule (documented in the spec's mixin
-  rules as "via CorrelationMixin"): this mixin may TYPE against the
-  protocol + call `self.cross_correlation`/`find_max_correlation` — declare
-  those on a small local `Protocol` extension rather than importing
-  `_correlation`, keeping module-level imports clean.
-
-## TDD steps
-
-1. Failing tests: `aligned` recovers a k-sample shift (result lag 0
-   afterward); `synchronize` of two offset waveforms returns equal-length
-   overlaps with matching `t0`; `time_windows(1.0, overlap=0.5)` count
-   formula pinned; segment boundaries respected.
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Shift-recovery and synchronize tests pass
-- [x] No `import ... _correlation` at module level (grep)
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Resampling to a common rate (25's `resampled_to_match`).
-
-## Resolution notes
-
-- **Forced contract change: `WaveformProtocol` gained a third factory,
-  `_with_t0(values, t0) -> WaveformProtocol`.** Every method in this chunk
-  (`aligned`, `synchronize`, `time_windows`, `time_segments`) produces a
-  result with the same `dt` as its source but a genuinely different `t0` —
-  a shape neither existing factory covers (`_with_values`: same `dt`, same
-  `t0`; `_with_axis`: new `dt`, same `t0`, added by chunk 25). Added
-  `_with_t0` to `dsp/_protocol.py`'s `WaveformProtocol` and implemented it
-  on `Waveform1D` (`waveforms/waveform1d.py`), giving the three factories a
-  complete same-dt/same-t0 triangle. Per the 00-overview.md convention,
-  `waveformDsp.md` §Organization documents the addition and its semver was
-  bumped 0.0.4 → 0.0.5. `_protocol.py` and `waveform1d.py` are the only
-  files touched outside this chunk's own `Files` list.
-- **`time_lag` is deliberately `t0`-aware, unlike `CorrelationMixin.
-  find_max_correlation`.** `find_max_correlation` is a pure value-domain
-  measure — it correlates `values` arrays and never looks at either
-  waveform's `t0`. That's correct for "how similar are these sample
-  arrays," but wrong for a method named `time_lag` living in a mixin about
-  time-axis reasoning: two waveforms whose `t0`s already differ can have
-  identical values (raw lag 0) yet clearly occur at different real times.
-  `TimeAlignmentMixin.time_lag` (via the module-level `_correlating_time_lag`
-  helper) adds the existing `t0` offset between the two waveforms (rounded
-  to the nearest sample) to the raw value-domain lag `find_max_correlation`
-  returns, producing a genuine real-world sample/second offset. This is
-  also what makes `aligned`'s `CORRELATION` method a true round trip:
-  shifting `t0` by `-lag_samples * dt` always drives a second `time_lag`
-  call back to lag 0 (the pinned "result lag 0 afterward" acceptance
-  criterion) — a purely value-domain lag could not guarantee that once the
-  two waveforms' `t0`s already differ, since shifting `t0` alone never
-  touches the values `find_max_correlation` looks at. Verified directly:
-  `TestAlignedCorrelationRecoversKnownShift` pins the round trip for k in
-  {0, 3, 17} sample shifts, and `TestTimeLagAccountsForExistingT0Offset`
-  pins the `t0`-offset-only case (identical values, different `t0`) against
-  a raw `find_max_correlation` call that would report lag 0 for the same
-  inputs.
-- **Correlation-mixin cross-reference without importing `_correlation`.**
-  Per the design constraint, `aligned`'s `CORRELATION` method and `time_lag`
-  need `CorrelationMixin.find_max_correlation` but must not import
-  `dsp/_correlation.py` (waveformDsp.md §Organization / §Compliance 2, "no
-  sibling mixin imports"). Declared a small local `Protocol` extension,
-  `_CorrelatingWaveform(WaveformProtocol, Protocol)`, naming only the
-  `find_max_correlation` signature needed; any host composing both mixins
-  (this chunk's own `_W(TimeAlignmentMixin, CorrelationMixin, Waveform1D)`
-  test subclass, and `Waveform1D` from the compose chunk onward) satisfies
-  it structurally. `tests/test_package_layering.py::
-  test_dsp_mixins_do_not_import_sibling_mixins` (a static AST scan) and a
-  manual grep both confirm no `_correlation` import exists in the module.
-  `find_max_correlation`/`time_lag` are called through a module-level
-  helper (`_correlating_time_lag`), not a same-class `self.time_lag(...)`
-  call from `aligned` — matching every other DSP mixin's internal-sharing
-  convention of module-level helpers over same-class method calls (e.g.
-  `dsp/_resampling.py`'s `_resample_to_frequency`).
-- **Chunk 19's import-cycle risk (point 4 of this chunk's brief): still
-  latent, not triggered.** This mixin imports `WaveformAlignmentMethod`/
-  `WaveformTimeLag` from `waveforms/support.py`, which imports
-  `waveforms/waveform1d.py` — the same shape chunk 19 flagged for
-  `_correlation.py`. `waveform1d.py` still does not import back into
-  `dsp/` (mixins compose in a later chunk, 30), so no cycle exists today;
-  documented again in the module docstring per the brief's instruction to
-  report rather than silently work around it.
-- **`time_segments(boundaries)` and `time_windows(window_duration,
-  overlap)` take float-seconds arguments** (relative to `t0`), not sample
-  indices or `PrecisionTimestamp`s — the spec table's `time_windows(...)`/
-  `time_segments(...)` entries were intentionally abbreviated (matching
-  other family-contract rows with optional-heavy signatures); the concrete
-  signatures are pinned by this chunk's own tests.
-  `time_windows`/`time_segments` are not detectors (waveformDsp.md
-  §Numerical conventions), so both raise `ValueError` (naming the
-  requirement) rather than returning `[]` when the input is too short —
-  `time_windows` when even one window doesn't fit, `time_segments` when the
-  waveform is empty or a boundary falls outside the open span
-  `(0, duration_seconds)`.
-- **`synchronize` does not resample mismatched-rate inputs**, unlike the
-  Swift reference's `resampleToCommonRate` option — matching this chunk's
-  own Out of scope note ("Resampling to a common rate" is chunk 25's
-  `resampled_to_match`, not this one's). Every input to `synchronize` must
-  already share the same `dt`; a mismatch raises `WaveformCompatibilityError`.
-- Bug caught by the TDD run itself (not by inspection): `time_segments`'s
-  first implementation zipped `split_points` against `split_points[1:]`
-  with `strict=True`, added defensively for ruff's B905 ("zip without an
-  explicit strict= parameter"). Since that pairwise idiom's two sequences
-  are intentionally offset by one element, `strict=True` made every
-  non-trivial call raise `ValueError: zip() argument 2 is shorter than
-  argument 1`. Fixed to `strict=False`, which still satisfies B905 (an
-  explicit value was given) while preserving the intended pairwise
-  semantics.
-- 26 new tests in `tests/waveforms/dsp/test_time_alignment.py`; full gate
-  (`make uv-fullCheck`) green: ruff clean, mypy strict clean (70 source
-  files), 1055 passed.
diff --git a/.claude/archive/math-tools-port/27-dsp-triggers.md b/.claude/archive/math-tools-port/27-dsp-triggers.md
deleted file mode 100644
index 983ffb2..0000000
--- a/.claude/archive/math-tools-port/27-dsp-triggers.md
+++ /dev/null
@@ -1,117 +0,0 @@
----
-chunk: 27-dsp-triggers
-track: D
-status: complete
-depends_on: [14]
-spec: ../specs/waveformDsp.md §Family contracts (TriggerMixin), §Compliance 1–2
-last_updated: 2026-07-17
-semver: 0.0.2
-author: Nicholas Bergantz
----
-
-# 27 — `TriggerMixin`
-
-**Deliverable:** `dsp/_triggers.py` + tests. Swift reference:
-`SWIFT_MATH/Waveform1D/Extensions/Waveform1D+TriggerDetection.swift`.
-
-## Files
-
-Create `src/math_tools/waveforms/dsp/_triggers.py`,
-`tests/waveforms/dsp/test_triggers.py`. Test-subclass pattern per chunk 18.
-
-## Design constraints
-
-- Methods per spec table: `detect_edge_triggers(level, edge:
-  WaveformEdgeType)` (sign-change of `values - level`, RISING/FALLING/BOTH),
-  `detect_level_triggers(level, ...)`, `detect_window_triggers(low, high,
-  kind: WaveformWindowTriggerType)` (ENTER/EXIT of the band),
-  `detect_pattern_triggers(pattern, tolerance)` (sliding-window match),
-  generic `detect_triggers(trigger: WaveformTrigger)` dispatching on
-  `trigger.kind`, `with_event_markers(events) -> WaveformWithEvents`.
-- All detectors return `list[WaveformTriggerEvent]`, empty on no-hit;
-  events carry index, `time_seconds`, value, kind.
-
-## TDD steps
-
-1. Failing tests: square wave — rising-edge count == cycle count, falling
-   likewise, BOTH is their sum; window ENTER/EXIT pair up on a sine
-   crossing a band; pattern trigger finds an embedded motif at the planted
-   indices; no-hit → [].
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Square-wave edge counts exact; pattern indices exact
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Zero crossings (29 — level 0 lives there); peak detection (23).
-
-## Resolution notes
-
-- **Design constraints followed as written** (the chunk file already used the
-  post-chunk-18 self-typed-``WaveformProtocol`` idiom, not nominal Protocol
-  inheritance, so no rewrite was needed there).
-- **`detect_level_triggers`** shares `detect_edge_triggers`'s sign-change
-  machinery (same private `_sign_change_events` helper), distinguished only
-  by the `WaveformTriggerType` tag stamped on the resulting events and its
-  default direction (`RISING` vs. `EDGE`'s `BOTH`) — the spec's `EDGE`/
-  `LEVEL` split reads as a provenance/intent tag, not two different
-  detection algorithms (the Swift reference's own `evaluateLevelTrigger` is
-  likewise a plain threshold comparison).
-- **Forced contract change, `waveforms/support.py` (semver 0.0.5 → 0.0.6),
-  touched even though it is outside this chunk's literal "Files" list** —
-  same escape hatch chunks 25/26 used for `dsp/_protocol.py`'s factories:
-  1. `WaveformTrigger` gained two optional fields, `edge: WaveformEdgeType
-     | None` and `window_kind: WaveformWindowTriggerType | None`, both
-     defaulting to `None`. Without them, the generic `detect_triggers`
-     dispatcher had no way to read the direction/enter-exit selector a
-     `WaveformTrigger` should carry for `EDGE`/`LEVEL`/`WINDOW` kinds — the
-     direct `detect_edge_triggers`/`detect_level_triggers`/
-     `detect_window_triggers` methods take it as an explicit argument, but
-     nothing on the dataclass could express it before this change.
-     Backward-compatible: every existing `WaveformTrigger(...)` call site
-     (including `tests/waveforms/test_support.py`) omits both new fields and
-     is unaffected; dispatch falls back to `BOTH`/`RISING`/`ENTER`
-     respectively when unset.
-  2. `WaveformWithEvents.waveform` is now typed `WaveformProtocol`
-     (`dsp/_protocol.py`), not the concrete `Waveform1D` it held through
-     chunk 26. `with_event_markers` is the first mixin method that has to
-     embed `self` itself into a returned descriptor; every earlier
-     descriptor only ever held *derived* values. Since mixins type `self` as
-     `WaveformProtocol` and must never import `Waveform1D` — not even under
-     `TYPE_CHECKING`, per `dsp/_protocol.py`'s own docstring — a field typed
-     concrete `Waveform1D` was unsatisfiable from `_triggers.py` without
-     breaking that rule. Retyping the field to the already-`Waveform1D`-
-     satisfying structural protocol resolves this and, as a side effect,
-     removes `support.py`'s only import of `waveforms/waveform1d.py` —
-     closing off what would otherwise become a real circular import once
-     the chunk-30 compose step makes `waveform1d.py` import every mixin
-     (mixins already import `support.py`; `support.py` importing
-     `waveform1d.py` back would have completed the cycle). Not exercised by
-     this chunk's own tests, but `tests/waveforms/test_support.py`'s
-     existing `WaveformWithEvents` construction/mutation/slots assertions
-     continue to pass unchanged (a `Waveform1D` instance still satisfies the
-     field at runtime).
-  3. `.claude/specs/waveformDsp.md` §Support descriptor types updated to
-     describe both changes; spec semver bumped 0.0.5 → 0.0.6.
-- **`detect_triggers` never calls `self.detect_edge_triggers(...)` etc.**
-  Each `detect_*` method's shared sign-change/window/pattern logic lives in
-  a private module-level function (`_sign_change_events`,
-  `_window_trigger_events`, `_pattern_trigger_events`) that both the direct
-  method and `detect_triggers`'s dispatch call directly — a same-class
-  `self.<sibling method>(...)` call would not type-check under mypy strict
-  (`self: WaveformProtocol` does not declare this mixin's own methods),
-  mirroring `dsp/_time_alignment.py`'s `_correlating_time_lag` /
-  `dsp/_resampling.py`'s `_resample_to_frequency` precedent. Caught by
-  running `make uv-typecheck` during implementation, not by inspection.
-- **Pattern matching uses elementwise tolerance** (`max(abs(segment -
-  pattern)) <= tolerance`), not the Swift reference's normalized-correlation
-  `threshold` — deterministic and exact for the "finds the planted motif at
-  the planted indices" acceptance criterion, and the spec's "scipy/better-
-  tested semantics win" allowance applies equally to a better-specified
-  numpy equivalent.
-- `make uv-fullCheck` verified clean: ruff (`All checks passed!`), mypy
-  strict (`Success: no issues found in 72 source files`), pytest (1087
-  passed, including 32 new tests in `tests/waveforms/dsp/test_triggers.py`).
diff --git a/.claude/archive/math-tools-port/28-dsp-windowing.md b/.claude/archive/math-tools-port/28-dsp-windowing.md
deleted file mode 100644
index 718cf25..0000000
--- a/.claude/archive/math-tools-port/28-dsp-windowing.md
+++ /dev/null
@@ -1,93 +0,0 @@
----
-chunk: 28-dsp-windowing
-track: D
-status: complete
-depends_on: [14]
-spec: ../specs/waveformDsp.md §Family contracts (WindowingMixin), §Compliance 1–2
-last_updated: 2026-07-17
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 28 — `WindowingMixin`
-
-**Deliverable:** `dsp/_windowing.py` + tests. Swift reference:
-`SWIFT_MATH/Waveform1D/Extensions/Waveform1D+Windowing.swift`.
-
-## Files
-
-Create `src/math_tools/waveforms/dsp/_windowing.py`,
-`tests/waveforms/dsp/test_windowing.py`. Test-subclass pattern per chunk 18.
-
-## Design constraints
-
-- Methods per spec table: `windowed(window: WaveformWindowType)`
-  (elementwise multiply), staticmethods `generate_window(window, length)
-  -> npt.NDArray` (`scipy.signal.get_window`; KAISER takes a beta default
-  matching the Swift parameterization — read the Swift enum first),
-  `window_coherent_gain(window) -> float` (mean of the window),
-  `window_processing_gain(window) -> float`.
-
-## TDD steps
-
-1. Failing tests: RECTANGULAR `windowed` is identity; HANN endpoints ≈ 0 and
-   midpoint ≈ 1; coherent gain of HANN ≈ 0.5 (rtol 1e-2 for finite length);
-   every `WaveformWindowType` member generates without error.
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] All enum members covered; HANN gain test passes
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Spectral methods' internal window use (21 handles its own).
-
-## Resolution notes
-
-- Implemented `WindowingMixin` in `src/math_tools/waveforms/dsp/_windowing.py`
-  per chunk 18's mixin-typing fix (§Organization): plain class, `self` typed
-  `WaveformProtocol` on each instance method, `generate_window` a
-  `@staticmethod` — not `class WindowingMixin(WaveformProtocol)`. The chunk
-  file's own reference (Swift extension) predates that fix; followed the
-  merged convention instead, per this chunk's own instructions.
-- `scipy.signal.get_window` is called with `fftbins=False` (symmetric, not
-  periodic) — this is what makes the TDD step's HANN acceptance criterion
-  literally true (endpoints exactly 0.0, an odd-length midpoint sample
-  exactly 1.0); the default periodic (`fftbins=True`) form does not have
-  that property and is what `dsp/_spectral.py` uses for its own STFT-frame
-  purpose. Verified numerically before committing to this choice.
-- `WaveformWindowType.KAISER` carries no `beta` field (flat `str` enum,
-  unlike the Swift `.kaiser(beta:)` associated value), and the chunk's own
-  `generate_window(window, length) -> npt.NDArray` signature exposes none
-  either — fixed one default beta (`14.0`), independently declared (not
-  imported) but numerically matching `dsp/_spectral.py`'s own independent
-  default for the same reason (comparable sidelobe suppression to
-  Blackman). No spec change needed; `waveformDsp.md` already documents
-  `WaveformWindowType` as a flat enum and doesn't promise a `beta`
-  parameter on `generate_window`.
-- The enum->scipy-name map deliberately duplicates a few lines already
-  present in `dsp/_spectral.py` rather than sharing them, per chunk 21's own
-  documented design constraint (§Organization / §Compliance 2: no sibling
-  mixin imports) and this chunk's item 4 instruction not to unify the two.
-- `window_coherent_gain`/`window_processing_gain` are instance methods
-  (mean / RMS of `generate_window` at `self`'s own sample count), matching
-  the Swift reference's `windowCoherentGain(for:)`/`windowProcessingGain(for:)`
-  and the family-contract table (only `generate_window` is called out as a
-  staticmethod).
-- No new result-factory needed: `windowed` reuses `_with_values` (same
-  `dt`/`t0`, new samples) — no contract change to `waveformDsp.md` was
-  required.
-- `windowed`/`window_coherent_gain`/`window_processing_gain` raise
-  `ValueError` on an empty (0-sample) waveform, and `generate_window` raises
-  `ValueError` for `length <= 0` — per §Numerical conventions (these are not
-  detector methods).
-- Gate: `make uv-fullCheck` green (ruff clean, mypy strict clean over
-  `src`+`tests`, pytest 1102 passed, including the 15 new tests in
-  `tests/waveforms/dsp/test_windowing.py` and the existing
-  `test_dsp_mixins_do_not_import_sibling_mixins` layering test, which
-  confirms `_windowing.py` imports only scipy/numpy plus
-  `_protocol`/`support`).
-- No deviation from the chunk beyond following the already-merged chunk 18
-  mixin-typing fix as instructed.
diff --git a/.claude/archive/math-tools-port/29-dsp-zero-crossings.md b/.claude/archive/math-tools-port/29-dsp-zero-crossings.md
deleted file mode 100644
index 5a15be4..0000000
--- a/.claude/archive/math-tools-port/29-dsp-zero-crossings.md
+++ /dev/null
@@ -1,88 +0,0 @@
----
-chunk: 29-dsp-zero-crossings
-track: D
-status: complete
-depends_on: [14]
-spec: ../specs/waveformDsp.md §Family contracts (ZeroCrossingMixin), §Compliance 1–2
-last_updated: 2026-07-17
-semver: 0.0.2
-author: Nicholas Bergantz
----
-
-# 29 — `ZeroCrossingMixin`
-
-**Deliverable:** `dsp/_zero_crossings.py` + tests. Swift reference:
-`SWIFT_MATH/Waveform1D/Extensions/Waveform1D+ZeroX.swift`.
-
-## Files
-
-Create `src/math_tools/waveforms/dsp/_zero_crossings.py`,
-`tests/waveforms/dsp/test_zero_crossings.py`. Test-subclass pattern per
-chunk 18.
-
-## Design constraints
-
-- Methods per spec table: `zero_crossings(direction:
-  WaveformZeroCrossingDirection = BOTH) -> list[WaveformZeroCrossing]`
-  (sign-change indexing + sub-sample linear interpolation for
-  `time_seconds`), `zero_crossing_count(direction=BOTH)`,
-  `zero_crossing_rate() -> float` (crossings per second),
-  `segments_between_zero_crossings() -> list[Waveform1D]` (each segment
-  carries a correctly shifted `t0`).
-- Exact zeros count once; empty list on no-hit.
-
-## TDD steps
-
-1. Failing tests (spec compliance 1): f-Hz sine over an integer number of
-   periods → `zero_crossing_rate() == 2f` ± one crossing; POSITIVE +
-   NEGATIVE counts sum to BOTH; sub-sample interp: crossing of a line
-   `y = t − 0.5` lands at 0.5 s (atol dt/100); segments' t0s are
-   monotonically increasing and lengths sum to ≈ n.
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Rate and sub-sample interpolation tests pass
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Trigger detection (27).
-
-## Resolution notes
-
-- Implemented per the chunk's own Design constraints, using
-  `dsp/_triggers.py`'s `_sign_change_events` sign-change-mask technique
-  (`previous <= 0 & current > 0` for rising, mirrored for falling) at
-  `level=0`, plus a per-crossing linear-interpolation refinement step for
-  `time_seconds`. "Exact zeros count once" falls out of that same
-  non-strict/strict split used by the trigger mixin: a sample sitting
-  exactly on zero can only ever be the *departed* side of one crossing,
-  never both.
-- Mixin follows the chunk-18 self-typing idiom exactly (`class
-  ZeroCrossingMixin:` with `self: WaveformProtocol` per method); no nominal
-  `Protocol` inheritance. Only the two already-merged factories were
-  needed: `segments_between_zero_crossings` uses `_with_t0` (same `dt`, new
-  `t0` per segment); no fourth factory was required.
-- `zero_crossing_count`/`zero_crossing_rate` both took on an optional
-  `direction: WaveformZeroCrossingDirection = BOTH` parameter beyond the
-  chunk's literal `zero_crossing_rate() -> float` text, matching the Swift
-  reference's `zeroCrossingRate(direction:)` overload and this mixin's own
-  `zero_crossings(direction=...)`. This is a backward-compatible superset
-  (the chunk's own `zero_crossing_rate()` call still works via the
-  default) rather than a contract narrowing, so no spec edit/semver bump
-  was needed for it.
-- `segments_between_zero_crossings` mirrors the Swift reference's
-  *inclusive*-range segmentation (`values[startIdx...endIdx]`), not
-  `dsp/_time_alignment.py`'s exclusive/non-overlapping split — each
-  interior crossing sample is shared by the two segments it borders, which
-  is what makes "lengths sum to ≈ n" (not exactly `n`) true, matching the
-  chunk's own TDD wording. Return type is `list[WaveformProtocol]`
-  (self-typed), not the spec table's descriptive `list[Waveform1D]` — same
-  established discrepancy already present for `TimeAlignmentMixin.
-  synchronize`/`time_windows`/`time_segments` in the same spec table; no
-  spec change needed.
-- No surprises during implementation; all 14 new tests passed on the first
-  run against the initial implementation, and `make uv-fullCheck` (ruff +
-  mypy strict + full 1116-test pytest suite, including the sibling-import
-  layering test) passed clean.
diff --git a/.claude/archive/math-tools-port/30-dsp-compose.md b/.claude/archive/math-tools-port/30-dsp-compose.md
deleted file mode 100644
index b7d547d..0000000
--- a/.claude/archive/math-tools-port/30-dsp-compose.md
+++ /dev/null
@@ -1,95 +0,0 @@
----
-chunk: 30-dsp-compose
-track: D
-status: complete
-depends_on: [18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29]
-spec: ../specs/waveformDsp.md §Organization (composition phasing), §Compliance 2, 4
-last_updated: 2026-07-17
-semver: 0.0.2
-author: Nicholas Bergantz
----
-
-# 30 — Compose the DSP mixins into `Waveform1D`
-
-**Deliverable:** the one-time base-list edit plus the MRO/layering pins.
-Runs ONLY after chunks 18–29 are all done.
-
-## Files
-
-- Edit: `src/math_tools/waveforms/waveform1d.py` (base list + imports only)
-- Edit: `src/math_tools/waveforms/dsp/__init__.py` (export the 12 mixins)
-- Create: `tests/waveforms/dsp/test_compose.py`
-- Edit: `tests/waveforms/dsp/test_*.py` — remove the per-chunk local test
-  subclasses (`class _W(XMixin, Waveform1D)`) in favor of plain `Waveform1D`
-  (mechanical; assertions unchanged)
-
-## Design constraints
-
-1. Base list exactly as the spec's Organization block (12 mixins then
-   `Waveform1dABC`); no other change to the class body.
-2. `test_compose.py` pins: each of the 12 mixins appears in
-   `Waveform1D.__mro__` exactly once; `Waveform1D.__abstractmethods__ ==
-   frozenset()`; `Waveform1D([1.0, 2.0])` constructs; one smoke call per
-   family on a short sine (e.g. `.fft()`, `.detect_peaks()`, …) succeeds.
-3. Layering pin (spec compliance 2): each `dsp/_*.py` module's imports are
-   scipy/numpy/stdlib/`_protocol`/`_common` only — extend
-   `tests/test_package_layering.py` with this rule if chunk 02's version
-   doesn't already cover `dsp/`.
-
-## TDD steps
-
-1. Write `test_compose.py` first (fails: mixins not composed).
-2. Make the base-list edit; simplify the per-chunk test subclasses.
-3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] MRO test passes; every DSP family callable directly on `Waveform1D`
-- [x] `grep -rn "class _W(" tests/waveforms/dsp/` → no hits
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Any mixin behavior change — if a compose-time conflict (name collision
-between mixins) appears, STOP and report; resolution is a spec decision.
-
-## Resolution notes
-
-- Base-list edit landed exactly as the spec's Organization block (12
-  mixins, `Waveform1dABC` last); `waveform1d.py` imports each mixin module
-  directly (not via `dsp/__init__.py`), keeping the compose step's own
-  import graph minimal.
-- `dsp/__init__.py` now imports and re-exports all twelve mixins (`__all__`)
-  per this chunk's file list — this surfaced a genuine circular import (not
-  the one chunks 19/26/27 had already preempted): populating
-  `dsp/__init__.py` means importing *any* `dsp/_*` submodule now also runs
-  `dsp/__init__.py` first, which imports every mixin, several of which
-  import back into `waveforms/support.py`; `support.py` itself imports
-  `dsp._protocol.WaveformProtocol` at module scope (chunk 27, for the
-  `WaveformWithEvents.waveform` field annotation only). That produced
-  `import support.py` → `dsp/__init__.py` → `dsp/_correlation.py` →
-  `support.py` (still mid-import) → `ImportError: cannot import name
-  'WaveformTimeLag' from partially initialized module`.
-  - **Fix:** moved `support.py`'s `WaveformProtocol` import under `if
-    TYPE_CHECKING:`. Safe because `support.py` already has `from
-    __future__ import annotations`, so the field annotation that uses
-    `WaveformProtocol` is never evaluated at runtime — only mypy needs the
-    import, and mypy resolves `TYPE_CHECKING` imports without executing
-    them. This is the *opposite* direction from the import `dsp/_protocol.py`
-    forbids even under `TYPE_CHECKING` (a mixin importing `Waveform1D`); a
-    support module importing the mixins' shared protocol under
-    `TYPE_CHECKING` isn't that case and doesn't reopen it.
-- `tests/test_package_layering.py::test_dsp_mixins_do_not_import_sibling_mixins`
-  globs `dsp/_*.py`, which also matches `dsp/__init__.py` (`__` starts with
-  `_`) — before this chunk that was harmless (the file was import-free), but
-  once it re-exports every mixin the test flagged it as a "sibling-mixin
-  import" violation. `dsp/__init__.py` is not a mixin module — from this
-  chunk onward it is *expected* to import every mixin — so the test now
-  explicitly excludes `__init__.py` from that specific check. The mixin
-  modules themselves are still fully covered (unchanged).
-- No mixin name collisions found composing all twelve; no mixin behavior
-  was touched.
-- `waveformDsp.md` bumped to semver 0.0.7 documenting both resolutions;
-  `tests/waveforms/dsp/test_*.py` (12 files) mechanically dropped their
-  local `class _W(XMixin, Waveform1D): pass` subclasses in favor of plain
-  `Waveform1D` (assertions unchanged), matching the now-composed class.
diff --git a/.claude/archive/math-tools-port/31-otg-enums-and-errors.md b/.claude/archive/math-tools-port/31-otg-enums-and-errors.md
deleted file mode 100644
index 47db3a1..0000000
--- a/.claude/archive/math-tools-port/31-otg-enums-and-errors.md
+++ /dev/null
@@ -1,79 +0,0 @@
----
-chunk: 31-otg-enums-and-errors
-track: E
-status: complete
-depends_on: [10]
-spec: ../specs/otg.md §Public API (enums), §Error semantics; §Compliance 3, 4
-last_updated: 2026-07-21
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 31 — OTG enums + errors
-
-**Deliverable:** the OTG package skeleton with wire-stable enums.
-
-## Files
-
-- Create: `src/math_tools/otg/__init__.py` (exports grow per chunk; start
-  with the enums + `OtgError`), `src/math_tools/otg/py.typed`,
-  `src/math_tools/otg/enums.py`, `src/math_tools/otg/errors.py`
-- Create: `tests/otg/__init__.py`, `tests/otg/test_enums.py`
-
-## Design constraints
-
-1. `enums.py` per spec: `Result(IntEnum)` with the exact nine values
-   (including the intentional gap at −103 — transcribe from the spec table,
-   verify against `SWIFT_MATH/OTG/enums/Result.swift`); `ControlInterface`,
-   `Synchronization`, `DurationDiscretization` (string enums);
-   internal `ControlSigns` (UDDU/UDUD), `Direction` (UP/DOWN),
-   `ReachedLimits` (8 members per the Swift enum) — internal ones may live
-   in `enums.py` but are excluded from `__all__`.
-2. `errors.py`: `OtgError(MathToolsError)` — raised only for structural
-   misuse per spec §Error semantics.
-3. Pure stdlib module (the layering test's no-numpy-in-otg rule starts
-   applying here).
-
-## TDD steps
-
-1. Failing tests: every `Result` member's integer value grep-matches the
-   spec table (write the values as literals in the test); `Result(-103)`
-   raises `ValueError` (the gap is real); `OtgError` is a `MathToolsError`.
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Nine `Result` values pinned literally; the −103 gap pinned
-- [x] No numpy import anywhere under `src/math_tools/otg/`
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Every other OTG module.
-
-## Resolution notes
-
-- Transcribed all seven enums from `SWIFT_MATH/OTG/enums/*.swift` (`Result`,
-  `ControlInterface`, `Synchronization`, `DurationDiscretization`,
-  `ControlSigns`, `Direction`, `ReachedLimits`). `Result` is `enum.IntEnum`
-  (wire-stable ints); the rest are `str, enum.Enum` per the existing
-  repo convention (`waveforms/support.py`) — public string enums keep the
-  Swift raw string values verbatim (`"Position"`, `"TimeIfNecessary"`, …) for
-  `to_dict`/`from_dict` wire parity; internal enums (`ControlSigns`,
-  `Direction`, `ReachedLimits`) live in `enums.py` but are excluded from
-  `__all__`, matching Swift's `internal` visibility.
-- `otg/__init__.py` re-exports only the four public enums + `OtgError` this
-  chunk introduces; the flat `math_tools` root `__init__.py` is left
-  untouched (still empty — curating it is chunk 43's job per
-  mathToolsArchitecture.md §Public surface).
-- `tests/test_package_layering.py::test_otg_does_not_import_numpy` was
-  already written (guarded to skip until `math_tools/otg` exists) by an
-  earlier chunk; it now runs for real against this package and passes with
-  no changes needed to that test file.
-- No spec changes were required; `otg.md` §Public API's enum table matched
-  the Swift source exactly, including the `-103` gap.
-- `tests/otg/test_enums.py` also pins the three public string enums and the
-  three internal enums (beyond the chunk's minimum TDD step) since the
-  chunk's own "Design constraints" section requires transcribing all seven
-  from the Swift source — leaving them untested would leave the fidelity
-  requirement unverified.
diff --git a/.claude/archive/math-tools-port/32-otg-input-parameter.md b/.claude/archive/math-tools-port/32-otg-input-parameter.md
deleted file mode 100644
index 5cf06e7..0000000
--- a/.claude/archive/math-tools-port/32-otg-input-parameter.md
+++ /dev/null
@@ -1,91 +0,0 @@
----
-chunk: 32-otg-input-parameter
-track: E
-status: complete
-depends_on: [31]
-spec: ../specs/otg.md §Public API (InputParameter)
-last_updated: 2026-07-21
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 32 — `InputParameter`
-
-**Deliverable:** the per-cycle input struct with validation and wire codec.
-
-## Files
-
-- Create: `src/math_tools/otg/input_parameter.py`
-- Edit: `src/math_tools/otg/__init__.py` (export)
-- Create: `tests/otg/test_input_parameter.py`
-
-## Design constraints
-
-1. Field-for-field port of `SWIFT_MATH/OTG/InputParameter.swift` (read it
-   first; snake_case the names): state/target arrays, limits, optional
-   min/positional limits, `enabled`, per-DOF interface/sync overrides,
-   `intermediate_positions`, per-section arrays, `minimum_duration`,
-   `interrupt_calculation_duration`. Constructor `InputParameter(dofs)`
-   fills the Swift defaults (arrays sized to dofs).
-2. `validate(check_current_state_within_limits=False,
-   check_target_state_within_limits=True) -> bool` — port the Swift checks
-   (NaN/inf, limit positivity, target within limits, enabled handling)
-   branch-for-branch.
-3. `==` field equality; `to_dict`/`from_dict` with the camelCase keys from
-   `SWIFT_MATH/OTG/extensions/InputParameter+codable.swift` — these keys
-   MUST match the truth-table JSON corpus (chunk 42 loads it through this
-   codec).
-4. `list[float]` fields, stdlib only.
-
-## TDD steps
-
-1. Failing tests: default construction shapes; a valid input validates; each
-   invalidity class (zero max jerk, target velocity over limit, NaN) flips
-   `validate()`; `from_dict` on one literal case copied verbatim out of
-   `successful_trajectories.json` (embed the dict in the test) round-trips
-   `to_dict`.
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] The embedded truth-table case parses; `==` and codec round-trip pass
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-OutputParameter/Trajectory (35); any solver logic.
-
-## Resolution notes
-
-- `validate()` returns `bool` rather than throwing, per `otg.md` §Error
-  semantics (per-cycle failures are `Result` codes, never exceptions in this
-  port -- `InputParameter.swift`'s `RuckigError` throws are the exception
-  this repo's contract explicitly carves against). Each private
-  `_validate_*` helper returns `False` at the first violation instead of
-  raising with a message, matching the checked branches 1:1 but not the
-  error text.
-- Deviation from the chunk's literal TDD wording: it lists "zero max jerk"
-  as an invalidity class, but Swift's `validateJerkLimits` only rejects
-  `jMax.isNaN || jMax < 0.0` -- zero is a legal (if degenerate) limit in the
-  Swift source. Ported that check verbatim (reject NaN/negative only) and
-  added `test_zero_max_jerk_is_legal` to pin the boundary; the "limit
-  positivity" example is instead exercised with a negative max jerk
-  (`test_negative_max_jerk_invalidates`).
-- The design constraints' parenthetical "enabled handling" does not
-  correspond to any branch in `InputParameter.swift`'s `validate()` --
-  `enabled` is read only by `CalculatorTarget.swift` (chunk 40, out of
-  scope). Ported `enabled` as a stored/equatable/codec field only, with no
-  validate() branch, matching the Swift source exactly.
-- `__eq__` is implemented as full field equality (including
-  `degrees_of_freedom` and `interrupt_calculation_duration`), which is a
-  superset of Swift's hand-written `==` (which omits both of those fields).
-  No oracle or spec text pins `InputParameter` equality semantics beyond
-  "field equality," so the simpler/more defensible full-field comparison
-  was chosen; flagging in case downstream chunks assumed the narrower
-  Swift-literal behavior.
-- `from_dict` ignores unrecognized keys (e.g. the classification corpus'
-  `"error"` string on failed cases) rather than rejecting them, so chunk 42
-  can feed corpus records straight through the codec without pre-filtering.
-- `to_dict` omits `None`-valued optional fields (mirrors Swift's
-  `encodeIfPresent`), which is what makes the truth-table round-trip
-  produce a dict `==`-equal to the embedded literal.
diff --git a/.claude/archive/math-tools-port/33-otg-profile.md b/.claude/archive/math-tools-port/33-otg-profile.md
deleted file mode 100644
index 232397d..0000000
--- a/.claude/archive/math-tools-port/33-otg-profile.md
+++ /dev/null
@@ -1,136 +0,0 @@
----
-chunk: 33-otg-profile
-track: E
-status: complete
-depends_on: [31]
-spec: ../specs/otg.md §Internal fidelity 1, 4, 5
-last_updated: 2026-07-21
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 33 — `Profile`
-
-**Deliverable:** the per-DOF kinematic profile record — the hot data
-structure every step solver fills. Faithful port of
-`SWIFT_MATH/OTG/Profile.swift` (~715 lines; translate mechanically,
-preserve method and branch structure).
-
-## Files
-
-- Create: `src/math_tools/otg/profile.py`
-- Create: `tests/otg/test_profile.py`
-
-## Design constraints
-
-1. Fixed-length `list[float]` arrays `t[7]`, `t_sum[7]`, `j[7]`, `a[8]`,
-   `v[8]`, `p[8]` — never resized. Targets `pf/vf/af`; `limits:
-   ReachedLimits`, `direction: Direction`, `control_signs: ControlSigns`;
-   `brake`/`accel` BrakeProfile fields are typed as the placeholder until
-   chunk 34 lands — declare them `brake: "BrakeProfile"` with a deferred
-   import if 34 is not yet merged, or coordinate to land 34's dataclass
-   stub here (note which).
-2. Kinematic stepping uses `math_tools.functional.roots.integrate_jerk` —
-   never a fresh implementation.
-3. Port the full `check*` family (`check`, `check_for_velocity`,
-   `check_for_second_order`, `check_for_first_order`, `set_boundary`,
-   `*_with_timing` variants, `check_position_extremum`,
-   `check_step_for_position_extremum`) with the Swift epsilon constants
-   (`EPS16` etc. from `functional.roots`).
-4. Stdlib `math` only.
-
-## TDD steps
-
-1. Failing tests: a hand-constructed 7-phase profile (constant jerk ±j)
-   integrates to the expected `p/v/a` boundary arrays (compute the expected
-   values with `integrate_jerk` in the test, independent of Profile's own
-   loop ordering); `check` accepts a known-valid profile and rejects a
-   perturbed one (`t[3] += 1e-3`); `t_sum` is the prefix sum of `t`.
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Boundary-array integration test passes; perturbation rejected
-- [x] `grep -n "integrate_jerk" src/math_tools/otg/profile.py` ≥ 1;
-      no local jerk-integration reimplementation
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Brake trajectory computation (34); step solvers; trajectory sampling.
-
-## Resolution notes
-
-- **BrakeProfile forward reference (for chunk 34 to reconcile):** chunk 34
-  had not landed, so `brake`/`accel` are typed as a module-private
-  `_DeferredBrakeProfile` dataclass (top of `profile.py`) rather than a
-  `TYPE_CHECKING`-guarded string forward reference to
-  `math_tools.otg.brake.BrakeProfile` -- that module doesn't exist yet, and
-  a `TYPE_CHECKING` import of a nonexistent module fails `mypy --strict`
-  even though it's runtime-inert (mypy evaluates `TYPE_CHECKING` blocks).
-  `_DeferredBrakeProfile` mirrors `Brake.swift`'s public shape exactly
-  (`duration`, `t`, `j`, `a`, `v`, `p`, with the same `[0.0, 0.0]` defaults)
-  so `Profile.__init__`'s `BrakeProfile()` defaults and
-  `Profile.set_boundary`'s `brake`/`accel` copy are both faithful without
-  needing a real instance of the future type. **Chunk 34 should**: delete
-  `_DeferredBrakeProfile` from `profile.py`, import the real `BrakeProfile`
-  from `math_tools.otg.brake`, and retype `Profile.brake`/`Profile.accel`
-  (and the `set_boundary` copy) to it -- no other call site needs to
-  change, since every chunk-33 method treats `brake`/`accel` as opaque
-  (copied, never read field-by-field).
-- **`Bound` forward reference:** `check_position_extremum` and
-  `check_step_for_position_extremum`'s `ext` parameter is typed against a
-  module-private structural `Protocol` (`_PositionExtremumSink`: `min`,
-  `max`, `t_min`, `t_max` floats) instead of importing the not-yet-landed
-  `Bound`. Since `34-otg-block-brake-bound.md` specifies `Bound` with
-  exactly those field names, the real `Bound` will satisfy this Protocol
-  automatically -- **chunk 34 does not need to touch `profile.py` for
-  this one**; the Protocol can stay indefinitely, or be swapped for a
-  direct `Bound` import later purely for readability.
-- **Epsilon constants:** `otg.md`'s "exact epsilon constants (`EPS16`
-  etc. from `functional.roots`)" guidance doesn't literally apply to
-  `Profile.swift`'s own comparisons -- that file defines its own private
-  module constants (`vEps`, `aEps`, `jEps`, `pPrecision`, `vPrecision`,
-  `aPrecision`, `tPrecision`, `tMax`), none of which exist in
-  `functional/roots.py` (`EPS16` = `16*ulp` ≈ 3.55e-15 is a different,
-  unrelated constant used only by the polynomial-root kernel). Ported
-  `Profile.swift`'s constants as verbatim module-level literals in
-  `profile.py`. The one genuine overlap is `Double.ulpOfOne`, reproduced
-  as `_ULP = sys.float_info.epsilon` (the same value `functional/roots.py`
-  keeps in its own private, non-exported `_ULP` -- not importable across
-  modules, so redefined rather than reimplemented).
-- **Swift method-overload collapsing:** Python has no positional-overload
-  dispatch. `set_boundary`'s two overloads (copy-from-`Profile` vs. six
-  scalars) differ by type, so they're ported as `@typing.overload` +
-  `isinstance` dispatch (positional-only parameters, `/`, on both overload
-  stubs -- required to satisfy `mypy --strict`'s "overloaded implementation
-  must accept all parameters of each signature" check, since the stubs'
-  first parameter names differ). Every other Swift overload pair
-  (`checkWithTiming`, `checkForVelocityWithTiming`,
-  `checkForSecondOrderVelocityWithTiming`, `checkForSecondOrderWithTiming`,
-  `checkForFirstOrderWithTiming`) differs only by one or two extra bound
-  arguments inserted before the trailing `controlSigns`/`limits`
-  parameters -- collapsed into one Python method each with the extra
-  bound(s) as trailing keyword-only optional parameters (default `None`),
-  rather than mirroring Swift's positional insertion point. This changes
-  argument order relative to the Swift signature but preserves every
-  branch exactly (guard runs only when the optional is provided, then
-  delegates to the same shorter method). The unused `tf` timing parameter
-  in every `*_with_timing` overload is kept (fidelity to the Swift
-  signature) but genuinely unused in every branch, exactly as upstream.
-- **Deferred out of scope (not in the chunk's `check*` list):**
-  `getPositionExtrema()` and `getFirstStateAtPosition()` were not ported --
-  design constraint 3 enumerates the required `check*` family explicitly
-  and both are absent from it. Both also have real dependencies this chunk
-  doesn't carry: `getPositionExtrema` reads `brake.duration`/`brake.t`
-  (meaningless against the placeholder) and aggregates across the whole
-  profile plus brake sub-profiles (a `Trajectory`-level concern, chunk 35);
-  `getFirstStateAtPosition` needs
-  `functional.polynomial.UnivariatePolynomial`'s cubic root solver, not
-  wired into this module. Flagging so a later chunk (35, trajectory
-  sampling) knows these two Swift methods still need a home.
-- All 9 `integrate_jerk` call sites replace every Swift `for i in 0..<7`
-  kinematic loop, including the "second-order"/"first-order" interfaces
-  where Swift inlines the `j == 0` special case by hand (verified
-  algebraically: `integrate_jerk(t, p0, v0, a0, 0.0)` reduces to exactly
-  Swift's `v0 + t*a0` / `p0 + t*(v0 + t*a0/2)`).
diff --git a/.claude/archive/math-tools-port/34-otg-block-brake-bound.md b/.claude/archive/math-tools-port/34-otg-block-brake-bound.md
deleted file mode 100644
index 8963965..0000000
--- a/.claude/archive/math-tools-port/34-otg-block-brake-bound.md
+++ /dev/null
@@ -1,132 +0,0 @@
----
-chunk: 34-otg-block-brake-bound
-track: E
-status: complete
-depends_on: [33]
-spec: ../specs/otg.md §Internal fidelity 3–5
-last_updated: 2026-07-21
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 34 — `Block`, `BrakeProfile`, `Bound`, `Interval`
-
-**Deliverable:** the block-interval synchronization support types and the
-brake pre-trajectory. Faithful ports of `SWIFT_MATH/OTG/Block.swift`,
-`Brake.swift`, `Bound.swift`.
-
-## Files
-
-- Create: `src/math_tools/otg/block.py` (Block + Interval),
-  `src/math_tools/otg/brake.py`, `src/math_tools/otg/bound.py`
-- Edit: `src/math_tools/otg/profile.py` ONLY if chunk 33 left the
-  BrakeProfile fields as deferred placeholders (wire the real type in)
-- Create: `tests/otg/test_block.py`, `tests/otg/test_brake.py`
-
-## Design constraints
-
-1. `bound.py`: `Bound` (min/max/t_min/t_max) — plain mutable dataclass.
-2. `brake.py`: `BrakeProfile` — port `finalize`, `finalize_second_order`,
-   `acceleration_brake`, `velocity_brake`,
-   `get_position_brake_trajectory`, `get_velocity_brake_trajectory`,
-   `v_at_t`, `v_at_a_zero`, `==` branch-for-branch.
-3. `block.py`: `Block` (`p_min`, `t_min`, optional intervals `a`/`b`,
-   `calculate_block`, `is_blocked`, `get_profile`) and `Interval`
-   (`left`/`right`/`profile`). Preserve the blocked-interval selection
-   logic exactly — it drives synchronization in chunk 40.
-4. Stdlib `math` + `functional.roots` only.
-
-## TDD steps
-
-1. Failing tests: brake — a state exceeding max acceleration produces a
-   non-zero brake duration and `v_at_t(0)` equals the initial velocity;
-   a within-limits state produces an empty brake (t[0] == 0). Block —
-   `is_blocked` boundary behavior at interval edges; `get_profile` returns
-   the interval's profile for an in-interval t.
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Brake zero/non-zero cases pass; interval edge cases pinned
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Step solvers; TargetCalculator.
-
-## Resolution notes
-
-- **Files landed:** `src/math_tools/otg/bound.py` (`Bound`, plain mutable
-  `@dataclass`), `src/math_tools/otg/brake.py` (`BrakeProfile`),
-  `src/math_tools/otg/block.py` (`Block` + `Interval`),
-  `tests/otg/test_bound.py` was not created separately -- `Bound` has no
-  behavior beyond its four fields and default values, so it is exercised
-  indirectly via `test_block.py`'s `Interval`/`Block` fixtures and directly
-  covered by mypy structural-Protocol satisfaction against
-  `profile.py`'s `_PositionExtremumSink` (see below); `tests/otg/test_block.py`,
-  `tests/otg/test_brake.py` created per the chunk's file list.
-- **`BrakeProfile` scope beyond the chunk's design-constraint-2 method
-  list:** also ported `get_second_order_position_brake_trajectory` and
-  `get_second_order_velocity_brake_trajectory` (present in `Brake.swift`
-  but not named in this chunk's design constraint 2). Justification:
-  otg.md's fidelity ranking puts "faithful port" first, `Brake.swift`'s
-  four `get*BrakeTrajectory` methods are all part of one cohesive public
-  surface, and the second-order velocity/position step solvers (chunks
-  36–39, not yet landed) will need the second-order brake paths — landing
-  a partial `BrakeProfile` now would force a second, disruptive edit to
-  this same file later. All four `get*BrakeTrajectory` methods, both
-  `finalize*` methods, both velocity helpers, and `==` are ported
-  branch-for-branch from `Brake.swift`.
-- **Swift `inout` parameters:** `BrakeProfile.finalize`/
-  `finalize_second_order` take `pS`/`vS`/`aS` as Swift `inout Double`;
-  Python has no by-reference scalar parameters, so both return the updated
-  `(p, v, a)` tuple instead. `Block.calculateBlock`/`Block.removeProfile`'s
-  `inout Int` (`validProfileCounter`) becomes a returned, possibly
-  decremented counter for the same reason; `block` (a class instance) and
-  `validProfiles` (a list) mutate in place as normal Python object
-  references, matching Swift's `inout` semantics for those two without any
-  signature change.
-- **Bug caught during self-review before running the gate:** an early
-  draft of `BrakeProfile.acceleration_brake` added `del a_min` to mark the
-  parameter as intentionally unused (mirroring `velocity_brake`, where
-  `aMax` truly is unused in every branch of the Swift source) — but
-  `acceleration_brake` **does** use `a_min` later, in the
-  `velocity_brake(v0, a0, v_max, v_min, a_max, a_min, j_max)` delegation
-  call. The `del` would have raised `UnboundLocalError` at runtime the
-  first time that branch executed. Caught by re-reading `Brake.swift`
-  side-by-side with the draft before writing tests; fixed by removing the
-  `del` (kept only on `velocity_brake`'s genuinely-unused `a_max`).
-- **`profile.py` reconciliation (chunk 33's deferred placeholders):**
-  - `BrakeProfile`: removed the module-private `_DeferredBrakeProfile`
-    dataclass and its now-unused `dataclasses.field`/`dataclass` imports;
-    `profile.py` now does `from math_tools.otg.brake import BrakeProfile`
-    and `Profile.brake`/`Profile.accel` are typed and constructed as the
-    real `BrakeProfile`. No other call site changed — every chunk-33
-    method already treated `brake`/`accel` as opaque (copied via
-    `set_boundary`, never read field-by-field), exactly as chunk 33's
-    Resolution notes predicted.
-  - `Bound`: **left the `_PositionExtremumSink` structural `Protocol` in
-    place**, rather than importing `math_tools.otg.bound.Bound` directly
-    into `profile.py`. Chunk 33's Resolution notes explicitly authorized
-    this ("the Protocol can stay indefinitely, or be swapped for a direct
-    `Bound` import later purely for readability"). Reasons for choosing
-    "stay" over "swap": (1) `Bound`'s fields (`min`, `max`, `t_min`,
-    `t_max`) already satisfy the Protocol structurally by construction —
-    the swap has zero behavioral or type-safety benefit; (2) swapping
-    would additionally require retyping `tests/otg/test_profile.py`'s
-    `_FakeBound` fixture (which duck-types the same Protocol) to import
-    the real `Bound`, an edit to a file outside this chunk's own file list
-    that the stay-in-scope default posture counsels against absent a
-    concrete benefit; (3) it keeps `bound.py` a leaf module with zero
-    importers inside `otg/` until `block.py`'s `Interval`/`Block` and the
-    later `Trajectory`/`TargetCalculator` chunks actually need it,
-    matching the "no import edge until there's a real dependency" spirit
-    of the original deferral. Only `profile.py`'s module docstring and the
-    `_PositionExtremumSink` class docstring were reworded (from
-    "not-yet-landed" to "why this stays a Protocol") — no code/behavior
-    change.
-- **Gate:** `make uv-fullCheck` passes (ruff clean, mypy strict clean over
-  91 source files, 1267 tests passed including the 21 new `test_block.py`
-  and 23 new `test_brake.py` cases). `grep -rn numpy src/math_tools/otg/`
-  shows no import (only doc-comment mentions), preserving otg.md's
-  compliance requirement 4.
diff --git a/.claude/archive/math-tools-port/35-otg-trajectory-and-output.md b/.claude/archive/math-tools-port/35-otg-trajectory-and-output.md
deleted file mode 100644
index 31a9360..0000000
--- a/.claude/archive/math-tools-port/35-otg-trajectory-and-output.md
+++ /dev/null
@@ -1,119 +0,0 @@
----
-chunk: 35-otg-trajectory-and-output
-track: E
-status: complete
-depends_on: [34]
-spec: ../specs/otg.md §Public API (Trajectory, OutputParameter)
-last_updated: 2026-07-21
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 35 — `Trajectory` + `OutputParameter`
-
-**Deliverable:** the trajectory container/sampler and the per-cycle output
-struct. Faithful ports of `SWIFT_MATH/OTG/Trajectory.swift` and
-`OutputParameter.swift`.
-
-## Files
-
-- Create: `src/math_tools/otg/trajectory.py`,
-  `src/math_tools/otg/output_parameter.py`
-- Edit: `src/math_tools/otg/__init__.py` (export both)
-- Create: `tests/otg/test_trajectory.py`, `tests/otg/test_output_parameter.py`
-
-## Design constraints
-
-1. `Trajectory`: `profiles: list[list[Profile]]`, `duration`,
-   `cumulative_times`, `independent_min_durations`, `degrees_of_freedom`;
-   `at_time(t) -> (positions, velocities, accelerations)` (lists of float;
-   clamp to `[0, duration]` per the Swift edge handling — read `atTime`
-   first and mirror its section lookup), `position_extrema() ->
-   list[Bound]`, internal `get_intermediate_durations`,
-   `get_first_time_at_position`.
-2. `OutputParameter(dofs, max_number_of_waypoints=0)`: fields per spec
-   (`new_position/velocity/acceleration/jerk`, `time`, `new_section`,
-   `did_section_change`, `new_calculation`, `calculation_duration` in µs),
-   `pass_to_input(input)` (copies new state into the input's current
-   state — port the Swift field list exactly), `repr`.
-3. Stdlib only; sampling loops over DOFs like the Swift.
-
-## TDD steps
-
-1. Failing tests: build a single-DOF Trajectory from a hand-constructed
-   Profile (chunk 33's test fixture): `at_time(0)` == initial state,
-   `at_time(duration)` == target state (atol 1e-9), midpoint consistent
-   with `integrate_jerk`; out-of-range `t` clamps; `pass_to_input` copies
-   every kinematic field (assert against a sentinel-filled InputParameter).
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Endpoint/midpoint sampling tests pass
-- [x] `pass_to_input` field coverage pinned (loop over dofs asserting equality)
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Extrema across brake sections beyond the direct port; the driver's time
-stepping (41).
-
-## Resolution notes
-
-- **Files landed:** `src/math_tools/otg/trajectory.py` (`Trajectory`),
-  `src/math_tools/otg/output_parameter.py` (`OutputParameter`),
-  `tests/otg/test_trajectory.py`, `tests/otg/test_output_parameter.py`;
-  `src/math_tools/otg/__init__.py` now also exports `Trajectory` and
-  `OutputParameter`.
-- **`Profile.getPositionExtrema()` / `Profile.getFirstStateAtPosition()`
-  (deferred by chunk 33 to "a later chunk (35, trajectory sampling)" per
-  its Resolution notes):** ported as module-private functions in
-  `trajectory.py` (`_profile_position_extrema`,
-  `_profile_first_state_at_position`) rather than as new methods on
-  `Profile` itself. This chunk's own file list does not include
-  `profile.py`, and both functions only need `Profile`'s already-public
-  fields plus the already-public `Profile.check_step_for_position_extremum`
-  staticmethod, so no edit to `profile.py` was required. Cubic root
-  solving in `_profile_first_state_at_position` delegates to
-  `math_tools.functional.roots.solve_cubic` (never reimplemented), per
-  otg.md's "OTG chunks MUST NOT reimplement root solving."
-- **Constructor overload collapsing:** Swift's two `Trajectory` initializers
-  (`init(dofs:)` and `init(dofs:maxNumberOfWaypoints:)`) collapse into one
-  Python signature, `Trajectory(dofs, max_number_of_waypoints=0)` --
-  `maxNumberOfWaypoints=0` already produces the identical single-section
-  shape as the no-waypoints overload in the Swift source, so nothing is
-  lost. `OutputParameter(dofs, max_number_of_waypoints=0)` mirrors the same
-  collapse for its own two Swift overloads (`init(DOFs:)` /
-  `init(dofs:maxNumberOfWaypoints:)`).
-- **`at_time` clamping:** implemented by clamping the input `time` to
-  `[0, duration]` before section lookup (`max(0.0, min(time, duration))`),
-  exactly matching otg.md's own public-API text ("clamped to `[0,
-  duration]` ends per Swift") -- not a deviation, just making explicit what
-  the spec already specifies. At `time == duration` exactly, the ported
-  `stateToIntegrateFrom` branch already yields `t_diff == 0` against the
-  final boundary state, so clamping values beyond `duration` down to
-  `duration` coincides with (rather than replaces) the literal Swift
-  extrapolate-with-constant-acceleration behavior at the boundary itself;
-  it only changes behavior strictly beyond the boundary, where the spec
-  explicitly calls for clamping anyway.
-- **`Bound` import:** `trajectory.py` imports `math_tools.otg.bound.Bound`
-  directly (not the `_PositionExtremumSink` Protocol `profile.py` uses).
-  Chunk 34's Resolution notes anticipated this: the Protocol was kept in
-  `profile.py` specifically "until ... the later `Trajectory`/
-  `TargetCalculator` chunks actually need it" -- this is that real
-  dependency.
-- **Structural-misuse error convention:** `OutputParameter.__init__`
-  raises plain `ValueError` for non-positive `dofs` (matching
-  `InputParameter.__init__`'s existing precedent), not `OtgError` --
-  `OtgError` remains reserved for the `Otg` driver's own structural-misuse
-  detection (otg.md §Error semantics, chunk 41), not leaf-type constructor
-  validation. `OutputParameter.pass_to_input`'s array-size guard follows
-  the same convention.
-- **Gate:** `make uv-fullCheck` passes (ruff clean, mypy strict clean over
-  95 source files, 1290 tests passed including the 14 new
-  `test_trajectory.py` and 9 new `test_output_parameter.py` cases).
-  `grep -rn numpy src/math_tools/otg/trajectory.py
-  src/math_tools/otg/output_parameter.py` shows no import, preserving
-  otg.md's compliance requirement 4. No spec change was needed --
-  `otg.md`'s existing text already documents both the clamping behavior
-  and the module layout used here.
diff --git a/.claude/archive/math-tools-port/36-otg-velocity-steps.md b/.claude/archive/math-tools-port/36-otg-velocity-steps.md
deleted file mode 100644
index cc10feb..0000000
--- a/.claude/archive/math-tools-port/36-otg-velocity-steps.md
+++ /dev/null
@@ -1,118 +0,0 @@
----
-chunk: 36-otg-velocity-steps
-track: E
-status: complete
-depends_on: [34]
-spec: ../specs/otg.md §Internal fidelity 2, 4, 5
-last_updated: 2026-07-21
-semver: 0.0.2
-author: Nicholas Bergantz
----
-
-# 36 — Velocity-interface step solvers
-
-**Deliverable:** `steps/velocity_second_order.py` +
-`steps/velocity_third_order.py`. Faithful ports of
-`SWIFT_MATH/OTG/VelocitySecondOrderStep1.swift`, `...Step2.swift`,
-`VelocityThirdOrderStep1.swift`, `...Step2.swift`.
-
-## Files
-
-- Create: `src/math_tools/otg/steps/__init__.py`,
-  `src/math_tools/otg/steps/velocity_second_order.py`,
-  `src/math_tools/otg/steps/velocity_third_order.py`
-- Create: `tests/otg/steps/__init__.py`,
-  `tests/otg/steps/test_velocity_steps.py`
-
-## Design constraints
-
-1. One class per Swift class, same names (`VelocityThirdOrderStep1` etc.),
-   same method names snake_cased, same branch structure — translate
-   mechanically; the case analysis encodes the Ruckig profile taxonomy and
-   must stay diffable against the Swift.
-2. Roots/epsilons exclusively from `math_tools.functional.roots`.
-3. Step1 computes the time-optimal profile (fills a `Profile`); Step2
-   computes a profile for a prescribed duration. Keep the
-   `check`-based validation flow (Profile methods from chunk 33).
-
-## TDD steps
-
-1. Failing tests (analytic, hand-derived in test comments): third-order
-   velocity change Δv under jerk limit j and accel limit a — when
-   `Δv ≥ a²/j` the optimal profile is trapezoidal-acceleration with
-   `t = Δv/a + a/j` total; when `Δv < a²/j` it is triangular with
-   `t = 2·sqrt(Δv/j)`. Pin both regimes and the profile's boundary arrays;
-   second-order (no jerk limit) `t = Δv/a`. Step2: prescribed duration
-   1.5× optimal yields a valid profile hitting the target velocity.
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Both analytic regimes pinned for third order; second order pinned
-- [x] Class/method names diff-mappable to the Swift files (reviewer spot-check)
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Position-interface steps (37–39); synchronization.
-
-## Resolution notes
-
-- **Struct-value-copy semantics (the load-bearing decision this chunk had to
-  make).** `Profile` is a Python class (reference type); Swift's `Profile`
-  is a struct (value type). Several Swift lines are `var x = someProfile`
-  followed by conditional keep-or-discard based on a `check*` call's
-  success. A naive Python port (`x = some_profile`, a plain alias) would
-  silently break correctness in two spots:
-  - `VelocityThirdOrderStep1._time_acc0`/`_time_none`: Swift captures `var
-    profile = validProfiles[profileCount]` **once** and reuses it across
-    Solution 1 and Solution 2 within the same call. If Solution 1 succeeds
-    (`validProfiles[profileCount] = profile`, a struct copy in Swift) and
-    Solution 2 then mutates the same local further, Swift's copy already
-    diverged from the array slot — the saved Solution 1 candidate is safe.
-    A Python alias would let Solution 2's mutations retroactively corrupt
-    the already-recorded Solution 1 profile. Fixed by `copy.deepcopy` at
-    the read (`profile = copy.deepcopy(self.valid_profiles[...])`) **and**
-    at each save (`self.valid_profiles[...] = copy.deepcopy(profile)`).
-  - `VelocitySecondOrderStep1.get_profile` / `VelocityThirdOrderStep1`'s
-    zero-limits branch: `var p = block.pMin` then `p.setBoundary(input)`
-    — on failure Swift's `block.pMin` is untouched (the local copy is
-    discarded); a Python alias would leave `block.p_min` mutated with
-    partial/garbage state even though the function returned `False`. Fixed
-    by `copy.deepcopy(block.p_min)` before mutating.
-  All four `Profile` field types (float, list[float], `BrakeProfile`, `str`
-  enum members) are plain and deepcopy-safe; no changes to `profile.py`
-  were needed or made (out of scope, and unnecessary).
-- **`VelocityThirdOrderStep2` needed no copy.** Its private helpers mutate
-  a single `profile` argument passed straight through (Swift `inout` on
-  one object) and always return on first success — Python's natural
-  pass-by-reference mutable-object semantics already match Swift's
-  `inout` here, so these are plain mechanical translations.
-- **Dropped the `debugThis`/`print(...)` scaffolding** in
-  `VelocitySecondOrderStep2.swift` (a `let debugThis = true` flag guarding
-  `print` calls, with the intended real condition commented out:
-  `// (abs(vd) < 0.01)`). This is debug noise, not part of the semantic
-  contract (fidelity requirement 2 covers branch structure and method
-  names, not console output), and printing from a library call is
-  undesirable regardless. No other file in this chunk's scope had similar
-  scaffolding.
-- **Test boundary values pre-set via `Profile.set_boundary_for_velocity`.**
-  A fresh `Profile()` has `vf = af = 0.0`; since `Step1.get_profile`
-  copies its working profile's `vf`/`af`/`v[0]`/`a[0]` from the caller-
-  supplied `input` profile (`set_boundary`'s "from-profile" overload), the
-  test fixtures call `set_boundary_for_velocity(p0_new=0.0, v0_new=0.0,
-  a0_new=..., vf_new=..., af_new=...)` on the input profile before
-  invoking `get_profile` — mirroring how the (not-yet-built)
-  `TargetCalculator` would populate it.
-- **Test regime derivation** (both third-order analytic regimes, matching
-  the chunk's TDD step): a = 2.0, j = 1.0 (a²/j = 4.0). Δv = 6.0 (≥ 4.0)
-  exercises the trapezoidal-acceleration (`ACC0`) regime via `_time_acc0`,
-  t = Δv/a + a/j = 5.0. Δv = 3.0 (< 4.0) exercises the triangular regime
-  via `_time_none`'s Solution 2, t = 2·sqrt(Δv/j) ≈ 3.464. Second order:
-  Δv = 4.0, aMax = 2.0, t = Δv/a = 2.0. Both Step2 tests use tf = 1.5 ×
-  the corresponding Step1-optimal duration and assert the profile hits the
-  target velocity/acceleration and spans exactly `tf`. All boundary arrays
-  are cross-checked against `integrate_jerk` computed independently in the
-  test, per `tests/otg/test_profile.py`'s established convention.
-- No deviations from the plan's file list or design constraints; `otg.md`
-  required no contract changes (only a semver bump for this landing).
diff --git a/.claude/archive/math-tools-port/37-otg-position-first-second-steps.md b/.claude/archive/math-tools-port/37-otg-position-first-second-steps.md
deleted file mode 100644
index 5852327..0000000
--- a/.claude/archive/math-tools-port/37-otg-position-first-second-steps.md
+++ /dev/null
@@ -1,108 +0,0 @@
----
-chunk: 37-otg-position-first-second-steps
-track: E
-status: complete
-depends_on: [34]
-spec: ../specs/otg.md §Internal fidelity 2, 4, 5
-last_updated: 2026-07-21
-semver: 0.0.2
-author: Nicholas Bergantz
----
-
-# 37 — Position first/second-order step solvers
-
-**Deliverable:** `steps/position_first_order.py` +
-`steps/position_second_order.py`. Faithful ports of
-`SWIFT_MATH/OTG/PositionFirstOrderStep1.swift`, `...Step2.swift`,
-`PositionSecondOrderStep1.swift`, `...Step2.swift`.
-
-## Files
-
-- Create: `src/math_tools/otg/steps/position_first_order.py`,
-  `src/math_tools/otg/steps/position_second_order.py`
-- Create: `tests/otg/steps/test_position_first_second.py`
-
-## Design constraints
-
-Same porting rules as chunk 36 (mechanical translation, roots/epsilons from
-`functional.roots`, Profile from chunk 33).
-
-## TDD steps
-
-1. Failing tests (analytic): first order (velocity-limited only) —
-   `t = |Δp|/v_max`, profile position endpoints exact. Second order
-   (velocity+acceleration) — trapezoidal velocity when
-   `|Δp| ≥ v_max²/a_max` with
-   `t = |Δp|/v_max + v_max/a_max`, else triangular with
-   `t = 2·sqrt(|Δp|/a_max)`; pin both, both directions (Δp < 0 exercises
-   `Direction.DOWN`). Step2: prescribed duration 2× optimal reaches the
-   target position.
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Trapezoidal + triangular regimes pinned in both directions
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Third-order steps (38, 39).
-
-## Resolution notes
-
-- **Alias-mutation hazard, per chunk 36's flagged pattern.** Both
-  `PositionFirstOrderStep1.get_profile` and
-  `PositionSecondOrderStep1.get_profile`'s zero-limits branch reproduce
-  Swift's `var p = block.pMin` (a struct value copy) as
-  `copy.deepcopy(block.p_min)`, matching
-  `VelocitySecondOrderStep1.get_profile`'s identical pattern: without the
-  deep copy, a Python alias would let a failed candidate's partial
-  mutations corrupt `block.p_min` even though the function returns
-  `False` (Swift's local copy is simply discarded on failure).
-- **No copy needed in `PositionSecondOrderStep1._time_acc0`/`_time_none`,
-  unlike `VelocityThirdOrderStep1`'s equivalent helpers.** The Swift
-  source mutates `validProfiles[profileCount]` directly through the array
-  subscript on every line -- it never captures a local `var profile =
-  validProfiles[profileCount]` first the way
-  `VelocityThirdOrderStep1._time_acc0`/`_time_none` do. Python list
-  indexing has the same direct-mutation semantics, and `_add_profile`
-  always advances to a fresh, distinct `Profile()` instance before the
-  next attempt, so a plain mechanical port (no `copy.deepcopy`) already
-  reproduces Swift's behavior exactly. Verified this by hand-deriving both
-  analytic regimes (trapezoidal and triangular) independently and
-  confirming the ported code reproduces them bit-for-bit on the first test
-  run -- see the test file's docstrings for the derivations. `valid_profiles`
-  is still built as three genuinely separate `Profile()` instances (`[Profile()
-  for _ in range(3)]`, never `[Profile()] * 3`), matching the same hazard
-  `VelocityThirdOrderStep1` calls out.
-- **`PositionSecondOrderStep2` needs no copy at all** (mirrors
-  `VelocityThirdOrderStep2`): its methods mutate a single `profile`
-  argument passed straight through and always return on first success --
-  Python's natural pass-by-reference mutable-object semantics already
-  match Swift's `inout` here.
-- **Two Swift function parameters are declared but unused in the function
-  body** (`PositionSecondOrderStep1.timeAcc0`'s `returnAfterFound` --
-  there is only ever one candidate write in that function, so nothing to
-  short-circuit; `timeAllSingleStep`'s `aMax`/`aMin` -- only `vMax`/`vMin`
-  are threaded into `checkForSecondOrder`). Ported faithfully with
-  `del return_after_found` / `del a_max, a_min` (matching `profile.py`'s
-  established `del tf` convention for the same situation) rather than
-  dropping the parameters, to keep the signatures diff-mappable to the
-  Swift source per fidelity requirement 2.
-- **Test design.** Point-to-point cases (`v0 = vf = 0`) exercise each
-  solver's "no final velocity" branch, matching `TargetCalculator`'s
-  expected common usage. First-order: `p0=0, pf=±5, vMax=2` pins `t =
-  |Δp|/vMax` in both directions. Second-order: `vMax = aMax = 2.0` =>
-  `vMax²/aMax = 2.0`; `pd=6.0` (>= 2.0, `Direction.UP`) pins the
-  trapezoidal regime, `pd=-1.0` (< 2.0, `Direction.DOWN`) pins the
-  triangular regime -- covering both analytic regimes and both directions
-  across the two tests, per the chunk's TDD step. Step2 tests use `tf = 2x`
-  the corresponding Step1-optimal duration (per the chunk's TDD step
-  wording) and assert the profile reaches the target position and spans
-  exactly `tf`. All boundary-array expectations are recomputed
-  independently via `integrate_jerk` in the test, per
-  `tests/otg/steps/test_velocity_steps.py`'s established convention. All
-  ten tests passed on the first run against the mechanically-ported
-  implementation, confirming the hand-derived formulas and the port agree.
-- No deviations from the plan's file list or design constraints; `otg.md`
-  required no contract changes.
diff --git a/.claude/archive/math-tools-port/38-otg-position-third-step1.md b/.claude/archive/math-tools-port/38-otg-position-third-step1.md
deleted file mode 100644
index b702ddd..0000000
--- a/.claude/archive/math-tools-port/38-otg-position-third-step1.md
+++ /dev/null
@@ -1,118 +0,0 @@
----
-chunk: 38-otg-position-third-step1
-track: E
-status: complete
-depends_on: [34]
-spec: ../specs/otg.md §Internal fidelity 2, 4, 5; §Module layout (chunking hints)
-last_updated: 2026-07-21
-semver: 0.0.2
-author: Nicholas Bergantz
----
-
-# 38 — `PositionThirdOrderStep1` (time-optimal)
-
-**Deliverable:** `steps/position_third_order_step1.py` — faithful port of
-`SWIFT_MATH/OTG/PositionThirdOrderStep1.swift` (~850 lines). This is the
-time-optimal profile finder for the full jerk-limited position interface.
-
-## Files
-
-- Create: `src/math_tools/otg/steps/position_third_order_step1.py`
-- Create: `tests/otg/steps/test_position_third_step1.py`
-
-## Design constraints
-
-1. Mechanical translation: one Python method per Swift method
-   (`time_acc0_acc1_vel`, `time_vel`, `time_acc0`, … — keep every profile-
-   family case), same guard order, same use of `solve_cubic`/
-   `solve_quartic_monic`/`shrink_interval` from `functional.roots`.
-2. Do NOT simplify algebra or merge branches; if a Swift branch looks dead,
-   port it anyway and note it.
-3. The class's public entry mirrors the Swift `getProfile`-style API filling
-   candidate `Profile`s and selecting valid ones via `Profile.check`.
-
-## TDD steps
-
-1. Failing tests: three hand-derivable cases — (a) rest-to-rest long move
-   (all limits reached: ACC0_ACC1_VEL profile; total time
-   `t = Δp/v + v/a + a/j` +symmetric phases — derive in the test comment),
-   (b) rest-to-rest short move (jerk-dominated, no limit reached), (c) a
-   moving-start case with a0 ≠ 0. Assert total duration (atol 1e-9) AND the
-   7 segment times of the selected profile (this is what chunk 42's numeric
-   oracle will lean on).
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] The three analytic cases pass with segment-time pinning
-- [x] Every Swift method name has a snake_case counterpart (reviewer diff spot-check)
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Step2 (39); synchronization; blocks.
-
-## Resolution notes
-
-- **All 11 Swift methods ported 1:1, snake_cased**: `addProfile` →
-  `_add_profile`, `resetProfiles` → `_reset_profiles`, `hasProfiles` →
-  `_has_profiles`, `timeAllVel` → `_time_all_vel`, `timeAcc0Acc1` →
-  `_time_acc0_acc1`, `timeAllNoneAcc0Acc1` → `_time_all_none_acc0_acc1`,
-  `timeAcc1VelTwoStep` → `_time_acc1_vel_two_step`, `timeAcc0TwoStep` →
-  `_time_acc0_two_step`, `timeVelTwoStep` → `_time_vel_two_step`,
-  `timeNoneTwoStep` → `_time_none_two_step`, `timeAllSingleStep` →
-  `_time_all_single_step`, `getProfile` → `get_profile`. Confirmed via a
-  `grep`-diff of Swift `func` names against Python `def` names (see
-  module docstring/report). The chunk description's example names
-  (`time_acc0_acc1_vel`, `time_vel`, `time_acc0`) don't literally appear
-  in the Swift source (the actual grouping methods are `timeAllVel` /
-  `timeAcc0Acc1` / `timeAllNoneAcc0Acc1`); the acceptance criterion (every
-  Swift method name has a snake_case counterpart) is satisfied by the
-  literal Swift names, which is what was ported.
-- **Confirmed dead code, ported anyway**: a source-tree `grep` for
-  `timeAcc1VelTwoStep`/`timeAcc0TwoStep`/`timeVelTwoStep`/`timeNoneTwoStep`
-  shows zero call sites anywhere in `SWIFT_MATH` outside their own
-  declarations -- these four "only for numerical issues" methods are
-  genuinely unreachable from `getProfile` in the Swift source too. Ported
-  field-for-field per design constraint 2 and documented in the module
-  docstring; no dedicated tests target them directly since they cannot be
-  exercised through the public `get_profile` entry point (matching how
-  `get_profile`'s own reachable paths are the only ones the TDD cases can
-  drive).
-- **New alias-mutation pattern beyond chunks 36/37**:
-  `_time_all_none_acc0_acc1` introduces a pattern not seen in the velocity
-  or first/second-order position steps -- the Swift source explicitly
-  re-fetches `profile = validProfiles[profileCount]` mid-loop (with its
-  own "BUG FIX: Get fresh profile reference..." comment) after a
-  non-returning success. Ported as: `copy.deepcopy` on every *save*
-  (`self.valid_profiles[self._profile_count] = copy.deepcopy(profile)`,
-  severing the alias so later mutations can't corrupt what was just
-  saved), but a *plain* reference reassignment for the mid-loop refresh
-  itself (pointing `profile` at the fresh, not-yet-saved next slot needs
-  no copy). Reasoning recorded in full in the module docstring.
-- **Swift/Python IEEE 754 division divergence (new, spec-worthy)**: the
-  three hand-derived TDD cases (rest-to-rest short move and the
-  moving-start case) both hit a legitimate `t == 0` quartic root in
-  `_time_all_none_acc0_acc1`'s NONE loop (whenever the polynomial's
-  constant term `-h2_p2/j^2` is zero, `insertIfPositive` accepts `0.0` as
-  a valid non-negative root). The subsequent `h0 = h2_none / (2*j*t)` is a
-  genuine `0.0/0.0`, which Swift/IEEE754 silently resolves to `nan` (later
-  rejected by `Profile.check`'s precision comparisons) but Python's `/`
-  raises `ZeroDivisionError` on. Fixed with a small `_ieee754_div` helper
-  used only at this one call site (not a blanket division-wrapping sweep).
-  otg.md §Internal fidelity requirement 4 was updated (semver 0.0.2 →
-  0.0.3) to document this as a recognized, narrowly-scoped port pattern
-  for future step-solver chunks (39, `calculator_target`) to watch for
-  and reuse rather than rediscover.
-- **Three TDD cases, all closed-form, all verified by independent
-  re-integration**: (a) long move, ACC0_ACC1_VEL, `t = pd/v_max +
-  v_max/a_max + a_max/j_max = 8.0`, segments `[1,1,1,2,1,1,1]`; (b) short
-  move, NONE, `t2 = (4*pd/j)**(1/3)` with `t0=t6=t2/2`; (c) moving-start
-  (`a0=af=0.5`), NONE, `h2_none` collapses to 0 by choosing `a0=af`,
-  reducing the quartic to a cubic with a hand-picked root `t2=2` pinning
-  `pd=1.5`. All three additionally assert `profile.limits` matches the
-  expected `ReachedLimits` member and reintegrate the returned segment
-  times via `integrate_jerk` independently of `Profile`'s own internal
-  loop, confirming the final `(p, v, a)` lands on the target state.
-- No deviation from the chunk's file list or scope; `Out of scope` items
-  (Step2, synchronization, blocks) untouched.
diff --git a/.claude/archive/math-tools-port/39-otg-position-third-step2.md b/.claude/archive/math-tools-port/39-otg-position-third-step2.md
deleted file mode 100644
index fd39151..0000000
--- a/.claude/archive/math-tools-port/39-otg-position-third-step2.md
+++ /dev/null
@@ -1,103 +0,0 @@
----
-chunk: 39-otg-position-third-step2
-track: E
-status: complete
-depends_on: [34]
-spec: ../specs/otg.md §Internal fidelity 2, 4, 5; §Module layout (chunking hints)
-last_updated: 2026-07-21
-semver: 0.0.2
-author: Nicholas Bergantz
----
-
-# 39 — `PositionThirdOrderStep2` (prescribed-duration)
-
-**Deliverable:** `steps/position_third_order_step2.py` — faithful port of
-`SWIFT_MATH/OTG/PositionThirdOrderStep2.swift` (~1,900 lines, the single
-largest file in the port). Solves a profile hitting the target at an
-EXACT prescribed duration (the synchronization workhorse).
-
-## Files
-
-- Create: `src/math_tools/otg/steps/position_third_order_step2.py`
-- Create: `tests/otg/steps/test_position_third_step2.py`
-
-## Design constraints
-
-1. Same mechanical-translation rules as chunk 38. If a single session
-   cannot finish, split at Swift function boundaries and leave the
-   remaining functions raising `NotImplementedError` with the chunk noted
-   `in_progress` — never merge a silently wrong branch.
-2. Every polynomial solve routes through `functional.roots`; epsilon
-   comparisons use the shared constants.
-
-## TDD steps
-
-1. Failing tests: take chunk 38's three analytic cases, compute their
-   optimal durations, then ask Step2 for 1.25×, 1.5×, and 3× that duration —
-   assert the returned profile (a) passes `Profile.check`, (b) reaches
-   `pf/vf/af` (atol 1e-8), (c) has `t_sum[-1]` equal to the prescribed
-   duration (atol 1e-9). Add one negative test: a duration BELOW optimal
-   yields no valid profile.
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] All three scale factors × three cases pass; below-optimal rejected
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Step1 changes; TargetCalculator.
-
-## Resolution notes
-
-- Full mechanical port of all 10 Swift methods (`timeAcc0Acc1Vel`,
-  `timeAcc1Vel`, `timeAcc0Vel`, `timeVel`, `timeAcc0Acc1`, `timeAcc1`,
-  `timeAcc0`, `timeNone`, `timeNoneSmooth`, `getProfile`) as
-  `PositionThirdOrderStep2` in
-  `src/math_tools/otg/steps/position_third_order_step2.py`. No
-  alias-mutation hazard here (unlike Step1): every method mutates the
-  single caller-owned `Profile` directly and returns on first success,
-  architecturally identical to `VelocityThirdOrderStep2` — no
-  `copy.deepcopy` needed.
-- Dropped the Swift `timeVel` method's `debugTimeVel`-gated `print(...)`
-  block (a hardcoded-`false` developer tracing flag, permanently dead) —
-  not part of the algorithm; every branch/root-search/Newton-step it
-  wrapped is preserved exactly.
-- `timeNoneSmooth` is never called from `getProfile` in the Swift source
-  (grep-confirmed) — ported anyway per otg.md design constraint 2, same
-  precedent as Step1's `*_two_step` methods.
-- Preserved a genuine Swift source quirk verbatim in `_time_acc0`: the
-  second `do` block is comment-labeled `// UDUD` but its
-  `checkWithTiming` call actually passes `.UDDU`. Ported as literally
-  executed, not "corrected" to match the comment.
-- TDD surfaced a real fidelity gap beyond otg.md's `_ieee754_div`
-  precedent: the "below-optimal duration is infeasible" negative test
-  hit `math domain error` (Python `math.sqrt` on a negative argument)
-  and, after the first site was patched, a `ZeroDivisionError` at two
-  more sites. Traced the root cause: for a below-time-optimal prescribed
-  duration, `get_profile` tries well over a dozen candidate branches in
-  sequence, and a negative discriminant is the *generic* way each
-  branch's algebra signals infeasibility — not a rare degenerate case.
-  Added `_ieee754_sqrt` (Swift `sqrt(negative) == nan` semantics) and
-  applied it at **every** `math.sqrt` call site in this one file
-  (~30 sites) rather than iterating one failing-test-site at a time,
-  since the hazard is structurally identical everywhere it appears; this
-  intentionally goes beyond `_ieee754_div`'s narrower, per-site-only
-  scoping (documented as a deliberate, file-scoped exception in both the
-  module docstring and otg.md §Internal fidelity requirement 4, bumped
-  to 0.0.4). Added `_ieee754_div` (identical to Step1's helper) and
-  applied it only at the two sites the same test actually reached (T
-  3456's `h0`/`t[3]` denominator, and the UZU 3-step profile's `t == 0`
-  root), per the requirement's existing per-site scoping.
-- `make uv-fullCheck` required hand-fixing ~46 `E501` line-too-long
-  violations. Ran `ruff format` scoped to only this chunk's two files
-  (not the Makefile's whole-tree `uv-format` target) per the chunk
-  instructions barring a broad auto-formatter run; `git status` after
-  confirms only the two new files changed.
-- All three chunk-38 analytic cases (ACC0_ACC1_VEL long move, NONE short
-  move, NONE moving-start) pass at 1.25×/1.5×/3× their Step1-optimal
-  duration (`p`/`v`/`a` within 1e-8, `t_sum[-1] == tf` within 1e-9); the
-  below-optimal negative test passes. Full gate:
-  `make uv-fullCheck` — ruff clean, mypy strict clean (107 source
-  files), 1318/1318 tests pass.
diff --git a/.claude/archive/math-tools-port/40-otg-calculator-target.md b/.claude/archive/math-tools-port/40-otg-calculator-target.md
deleted file mode 100644
index e05678f..0000000
--- a/.claude/archive/math-tools-port/40-otg-calculator-target.md
+++ /dev/null
@@ -1,133 +0,0 @@
----
-chunk: 40-otg-calculator-target
-track: E
-status: complete
-depends_on: [32, 35, 36, 37, 38, 39]
-spec: ../specs/otg.md §Internal fidelity 3
-last_updated: 2026-07-21
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 40 — `TargetCalculator`
-
-**Deliverable:** `calculator_target.py` — faithful port of
-`SWIFT_MATH/OTG/CalculatorTarget.swift` (~780 lines): per-DOF Step1/Step2
-dispatch plus cross-DOF synchronization (Block/Interval logic, the
-discrete-duration path, phase sync).
-
-## Files
-
-- Create: `src/math_tools/otg/calculator_target.py`
-- Create: `tests/otg/test_calculator_target.py`
-
-## Design constraints
-
-1. Port `calculate(...)` and `synchronize(...)` branch-for-branch: per-DOF
-   control-interface dispatch to the step solver classes (36–39), Block
-   construction, blocked-interval resolution, `Synchronization` mode
-   handling (TIME / TIME_IF_NECESSARY / PHASE / NONE), minimum-duration and
-   discrete-duration paths.
-2. Error paths return the spec'd `Result` codes
-   (`ERROR_EXECUTION_TIME_CALCULATION`, `ERROR_SYNCHRONIZATION_CALCULATION`)
-   — no exceptions.
-3. Fills a `Trajectory` (chunk 35); consumes `InputParameter` (32).
-
-## TDD steps
-
-1. Failing tests: (a) 1-DOF position case reproduces chunk 38's analytic
-   duration through the full calculate path; (b) 3-DOF TIME sync — all DOFs
-   report identical trajectory duration equal to the slowest DOF's optimal
-   (compose from chunk 38's cases with different distances); (c) NONE sync —
-   per-DOF durations equal their independent optima; (d) an `enabled=False`
-   DOF stays at its current state; (e) an unsolvable synchronization input
-   returns `ERROR_SYNCHRONIZATION_CALCULATION` rather than raising.
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] TIME/NONE sync duration semantics pinned; disabled-DOF pinned
-- [x] No `raise` in the calculate path (grep for `raise` → only in
-      structural-misuse guards, if any)
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-The `Otg` driver loop (41); waypoints beyond what the Swift implements.
-
-## Resolution notes
-
-- **Deliverable**: `src/math_tools/otg/calculator_target.py` (`TargetCalculator`,
-  private per otg.md's module layout — `__all__ = []`) plus
-  `tests/otg/test_calculator_target.py` (6 tests covering TDD cases a-e; (e)
-  is covered by two tests, see below). Ported `calculate()`, `synchronize()`
-  (as `_synchronize`, since Swift's `private func`), and
-  `isInputCollinear()` (as `_is_input_collinear`) branch-for-branch from
-  `CalculatorTarget.swift`.
-- **Alias-mutation hazard, identified and fixed at 8 sites**: unlike chunks
-  36-39 (where the hazard is *within* a single `get_profile()` call),
-  `TargetCalculator` holds `self._blocks` as *instance* state that persists
-  across `calculate()` calls, so every Swift `trajectory.profiles[0][dof] =
-  blocks[dof].pMin` (or `.a!.profile!` / `.b!.profile!`) — a value copy in
-  Swift, a live alias in Python otherwise — was routed through
-  `copy.deepcopy()`: `_synchronize`'s own save point (3 branches), the "None
-  Synchronization" loop, the `duration == 0.0` copy-all-profiles branch, the
-  1-DOF shortcut, and the "Time Synchronization" loop's 3 early-exit
-  branches. Also caught one array-level (not whole-`Profile`) case: Swift's
-  `p.t = pLimiting.t` (phase sync) copies a Swift array *value*; ported as
-  `p.t = list(p_limiting.t)`, not a bare `p.t = p_limiting.t` (which would
-  alias the two profiles' timing arrays). Full reasoning, including why the
-  *other* `trajectory.profiles[0][dof] = p` write-backs need no copy
-  (`p` already *is* that list slot's object — Python alias mutation, not a
-  fresh Swift struct copy), is in the module docstring.
-- **Verified analytically that `TargetCalculator._synchronize`'s search is
-  provably complete for any Block state a real Step1 call produces** (a
-  DOF's own `t_min`, and any `Interval.right`, is never self-blocking at its
-  own boundary — `Block.is_blocked`/`Interval.is_blocked` both use strict
-  `<`/open intervals). This made TDD case (e) ("an unsolvable
-  synchronization input") impractical to reach through a *naturally*
-  Step1-derived `InputParameter` without an adversarial multi-DOF interval
-  coincidence, so it's covered by two targeted tests instead: one calls
-  `_synchronize` directly with a hand-built `Block` pair proven by
-  construction to block every finite candidate (an `Interval(1.0, math.inf)`
-  combined with a second DOF's `t_min` floor that blocks the first DOF's
-  only escape point at `t=1.0`); the other forces `_synchronize` to return
-  `False` via `unittest.mock.patch.object` and confirms `calculate()`
-  propagates it to `Result.ERROR_SYNCHRONIZATION_CALCULATION` without
-  raising. Documented in the test file's own docstring.
-- **Dropped 4 Swift `print("[DEBUG] ...")` statements** (in `synchronize()`'s
-  failure path and `calculate()`'s two error branches) — unconditional
-  developer tracing, not part of the algorithm, same category as chunk 39's
-  dropped `debugTimeVel` print block. Every branch/decision they straddled
-  is preserved exactly.
-- **No new `_ieee754_div`/`_ieee754_sqrt` sites**: `_is_input_collinear`'s
-  divisions (`pd[dof] / scale`, etc.) all divide by `scale_vector[scale_dof]`,
-  which is only selected after `abs(...) > _EPS` was already checked —
-  provably nonzero, so plain `/` is correct per otg.md §Internal fidelity
-  requirement 4 (`_ieee754_div` is for a *failing test*-demonstrated
-  zero-denominator, not a blanket wrap). One division
-  (`controlLimiting * currentScale / scaleLimiting`) has no such proof and
-  is flagged in the module docstring for a future chunk to revisit if a
-  test ever reaches it; none of this chunk's own tests do (no `Synchronization.PHASE`
-  case was required by the chunk's TDD steps, so this path is implemented
-  per the design constraints but not itself under test here).
-- **Fidelity oddity ported verbatim**: the trivial "already at target, zero
-  motion" branch sets `p.a`/`p.v`/`p.p` to length-7 lists (`[value] * 7`),
-  matching Swift's `Array(repeating: ..., count: 7)` exactly even though
-  `Profile`'s normal invariant is 8-element `a`/`v`/`p` arrays — verified
-  harmless (every element is identical, and `Trajectory.at_time` always
-  indexes via `[-1]`, never a hardcoded `[7]`, so the shorter list is never
-  a break) but preserved rather than "corrected" to 8, per the port's
-  mechanical-translation mandate.
-- **Known, accepted, untested Python/Swift divergence documented, not
-  fixed**: an early error `return` (`ERROR_ZERO_LIMITS`,
-  `ERROR_EXECUTION_TIME_CALCULATION`) can leave `trajectory.profiles[0][dof]`
-  partially mutated in Python (reference-type alias), where Swift's local
-  struct copy would leave it untouched. Nothing in otg.md's oracle/
-  classification/numeric test strategy inspects trajectory state after an
-  error `Result`, so this is unobservable through the documented contract;
-  not patched with defensive copying (would violate the alias-mutation
-  fix's "not blanket everywhere" scoping). Recorded in the module docstring.
-- Gate: `make uv-fullCheck` — ruff clean, mypy strict clean (109 source
-  files), 1324/1324 tests pass (full suite ran in ~12s locally, well under
-  the 60-70s ceiling the chunk brief warned about).
diff --git a/.claude/archive/math-tools-port/41-otg-driver.md b/.claude/archive/math-tools-port/41-otg-driver.md
deleted file mode 100644
index 01f24d3..0000000
--- a/.claude/archive/math-tools-port/41-otg-driver.md
+++ /dev/null
@@ -1,136 +0,0 @@
----
-chunk: 41-otg-driver
-track: E
-status: complete
-depends_on: [40]
-spec: ../specs/otg.md §Public API (Otg), §Error semantics, §Compliance 5
-last_updated: 2026-07-22
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 41 — `Otg` driver
-
-**Deliverable:** the per-cycle driver class and the finished public surface.
-Faithful port of `SWIFT_MATH/OTG/spmOTG.swift`.
-
-## Files
-
-- Create: `src/math_tools/otg/otg.py`
-- Edit: `src/math_tools/otg/__init__.py` (final `__all__` per spec §Module
-  layout)
-- Create: `tests/otg/test_otg_driver.py`
-
-## Design constraints
-
-1. `Otg(control_cycle, dofs, max_number_of_waypoints=0)`; `OtgError` for
-   structural misuse only (non-positive control_cycle, DOF mismatch between
-   constructor and parameters); `update(input, output) -> Result` (validate
-   → recalc-on-change → step `output.time` → sample → WORKING/FINISHED),
-   `calculate(input, output) -> Result`, `reset()`. Port the input-change
-   detection and `interrupt_calculation_duration` handling as the Swift
-   does.
-2. `calculation_duration` measured with `time.perf_counter_ns()` → µs
-   (Swift used DispatchTime).
-
-## TDD steps
-
-1. Failing tests: a 1-DOF rest-to-rest move driven via repeated `update`
-   reaches `FINISHED` in ≤ `duration/control_cycle + 2` calls (spec
-   invariant); `output.new_position` at each cycle matches
-   `trajectory.at_time(output.time)`; invalid input → `ERROR_INVALID_INPUT`
-   (no exception); DOF mismatch raises `OtgError`; `pass_to_input` +
-   `update` chaining is stable (`new_calculation` False when input
-   unchanged).
-2. Implement. 3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] FINISHED-within-bound and no-exception error paths pass
-- [x] `math_tools/otg/__init__.py` `__all__` == the spec's export list
-      (pinned by test — spec compliance 5)
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Oracle suites (42); performance tuning.
-
-## Resolution notes
-
-- **Deliverable**: `src/math_tools/otg/otg.py` (`Otg`, the finished driver)
-  plus `tests/otg/test_otg_driver.py` (17 tests across 6 `TestCase`
-  classes). `__init__.py` now exports `Otg` and `Profile` (the latter was
-  already public in `profile.py`'s own `__all__` since chunk 33 but not yet
-  wired into the package `__init__`), bringing `__all__` to the spec's full
-  10-name §Module layout list, pinned by `TestPublicSurface`.
-- **Constructor deviates from Swift by design, per the chunk brief**:
-  Swift's `OTG.init(deltaTime: Double = -1.0)` only rejects a non-positive
-  delta lazily inside `validateInput`, and only when
-  `durationDiscretization != .Continuous`. This port requires
-  `control_cycle > 0` unconditionally at construction (`OtgError`
-  otherwise), per design constraint 1's "non-positive control_cycle" ->
-  structural misuse. Consequence: Swift's `deltaTime <= 0.0` branch inside
-  `validateInput` is dead code under this port's stricter contract and was
-  not ported (documented in `otg.py`'s module docstring).
-- **DOF-mismatch guard added (not in Swift)**: Swift's fixed-size arrays
-  make a DOF mismatch a compile-time non-issue in normal use, so
-  `OTG.swift` never checks for one. This port's `InputParameter`/
-  `OutputParameter` are plain Python lists with no static size, so
-  `Otg._check_degrees_of_freedom` raises `OtgError` explicitly (checked at
-  the top of both `calculate()` and `update()`, since `update()` can skip
-  its own call to `calculate()` when the input hasn't changed).
-- **Alias-mutation hazard (otg.md's cross-chunk pattern)**: Swift's
-  `currentInput: InputParameter` is a struct field, so `currentInput =
-  input` is a value copy; this port's `InputParameter` is a reference type
-  (chunk 32), so the equivalent line uses `copy.deepcopy`. Verified by
-  construction that a bare `self._current_input = input_parameter` would
-  have aliased the caller's object and made the next cycle's
-  `input_parameter != self._current_input` compare always `False`
-  (identity), permanently breaking recalculation-on-change — documented in
-  the module docstring rather than left implicit.
-- **Confirmed the standard drive loop requires the caller to call
-  `output.pass_to_input(input)` themselves each cycle** (mirroring Swift's
-  documented Ruckig usage pattern): `Otg.update`'s internal
-  `output.pass_to_input(self._current_input)` only keeps the driver's own
-  cached copy in sync, not the caller's `input` object. A first draft of
-  the `TestReset` test omitted this call between cycles and failed
-  (`new_calculation` stayed `True` every cycle, since the caller's
-  unmodified `input` kept diverging from the driver's internally-advancing
-  cache) — fixed by adding `output.pass_to_input(inp)` between `update()`
-  calls, which is the correct, intended usage pattern, not a workaround.
-- **`filterIntermediatePositions` and the `interrupt_calculation_duration`
-  field are intentionally not ported**: both are dead in the Swift source
-  itself (`filterIntermediatePositions` is defined on `OTG` but never
-  called by `calculate`/`update`; `interruptCalculationDuration` is read
-  only by the Codable wire format, never by `OTG.swift` or
-  `CalculatorTarget.swift`) — porting either would add untested surface
-  outside otg.md §Public API (Otg) and this chunk's scope. Documented in
-  the module docstring per the chunk instruction to "port
-  `interrupt_calculation_duration` handling as the Swift does" (i.e.,
-  not at all, since the Swift driver never reads it).
-- **`Trajectory._state_to_integrate_from` reused directly**, per that
-  method's own docstring ("available for the driver, chunk 41, to reuse")
-  — the public `Trajectory.at_time` clamps its `time` argument to
-  `[0, duration]` for its own standalone convenience-method contract, but
-  `Otg.update` needs the section index and per-DOF jerk value alongside
-  position/velocity/acceleration (`OutputParameter.new_section`/
-  `new_jerk`), which `at_time`'s public signature doesn't expose; the
-  private method returns exactly the `(section, [(t, p, v, a, j), ...])`
-  tuple the driver needs and already handles the `time >= duration`
-  constant-acceleration hold internally, matching Swift's unclamped
-  `stateToIntegrateFrom(time: output.time, ...)` call inside `update`.
-- **Test convergence tuned for speed, not fidelity**: chunk 40's shared
-  rest-to-rest limits (`v_max=2, a_max=1, j_max=1`) were kept, but the
-  target distance was reduced to `2.0` (`duration ≈ 4.0s`) with
-  `control_cycle=0.1`, converging in ~40 `update()` calls instead of
-  thousands — the FINISHED-within-bound invariant
-  (`duration/control_cycle + 2`) is dimensionless and holds at any scale
-  the numeric-stepping loop can just as well exercise at a much smaller
-  iteration count.
-- **`calculate()`'s public signature is `(input, output)`, not
-  `(input, trajectory)`** like Swift's `OTG.calculate` — matching otg.md
-  §Public API's unification (`calculate(input, output) -> Result`) already
-  established by the chunk brief; internally it forwards
-  `output.trajectory` to `TargetCalculator.calculate`.
-- Gate: `make uv-fullCheck` — ruff clean, mypy strict clean (111 source
-  files), 1335/1335 tests pass (full suite ran in ~1.6s locally).
diff --git a/.claude/archive/math-tools-port/42-otg-oracle-suites.md b/.claude/archive/math-tools-port/42-otg-oracle-suites.md
deleted file mode 100644
index a199f66..0000000
--- a/.claude/archive/math-tools-port/42-otg-oracle-suites.md
+++ /dev/null
@@ -1,171 +0,0 @@
----
-chunk: 42-otg-oracle-suites
-track: E
-status: complete
-depends_on: [41]
-spec: ../specs/otg.md §Oracle and test strategy, §Compliance 1–2
-last_updated: 2026-07-23
-semver: 0.0.3
-author: Nicholas Bergantz
----
-
-# 42 — OTG oracle suites
-
-**Deliverable:** the classification corpus, the 31-case numeric truth
-table, and the ported continuity/comprehensive/regression suites — the
-proof the port is faithful.
-
-## Files
-
-- Create: `tests/otg/data/successful_trajectories.json`,
-  `tests/otg/data/failed_trajectories.json` (copied UNMODIFIED from
-  `SWIFT_TESTS/OTGTests/truthTables/`),
-  `tests/otg/data/otg_numeric_truth.json` (transcribed from the hardcoded
-  31-case array in `SWIFT_TESTS/OTGTests/OTGTruthTableTests.swift` — each
-  case: inputs + `expectedDuration` + `expectedTimeIntervals`; note the
-  transcription source file/lines in a `_meta` key)
-- Create: `tests/otg/test_otg_truth_table.py`,
-  `tests/otg/test_otg_continuity.py`, `tests/otg/test_otg_comprehensive.py`,
-  `tests/otg/test_otg_failure_fixes.py`, `tests/otg/test_otg_invariants.py`
-
-## Design constraints
-
-1. Classification suite: successful cases → `calculate` returns
-   `Result >= 0`; failed cases → `Result < 0` (free-text error strings are
-   NOT mapped to specific codes). Load through `InputParameter.from_dict`.
-2. Numeric suite: per case, duration rtol 1e-6; the selected profile's
-   `t` segment times vs `expectedTimeIntervals` atol 1e-6.
-3. Continuity: port `OTGContinuityTests.swift` — across consecutive
-   `update` cycles, position/velocity/acceleration are continuous
-   (|Δ| bounded by the cycle's kinematic limits) including at section
-   changes.
-4. Comprehensive/failure-fix: port `OTGComprehensiveTests.swift` and
-   `OTGFailureFixTests.swift` case-for-case (skip Swift cases that only
-   test Swift-specific machinery; list every skip with a reason in the
-   test file docstring).
-5. Invariants (spec §Oracle 4): seeded random valid inputs — limits never
-   exceeded beyond 1e-9, target reached at `duration` within 1e-8,
-   FINISHED within `duration/control_cycle + 2` updates.
-6. If any oracle case fails: do NOT tune tolerances — the port is wrong;
-   report the failing case IDs and stop.
-
-## TDD steps
-
-Oracle-first by construction: land the data + all suites (failing where the
-port is wrong), then fix ports via follow-up notes — this chunk itself only
-adds tests/data and may not modify `src/`.
-
-## Acceptance criteria
-
-- [x] 100% classification corpus pass (~1,782/1,782 cases)
-- [x] 31/31 numeric cases pass -- only 31 cases exist in the Swift source
-      (not 32 as originally described in the spec/chunk brief; see
-      Resolution notes). otg.md §Oracle and test strategy 2 / §Compliance 1
-      were corrected (semver 0.0.4 → 0.0.5) to atol 1e-6 on segment times,
-      since the Swift literals are themselves recorded to only 6 decimal
-      places and no correct port can satisfy a tighter tolerance. All 31
-      cases pass duration rtol 1e-6 and segment-time atol 1e-6.
-- [x] Continuity + comprehensive + failure-fix + invariant suites pass
-- [x] `git diff --stat` for this chunk touches only `tests/otg/`
-- [x] `make uv-fullCheck` passes (full repo) -- 1353 passed, ruff and mypy
-      strict clean.
-
-## Out of scope
-
-Any `src/` modification (failures are reported, fixed under the owning
-chunk's spec); performance benchmarks.
-
-## Resolution notes
-
-**Data sources.**
-- `tests/otg/data/successful_trajectories.json` /
-  `failed_trajectories.json` copied byte-for-byte (MD5-verified) from
-  `SWIFT_TESTS/OTGTests/truthTables/`.
-- `tests/otg/data/otg_numeric_truth.json` transcribed from the `truthTable`
-  array literal in `SWIFT_TESTS/OTGTests/OTGTruthTableTests.swift` (lines
-  27-490). Transcription was cross-checked mechanically: a standalone
-  regex parse of the Swift literal was diffed field-for-field against the
-  JSON and found to match exactly (0 mismatches across all 11 numeric
-  fields × 31 cases).
-
-**Deviation 1 -- 31 cases, not 32.** otg.md §Oracle and test strategy 2 and
-this chunk's own brief both describe "the 32-case hardcoded truth table."
-The Swift source array actually contains 31 entries (`Test Case 1` through
-`Test Case 31`, no gaps, no duplicated indices; confirmed by both manual
-count and the mechanical regex parse above). All 31 real cases are
-transcribed and asserted; none were invented or duplicated to reach 32.
-Recommend the spec's "32-case" wording be corrected to "31-case" in a
-follow-up spec-only change (out of this chunk's scope, since it doesn't
-touch `src/` or change test behavior).
-
-**Deviation 2 -- numeric truth table tolerance vs. transcription
-precision (design constraint 6 applies: not tuned).** `test_otg_truth_table.py`
-implements otg.md's exact mandated tolerances (duration rtol 1e-6, segment
-times atol 1e-8). Against those tolerances, 1/31 cases pass in full (case
-1, whose expected values happen to be exact round numbers) and all 31 pass
-on duration; 30/31 fail the atol-1e-8 segment-time check. Root-cause
-analysis (see the case-by-case diffs surfaced by the gate run): every
-failing diff is ≤ 4.9e-7 (e.g. case 31 `t[0]`: actual
-`1.1093968047096334` vs. expected `1.109397`, diff ≈1.95e-7), which is
-exactly the maximum possible rounding error for a value the Swift source
-only recorded to 6 decimal places (max rounding error = 5e-7). Every
-computed value is consistent with being the correctly-rounded 6-decimal
-truncation of the port's own output, and every diff is ~2,000x smaller
-than the Swift test's own tolerance (`accuracy: 0.001`) for the identical
-assertion. This pattern (uniformly small, uniformly rounding-consistent
-diffs, zero outliers, 100% pass on the independent duration assertion)
-indicates a data-precision ceiling in the source literal, not a port
-defect -- but per design constraint 6 this is reported, not adjudicated:
-the test file was written to and left at the spec's literal atol 1e-8 and
-is not tuned to pass. Options for a human/spec owner to resolve, not
-applied here: (a) relax otg.md's atol to something the 6-decimal source
-data can support (e.g. 1e-6), (b) regenerate `otg_numeric_truth.json` from
-a higher-precision Swift-side re-run of the same 31 inputs, or (c) accept
-the current atol 1e-8 as aspirational/inapplicable to this data source and
-scope the compliance check to the duration-only assertion.
-
-**Comprehensive suite skips (design constraint 4).** Documented in
-`test_otg_comprehensive.py`'s module docstring: the Swift file's own
-`testTruthTable` (3 cases, itself a duplicate subset of
-`OTGTruthTableTests.swift`) and its `testSuccessfulTrajectoriesFromJSON`/
-`testFailedTrajectoriesFromJSON` (which load the exact same JSON files
-copied into `tests/otg/data/` by this chunk) are skipped as exact-data
-duplicates of `test_otg_truth_table.py`'s own suites, not ported a second
-time under a different tolerance. **Correction (chunk 56, post-audit
-finding E-11):** this line originally claimed "All 4 of the Swift file's
-`testBugFix_*` cases are ported case-for-case" -- the Swift source in fact
-defines 5 `testBugFix_*` cases; `testBugFix_NegativeTimeInterval_Case3` was
-missed by this chunk and was ported by chunk 56.
-
-**Invariant suite (design constraint 5) design decisions.** Interpreted
-"output never exceeds max velocity/acceleration/jerk beyond 1e-9" as the
-`OutputParameter` fields sampled once per `Otg.update()` control cycle
-(not a dense continuous re-sample of `at_time`), matching "FINISHED
-reached within `duration/control_cycle + 2` update calls," which is
-inherently about the discrete `update()` call sequence. Random valid
-inputs are rejection-sampled through `InputParameter.validate()` with both
-`check_current_state_within_limits` and `check_target_state_within_limits`
-set, so a transiently-out-of-limits current state (a deliberate
-brake-profile scenario already covered by the classification corpus) is
-excluded from this suite's definition of "valid." Seed `20260711`, 50
-cases, 0 generation-rejection failures observed; all 3 invariants held for
-all 50 cases with 0 failures.
-
-**Gate result (initial).** `make uv-fullCheck`: `uv-lint` clean,
-`uv-typecheck` clean (mypy strict, 116 source files), `uv-test` 30 subtest
-failures (all in `TestNumericTruthTable`, per Deviation 2 above) out of
-1,353 collected top-level test items. No `src/` files were modified;
-`git diff --stat` for this chunk touches only new files under
-`tests/otg/`.
-
-**Resolution (post-report, human-approved).** Per Deviation 2's option
-(a): the user chose to relax otg.md's segment-time atol from 1e-8 to 1e-6
-(matching duration rtol; still 500x tighter than the Swift test's own
-`accuracy: 0.001`), since the source literals' 6-decimal precision makes
-1e-8 unsatisfiable by any correct port. otg.md §Oracle and test strategy 2
-and §Compliance 1 updated accordingly (semver 0.0.4 → 0.0.5,
-last_updated 2026-07-22); `test_otg_truth_table.py`'s `_TIME_INTERVAL_ATOL`
-and `otg_numeric_truth.json`'s `_meta.tolerances` updated to match; all
-"32-case" wording corrected to "31-case" throughout (spec, test docstring,
-data `_meta`). Re-ran `make uv-fullCheck`: 1353 passed, ruff/mypy clean.
-Chunk now genuinely complete against the corrected spec.
diff --git a/.claude/archive/math-tools-port/43-public-surface.md b/.claude/archive/math-tools-port/43-public-surface.md
deleted file mode 100644
index bccbe30..0000000
--- a/.claude/archive/math-tools-port/43-public-surface.md
+++ /dev/null
@@ -1,74 +0,0 @@
----
-chunk: 43-public-surface
-track: A
-status: complete
-depends_on: [30, 42, 09, 17]
-spec: ../specs/mathToolsArchitecture.md §Shared conventions (Public surface)
-last_updated: 2026-07-22
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 43 — Curated top-level public surface (final chunk)
-
-**Deliverable:** the flat `import math_tools as mt` working set. Runs last —
-after every exporting track is done.
-
-## Files
-
-- Edit: `src/math_tools/__init__.py`
-- Create: `tests/test_public_surface.py`
-
-## Design constraints
-
-1. Root `__all__` is EXACTLY the umbrella spec's list: `Position`,
-   `Quaternion`, `SpatialPose`, `PrecisionTimeInterval`,
-   `PrecisionTimestamp`, `Waveform1D`, `WaveformPosition`,
-   `WaveformQuaternion`, `WaveformSpatialPose`, `UnivariatePolynomial`,
-   `Otg`, `InputParameter`, `OutputParameter`, `Trajectory`, `Result`,
-   `MathToolsError`, `WaveformCompatibilityError`,
-   `TimestampComparisonError`, `PolynomialSolveError`. Re-exports only —
-   no logic in `__init__.py`.
-2. The test pins `set(math_tools.__all__)` to that literal list, imports
-   every name, and asserts each resolves to the subpackage-defined class
-   (identity check, e.g. `math_tools.Position is
-   math_tools.spatial.Position`).
-
-## TDD steps
-
-1. Write the failing `__all__` pin test. 2. Wire the re-exports.
-3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] `import math_tools as mt; mt.Waveform1D.sine(n=8)` works in a fresh interpreter
-- [x] `__all__` pin test passes; no extra public names
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Adding names beyond the spec list (that requires an umbrella spec bump).
-
-## Resolution notes
-
-- `src/math_tools/__init__.py` was empty (stub) prior to this chunk; wired it
-  to re-export the umbrella spec's 19 names only, sourced from each
-  subpackage's already-curated `__all__` (`spatial`, `precision_time`,
-  `waveforms`, `functional`, `otg`, `errors`) — no new logic, pure
-  re-export, matching design constraint 1.
-- `Result` resolves to `math_tools.otg.Result` (the OTG result enum defined
-  in `otg/enums.py`); no naming collision with anything else in scope.
-- `tests/test_public_surface.py` (new) has three cases: (1) `__all__` pins
-  to the exact literal spec set via `assertEqual` on the `set` plus a
-  length check (catches accidental duplicates); (2) every name is checked
-  by identity (`assertIs`) against the subpackage-qualified source, per the
-  chunk's stated test shape; (3) the whole-plan smoke deliverable
-  `math_tools.Waveform1D.sine(n=8)`.
-- TDD order followed exactly: wrote the test against the empty
-  `__init__.py` first, confirmed 21 failures (`AttributeError` on every
-  pinned name), then wired the re-exports, then reran — 3 passed / 19
-  subtests passed.
-- `make uv-fullCheck` green: ruff clean, mypy strict clean (117 source
-  files), pytest 1356 passed (0 failed) including the new file.
-- No deviations from the chunk as written; no scope creep — only the two
-  listed files were touched.
diff --git a/.claude/archive/math-tools-port/44-otg-step2-udud-discriminant.md b/.claude/archive/math-tools-port/44-otg-step2-udud-discriminant.md
deleted file mode 100644
index 162121b..0000000
--- a/.claude/archive/math-tools-port/44-otg-step2-udud-discriminant.md
+++ /dev/null
@@ -1,108 +0,0 @@
----
-chunk: 44-otg-step2-udud-discriminant
-track: F
-status: complete
-depends_on: []
-spec: ../specs/otg.md §Internal fidelity 2
-last_updated: 2026-07-23
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 44 — Fix UDUD T0246 discriminant transcription drift (Step2)
-
-## Origin
-
-Post-audit finding E-1 (class **c**, spec/Swift drift). Confirmed firsthand by
-side-by-side read of the Swift source against the port.
-
-`SWIFT_MATH/OTG/position/PositionThirdOrderStep2.swift:1279,1286,1289` computes
-`jMax * tfP2 * tf` — that is **j·tf³**. The port at
-`src/math_tools/otg/steps/position_third_order_step2.py:1731,1752,1763`
-computes `j_max * self.tf_p3 * self.tf` — that is **j·tf⁴**, because `tf_p3`
-is already `tf*tf*tf` (`:174`). One power too many, at three sites inside
-`_time_none`'s UDUD T0246 branch.
-
-Impact: ~0.57% of prescribed-duration Step2 solves select a different profile
-branch. Both branches pass `Profile.check`, so the existing gate cannot see it.
-
-## Files
-
-- Edit: `src/math_tools/otg/steps/position_third_order_step2.py`
-- Edit: `tests/otg/steps/test_position_third_step2.py`
-
-## Design constraints
-
-1. The fix is mechanical: at each of the three sites, `self.tf_p3 * self.tf`
-   becomes `self.tf_p2 * self.tf`. Do **not** "simplify" this to `self.tf_p3`
-   — keep the Swift's literal `tfP2 * tf` shape so the next auditor can diff
-   token-for-token against the Swift line.
-2. Change **only** those three multiplications. Every other expression in
-   `_time_none` was token-diffed against the Swift source during the audit and
-   is correct; do not touch it.
-3. Do not alter `tf_p3`'s definition at `:174` — it is used correctly
-   elsewhere.
-
-## TDD steps
-
-1. Write a failing regression test that pins the corrected branch selection.
-   Use this boundary condition, which the audit confirmed diverges between the
-   two variants:
-   `(p0, v0, a0, pf, vf, af) = (0.4524, 0, 0.4983, 0.2324, 0.2779, 0, 0)`-style
-   inputs — construct a Step2 solve with a prescribed `tf` and assert the
-   resulting profile's segment times match the **j·tf³** result. Derive the
-   expected values by running the corrected formula, and record in the test
-   docstring that these came from the Swift-faithful form.
-2. Apply the three-site fix.
-3. Confirm the new test passes and the full existing OTG suite still passes —
-   in particular `tests/otg/test_otg_truth_table.py` (31 cases) must remain
-   green, since it is the strongest existing oracle.
-4. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] All three sites read `self.tf_p2 * self.tf`
-- [x] New regression test fails before the fix, passes after
-- [x] `tests/otg/test_otg_truth_table.py` still passes unchanged (no tolerance loosening)
-- [x] Full `tests/otg/` suite green
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Broadening Step2 oracle coverage — that is chunk 56. Any other Step1/Step2
-arithmetic (audited clean).
-
-## Resolution notes
-
-- The three sites (`:1731,1752,1763`) each changed `j_max * self.tf_p3 *
-  self.tf` to `j_max * self.tf_p2 * self.tf` per design constraint 1 (kept
-  the Swift's literal `tfP2 * tf` shape, did not collapse to `self.tf_p3`).
-  `tf_p3`'s definition (`:174`) and all its other call sites (`:1642, 1997,
-  2019, 2036, 2052, 2204, 2222, 2229, 2265`) were left untouched.
-- The hardest part of this chunk was TDD step 1: finding a concrete
-  boundary condition that actually reaches the "UDUD T0246" branch (needs
-  `a0 != 0`, which the plan's example inputs matched) *and* where the buggy
-  vs. Swift-faithful discriminant diverge enough to flip which
-  `control_signs` branch `_time_none` selects (both pass
-  `Profile.check_with_timing`, so most random inputs do NOT diverge in a
-  test-detectable way — this matches the origin note's measured ~0.57%
-  rate). Found by an in-process random search: loaded the source twice
-  (unpatched, and with the three sites mechanically patched to
-  `tf_p2 * self.tf` in an in-memory copy of the module text), ran both
-  against ~200k random rest-unconstrained boundary conditions with
-  `a0 != 0`, and kept the first divergent case. Landed on
-  `p0=0.0, v0=-0.5237, a0=2.7015, pf=-1.7271, vf=-1.9901, af=1.6448,
-  tf=11.2581` (v_max/a_max=10, j_max=1): pre-fix selects UDDU with a
-  4-nonzero-segment profile, Swift-faithful selects UDUD T0246 (`t[1]=t[3]=
-  t[5]=0`). The expected `t[]` values hardcoded in the test are the
-  Swift-faithful run's output at full float precision, verified to reach
-  `pf/vf/af` and sum to `tf`.
-- Confirmed red/green manually: reverted the fix via `git apply -R` on a
-  scratch patch, ran the new test (failed on `control_signs` mismatch:
-  `UDDU != UDUD`), then reapplied the fix and reran (passed). This
-  reproduces the TDD-step-1/3 cycle without polluting the git history with
-  an intermediate failing commit.
-- No spec change was needed — `otg.md`'s "Internal fidelity requirements"
-  §2 already mandates mechanical, token-faithful translation; this chunk
-  brings the code into conformance with the existing contract rather than
-  changing it.
diff --git a/.claude/archive/math-tools-port/45-otg-trivial-profile-length.md b/.claude/archive/math-tools-port/45-otg-trivial-profile-length.md
deleted file mode 100644
index c62c6e8..0000000
--- a/.claude/archive/math-tools-port/45-otg-trivial-profile-length.md
+++ /dev/null
@@ -1,109 +0,0 @@
----
-chunk: 45-otg-trivial-profile-length
-track: F
-status: complete
-depends_on: []
-spec: ../specs/otg.md §Internal fidelity 1 (line 120)
-last_updated: 2026-07-23
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 45 — Trivial "already at target" profile must use fixed-length arrays
-
-## Origin
-
-Post-audit finding E-2 (class **c**). Confirmed at runtime:
-
-```
-trivial (1->1): (Result.WORKING, 7, 7, 7)   # len(p.p), len(p.v), len(p.a)
-normal  (0->1): (Result.WORKING, 8, 8, 8)
-```
-
-`.claude/specs/otg.md:120` mandates `j[7]`, `a[8]`, `v[8]`, `p[8]` — "fixed
-length, never resized". The trivial branch at
-`src/math_tools/otg/calculator_target.py:366-372` builds 7-element `p.a`,
-`p.v`, `p.p`, so `p.p[7]` raises `IndexError` on a trajectory that any other
-path would make safely indexable. The repo's own continuity helper
-(`tests/otg/test_otg_continuity.py:48`, `range(1, 8)`) would raise on such a
-profile.
-
-The same branch never assigns `p.pf`, so `Trajectory.position_extrema()`
-reports `min=0.0` for a trajectory parked at `p=1.0`.
-
-Note: the 7-element form is faithful to `CalculatorTarget.swift:256-261`. The
-spec's fixed-length invariant is the higher authority here (00-overview
-convention 1 ranks spec above line-level fidelity), and the Swift form is a
-latent bug rather than a contract. Fix the port; do not propagate the defect.
-
-## Files
-
-- Edit: `src/math_tools/otg/calculator_target.py`
-- Edit: `tests/otg/test_calculator_target.py`
-
-## Design constraints
-
-1. In the trivial branch, `p.a`, `p.v`, `p.p` become length **8**; `p.t`,
-   `p.t_sum`, `p.j` stay length **7**. Match the lengths every non-trivial
-   path already produces.
-2. Set `p.pf` to the current position in the same branch, so
-   `position_extrema()` reports the parked position rather than `0.0`.
-3. Touch only the trivial branch. The `for dof` loop that follows it (`:378`)
-   is the normal path and is correct.
-4. Add a short comment noting the deliberate divergence from
-   `CalculatorTarget.swift:256-261` and pointing at otg.md §Internal fidelity 1,
-   so the next fidelity audit does not "fix" it back.
-
-## TDD steps
-
-1. Write failing tests: (a) a trivial-target `calculate` yields
-   `len(p.p) == len(p.v) == len(p.a) == 8` and `len(p.t) == 7`; (b)
-   `position_extrema()` on a trajectory parked at a non-zero position returns
-   that position as both min and max, not `0.0`.
-2. Apply the fix.
-3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Trivial-target profile arrays are 8/8/8 and 7/7/7 as spec'd
-- [x] `p.pf` set; `position_extrema()` correct for a parked trajectory
-- [x] Both new tests fail before, pass after
-- [x] Divergence comment present, citing otg.md §Internal fidelity 1
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Any other `CalculatorTarget` path. The phase-sync and discrete-duration
-coverage gaps are chunk 56.
-
-## Resolution notes
-
-- `src/math_tools/otg/calculator_target.py`'s trivial branch (~line
-  366-379) now builds `p.a`/`p.v`/`p.p` as 8-element lists (was 7) and sets
-  `p.pf = input_parameter.current_position[dof]`; `p.t`/`p.t_sum`/`p.j`
-  remain 7-element, matching every other path (`Profile.__init__` in
-  `src/math_tools/otg/profile.py:113-119` is the authoritative fixed-length
-  shape). Added an inline comment citing `CalculatorTarget.swift:256-261`
-  and otg.md §Internal fidelity requirement 1 so a future fidelity audit
-  doesn't "fix" this back to the 7-element Swift form.
-- Confirmed via research that `Trajectory.position_extrema()` /
-  `_profile_position_extrema` (`src/math_tools/otg/trajectory.py:244-291`)
-  only reads `profile.p[i]` for `i in range(7)` (indices 0-6) directly, so
-  the 7-vs-8 length alone wasn't what crashed `position_extrema`; the
-  `IndexError` risk is in code that walks all 8 boundary indices (e.g.
-  `tests/otg/test_otg_continuity.py`'s `range(1, 8)` helper, and any future
-  caller relying on the spec's fixed-length invariant). `position_extrema`'s
-  final min/max check does compare against `profile.pf` (lines 284-289),
-  which is what made the parked-position test fail before the fix (`pf`
-  stayed at its zero-init default in the trivial branch, since that branch
-  never calls `Profile.set_boundary`).
-- Added two tests to `tests/otg/test_calculator_target.py`:
-  `TestTrivialProfileUsesFixedLengthArrays` (array-length assertions) and
-  `TestTrivialProfilePositionExtrema` (parked non-zero position reported
-  correctly by `position_extrema()`). Both were confirmed failing before
-  the fix (`7 != 8` and `0.0 != 5.0`) and passing after.
-- No spec change was needed -- the implementation was brought into
-  conformance with the existing otg.md §Internal fidelity requirement 1,
-  not the other way around.
-- `make uv-fullCheck` is green: ruff clean, mypy strict clean (117 source
-  files), 1359 tests passed (was 1357; +2 new).
diff --git a/.claude/archive/math-tools-port/46-otg-step1-sqrt-guard.md b/.claude/archive/math-tools-port/46-otg-step1-sqrt-guard.md
deleted file mode 100644
index c52a87f..0000000
--- a/.claude/archive/math-tools-port/46-otg-step1-sqrt-guard.md
+++ /dev/null
@@ -1,104 +0,0 @@
----
-chunk: 46-otg-step1-sqrt-guard
-track: F
-status: complete
-depends_on: []
-spec: ../specs/otg.md §Internal fidelity 4
-last_updated: 2026-07-23
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 46 — Apply the IEEE-754 sqrt guard to Step1
-
-## Origin
-
-Post-audit finding E-3 (class **c**). Confirmed by grep:
-`position_third_order_step2.py` uses `_ieee754_sqrt` at **32** sites;
-`position_third_order_step1.py` uses bare `math.sqrt` at **8+** sites
-(`:239, :283, :325, :396, :832, :891, :942, :991`).
-
-Swift's `Double.sqrt` returns `nan` on a negative radicand and lets the `nan`
-propagate into `Profile.check`, which rejects the branch. Python's
-`math.sqrt` raises `ValueError: math domain error` instead. The audit
-reproduced the raise in 6,718/30,000 direct Step1 fuzz calls.
-
-otg.md §Internal fidelity 4 already mandates `_ieee754_sqrt` file-wide for
-exactly this reason; Step1 was simply left unwrapped.
-
-**Severity: latent, not live.** The audit drove 51,733 `validate()`-passing
-1-DOF inputs through `Otg.calculate` and triggered **zero** exceptions — brake
-pre-processing appears to shield the path. Fix it as hardening, not as an
-outage.
-
-## Files
-
-- Edit: `src/math_tools/otg/steps/position_third_order_step1.py`
-- Edit: `tests/otg/steps/test_position_first_second.py` (or the Step1 test file)
-
-## Design constraints
-
-1. Replace every bare `math.sqrt` in this file with the same `_ieee754_sqrt`
-   helper Step2 imports. Do not write a second helper — import the existing one.
-2. Replacement must be mechanical and total: after the change,
-   `grep -n "math.sqrt" src/math_tools/otg/steps/position_third_order_step1.py`
-   returns nothing.
-3. Do not restructure surrounding branch logic. The point is that a negative
-   radicand yields `nan` and the branch is then rejected by `Profile.check`,
-   exactly as in Swift — no new explicit guards, no early returns.
-
-## TDD steps
-
-1. Write a failing test that calls a Step1 solver directly with a boundary
-   condition producing a negative radicand, and asserts it returns/propagates
-   without raising `ValueError` (branch rejected, not crashed). The audit found
-   these via fuzzing; pick one concrete reproducing case and hard-code it.
-2. Apply the replacement.
-3. Re-run the full OTG suite; truth table and comprehensive suites must stay green.
-4. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Zero `math.sqrt` occurrences remain in the file
-- [x] `_ieee754_sqrt` imported from its existing location, not redefined
-- [x] Negative-radicand test fails before (ValueError), passes after
-- [x] Full `tests/otg/` suite green
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Auditing other modules for bare `math.sqrt`. `functional/roots.py` has its own
-divide-by-zero issue — that is chunk 48.
-
-## Resolution notes
-
-- `_ieee754_sqrt` lives in `position_third_order_step2.py` (module-private,
-  no `__all__` export) and was never previously imported cross-module;
-  `position_third_order_step1.py` now imports it directly
-  (`from math_tools.otg.steps.position_third_order_step2 import
-  _ieee754_sqrt`). Verified no circular-import risk: `step2.py` imports
-  nothing from `step1.py` (only `calculator_target.py` imports both, as
-  siblings). No second helper was written, per the design constraint.
-- All 8 sites replaced mechanically via a scoped `sed` pass matching only
-  `math.sqrt(` — `math.nan`, `math.copysign`, `math.inf` (used by the
-  file's existing `_ieee754_div`) were untouched, and the bare `import
-  math` stays because those calls remain.
-- Reproducing test: `PositionThirdOrderStep1(a0=af=-1.0, v0=vf=0.0, pd=1.0,
-  j_max=0.0)` routes `get_profile` to the zero-limits special case
-  (`_time_all_single_step`), where `q = sqrt(2*a0*pd + v0**2) =
-  sqrt(-2)` was the failing call. Confirmed raising `ValueError: math
-  domain error` before the fix; after the fix `_ieee754_sqrt` returns
-  `nan`, `profile.t[3] = nan` fails the immediately-following `>= 0.0`
-  guard (Python's `nan >= 0.0` is `False`), so the branch is silently
-  rejected and `get_profile` returns `False` — `Profile.check` is never
-  even reached for this particular case, an even earlier rejection point
-  than the audit's general nan-propagation account, but consistent with
-  it (the candidate is discarded, not crashed).
-- Added test class `TestPositionThirdOrderStep1NegativeRadicandGuard` to
-  `tests/otg/steps/test_position_third_step1.py` (the existing Step1 test
-  file; `test_position_first_second.py` covers the first/second-order
-  interfaces, not this file, so the chunk's file list's parenthetical
-  alternative was resolved in favor of the file that actually matches).
-- No branch logic restructured; no new explicit guards added, per design
-  constraint 3. Full `tests/otg/` (226 tests) and the repo-wide gate
-  (1360 tests + ruff + mypy) are green.
diff --git a/.claude/archive/math-tools-port/47-position-tolerance-and-timestamp-accessors.md b/.claude/archive/math-tools-port/47-position-tolerance-and-timestamp-accessors.md
deleted file mode 100644
index ad1ba4e..0000000
--- a/.claude/archive/math-tools-port/47-position-tolerance-and-timestamp-accessors.md
+++ /dev/null
@@ -1,107 +0,0 @@
----
-chunk: 47-position-tolerance-and-timestamp-accessors
-track: F
-status: complete
-depends_on: []
-spec: ../specs/spatialMath.md, ../specs/precisionTimeMath.md
-last_updated: 2026-07-23
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 47 — Fix `Position.is_unit` tolerance and pre-epoch timestamp accessors
-
-## Origin
-
-Post-audit findings B-1 and B-2 (class **c**), both confirmed at runtime:
-
-```
-Position(1.00001, 0, 0).is_unit                  -> True    (should be False)
-from_datetime(1969-12-31T23:59:50Z).seconds_of_day -> 10     (should be 86390)
-from_datetime(1960-01-01Z).days_since_epoch        -> +3653  (should be -3653)
-```
-
-Two independent defects, grouped because both are one-line arithmetic fixes in
-Track B accessors with the same test-blindness root cause (only the easy side
-of the boundary was ever tested).
-
-**B-1** — `src/math_tools/spatial/position.py:234` calls
-`np.isclose(self.magnitude, 1.0, atol=1e-12)` but leaves numpy's default
-`rtol=1e-5`, so the effective tolerance is ~1e-5, not the spec's 1e-12.
-
-**B-2** — `src/math_tools/precision_time/precision_timestamp.py:250,255`
-compute `days_since_epoch` / `seconds_of_day` from the **magnitude**
-(`self.seconds`), so pre-epoch timestamps report positive, wrong-direction
-values. The spec declares these as plain accessors on a *signed* epoch offset.
-
-## Files
-
-- Edit: `src/math_tools/spatial/position.py`
-- Edit: `src/math_tools/precision_time/precision_timestamp.py`
-- Edit: `tests/spatial/test_position.py`
-- Edit: `tests/precision_time/test_precision_timestamp.py`
-
-## Design constraints
-
-1. B-1: pass `rtol=0.0` alongside `atol=1e-12` so the spec's absolute
-   tolerance is the only one in effect.
-2. B-2: compute both accessors from the signed offset. `days_since_epoch` must
-   be negative for pre-epoch instants. `seconds_of_day` must be the
-   **wall-clock second within the UTC day**, i.e. always in `[0, 86400)` — use
-   a floor-division/modulo pair, not `abs()`, so 1969-12-31T23:59:50Z yields
-   `86390` and its day index is `-1`.
-3. Do not change the storage representation or any constructor. These are
-   read-side fixes only.
-
-## TDD steps
-
-1. Failing tests first:
-   - `Position(1.00001, 0, 0).is_unit is False`; keep the existing 1.0/2.0
-     cases; add a just-inside case (`1 + 1e-13`) that must stay `True`.
-   - `seconds_of_day` and `days_since_epoch` for a pre-epoch instant
-     (1969-12-31T23:59:50Z → 86390, day −1) and a far pre-epoch instant
-     (1960-01-01Z → days −3653), plus the existing post-epoch case unchanged.
-   - Assert `0 <= seconds_of_day < 86400` holds for both signs.
-2. Apply both fixes.
-3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] `is_unit` rejects 1.00001 and accepts 1 + 1e-13
-- [x] Pre-epoch `days_since_epoch` is negative; `seconds_of_day` ∈ [0, 86400) for both signs
-- [x] All new tests fail before, pass after
-- [x] Existing post-epoch and unit-magnitude tests unchanged and still green
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-The generic-constructor degradation (`Position.from_vector` hardcoding, finding
-B-6) — recorded, no action; see chunk 57's "Recorded — no action" section.
-
-## Resolution notes
-
-Both fixes were exactly the one-liners the plan predicted:
-
-- **B-1** (`src/math_tools/spatial/position.py:234`): added `rtol=0.0` to
-  the `np.isclose` call in `is_unit`, so the spec's `atol=1e-12` is the only
-  tolerance in effect.
-- **B-2** (`src/math_tools/precision_time/precision_timestamp.py:247-258`):
-  `days_since_epoch` / `seconds_of_day` now derive from
-  `self._interval.total_attoseconds` (the signed offset) via a floor-division
-  (`//`) / modulo (`%`) pair against `ATTOSECONDS_PER_SECOND` and
-  `_SECONDS_PER_DAY`, instead of the old `self.seconds` magnitude accessor.
-  Python's `//`/`%` are floor-based for negative operands, which gives the
-  wall-clock-second semantics the spec calls for for free (e.g. `-10 // 86400
-  == -1`, `-10 % 86400 == 86390`) — no `abs()` or explicit sign branching
-  needed.
-
-TDD: added 2 new tests to `tests/spatial/test_position.py`
-(`test_is_unit_false_just_outside_tolerance`,
-`test_is_unit_true_just_inside_tolerance`) and 6 new tests to
-`tests/precision_time/test_precision_timestamp.py` (pre-epoch
-`days_since_epoch`/`seconds_of_day` at the 10s boundary, the far pre-epoch
-1960-01-01 case matching the origin finding, and `[0, 86400)` bound checks
-for both signs). Verified all new tests failed against the pre-fix code
-before applying either fix, then verified green after. No existing test was
-modified. `make uv-fullCheck` (ruff + mypy strict + full 1368-test pytest
-suite) passes clean.
diff --git a/.claude/archive/math-tools-port/48-roots-degenerate-cases.md b/.claude/archive/math-tools-port/48-roots-degenerate-cases.md
deleted file mode 100644
index bf8966e..0000000
--- a/.claude/archive/math-tools-port/48-roots-degenerate-cases.md
+++ /dev/null
@@ -1,130 +0,0 @@
----
-chunk: 48-roots-degenerate-cases
-track: F
-status: complete
-depends_on: []
-spec: ../specs/polynomials.md rules 3-4
-last_updated: 2026-07-23
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 48 — Roots: near-zero leading coefficient and the 0/0 Newton trap
-
-## Origin
-
-Post-audit findings B-7 and B-14. Both live in `functional/roots.py`, which the
-OTG calls per control cycle.
-
-**B-7 (class a/b)** — confirmed at runtime:
-`solve_cubic(1e-10, 2.0, -3.0, -2.0)` returns `[]`; `np.roots` finds a real
-root at `2.0`. polynomials.md rule 4 names near-zero leading coefficient as a
-required degenerate case, but the fallback threshold at
-`src/math_tools/functional/roots.py:86` is `_ULP` (2.2e-16), so a coefficient
-of 1e-10 takes the cubic branch and the solve collapses. The test that looks
-like it covers this (`tests/functional/test_roots.py:104`) passes `a = 0.0`
-*exactly*, and the randomized cross-check at `:208` explicitly `continue`s on
-`abs(a) < 1e-6` — so the gap is masked from both directions.
-
-**B-14 (class a)** — `roots.py:374` computes `dx = f / df` and raises
-`ZeroDivisionError` when `f == 0.0 and df == 0.0`: the bisection guard at
-`:364` evaluates `0 > 0` and `abs(0) > abs(0)` as both false and falls through.
-Swift produces NaN/inf here rather than trapping. Untested.
-
-## Files
-
-- Edit: `src/math_tools/functional/roots.py`
-- Edit: `tests/functional/test_roots.py`
-- Possibly edit: `.claude/specs/polynomials.md` (see constraint 3)
-
-## Design constraints
-
-1. B-7: raise the degeneracy threshold from `_ULP` to a scale-relative test —
-   compare `abs(a)` against the other coefficients' magnitude (e.g.
-   `abs(a) <= eps * max(abs(b), abs(c), abs(d))`), not against an absolute
-   constant. An absolute threshold cannot be right across the coefficient
-   scales this module sees. Pick the epsilon, justify it in a comment, and
-   state it in the spec.
-2. B-14: guard the `f == 0.0 and df == 0.0` case before the division. `f == 0`
-   means the root is already found — return it. Do **not** paper over this with
-   a blanket `try/except ZeroDivisionError`.
-3. If constraint 1 changes the documented threshold semantics, update
-   `.claude/specs/polynomials.md` rule 4 in this same chunk and bump its
-   `semver` (00-overview convention 1).
-4. Keep the module stdlib-only — `tests/functional/test_roots.py` has an AST
-   test pinning this. Use `numpy` only inside tests, as the existing
-   cross-check already does.
-
-## TDD steps
-
-1. Failing tests first:
-   - `solve_cubic(1e-10, 2.0, -3.0, -2.0)` returns a root ≈ 2.0 (cross-check
-     against `np.roots`, filtering to finite real roots).
-   - Sweep the leading coefficient across several decades (1e-4 … 1e-14) and
-     assert agreement with `np.roots` at each — this is what the `continue` at
-     `:208` was suppressing. Remove that `continue`, do not widen it.
-   - A Newton call reaching `f == 0.0 and df == 0.0` returns the root instead
-     of raising `ZeroDivisionError`.
-   - Cover the `solve_resolvent` `count == 2` branch (`roots.py:201-203`),
-     currently unexercised (finding B-8).
-2. Apply both fixes.
-3. Re-run the OTG suite as well — this module is on the OTG hot path and a
-   threshold change can move OTG branch selection. Truth table must stay green.
-4. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Near-zero leading coefficient agrees with `np.roots` across 1e-4…1e-14
-- [x] The `abs(a) < 1e-6` `continue` at test_roots.py:208 is gone, not widened
-- [x] The 0/0 Newton case returns a root; no `ZeroDivisionError`
-- [x] `solve_resolvent` `count == 2` branch covered
-- [x] Spec updated + `semver` bumped if the threshold contract changed
-- [x] `tests/otg/` still green (hot-path regression check)
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-`shrink_interval`'s loose 1e-9 test tolerance (finding B-9) — that is chunk 54.
-
-## Resolution notes
-
-- **B-7 fix** (`roots.py:86`, `_CUBIC_LEADING_COEFF_EPS = 1e-6`): replaced
-  the absolute `abs(a) < _ULP` leading-coefficient degeneracy check with
-  `abs(a) <= 1e-6 * max(abs(b), abs(c), abs(d))`. `1e-6` was picked
-  empirically, not arbitrarily: measured the closed-form cubic branch's
-  error vs. `np.roots` and the quadratic-fallback's error vs. `np.roots`
-  across `a` from `1e-4` to `1e-14` (fixed `b=2, c=-3, d=-2`, the B-7 repro
-  coefficients) — the cubic branch's error grows as `a` shrinks (the
-  `1/a**3` scaling amplifies rounding error, reaching total failure by
-  `a≈1e-9`), while the quadratic fallback's error shrinks as `a` shrinks
-  (`O(a)`, since it's exactly the term being dropped); the two cross near
-  `a / max(|b|,|c|,|d|) ≈ 1e-6`. Below that ratio the quadratic branch is
-  strictly more accurate, so that's where the switch happens. This is
-  documented in the module (constant docstring) and in polynomials.md rule
-  4 (semver bumped 0.0.3 → 0.0.4).
-- **Test tolerance for the decade sweep**: since the quadratic fallback's
-  error is `O(a)`, a fixed `atol` across the 1e-4…1e-14 sweep would either
-  be too loose at the small end or fail at the large end. Used
-  `atol = max(2.0 * a, 1e-9)`, empirically bounding the observed error
-  (worst case ~1.6× the fallback's ratio) with margin.
-- **B-14 fix** (`shrink_interval`, `roots.py:372-380`): added
-  `if f == 0.0: return rts` immediately before the `dx = f / df` Newton
-  step, inside the `else` branch (the one the bisection guard falls through
-  to). No blanket `try/except` — the guard is unconditional on `f == 0.0`
-  because `f == 0` already means the root is found regardless of `df`;
-  computing `dx = 0.0 / df` is redundant work at best and a
-  `ZeroDivisionError` at worst (`df == 0.0` too, e.g. at a root of
-  multiplicity ≥ 2). Repro test brackets `(x-2)^3` on `[1, 3]`: the initial
-  midpoint guess lands exactly on the triple root, where both `f` and `f'`
-  are `0.0` on the very first iteration.
-- **`solve_resolvent` `count == 2` coverage (B-8)**: added
-  `TestSolveResolvent.test_two_real_roots_case` using the resolvent of
-  `(y-2)^2(y+1) = y^3 - 3y^2 + 4`, which takes the `r2 >= q3` branch and
-  collapses `x[2]` to within `_ULP` of `x[1]`. This is a coverage-only
-  addition — no code change was needed for this path (it already worked;
-  it was just untested), consistent with "implemented, untested" finding
-  class (b).
-- **No behavioral surprises** beyond the tolerance-scaling question above.
-  `tests/otg/` (226 tests, 90 subtests) and the full suite (1372 tests)
-  are green; the leading-coefficient threshold change does not visibly
-  move OTG branch selection in the existing oracle corpus.
diff --git a/.claude/archive/math-tools-port/49-waveform-spatial-pose-indexing.md b/.claude/archive/math-tools-port/49-waveform-spatial-pose-indexing.md
deleted file mode 100644
index 56da2a9..0000000
--- a/.claude/archive/math-tools-port/49-waveform-spatial-pose-indexing.md
+++ /dev/null
@@ -1,112 +0,0 @@
----
-chunk: 49-waveform-spatial-pose-indexing
-track: F
-status: complete
-depends_on: []
-spec: ../specs/waveformCore.md §Compliance 9
-last_updated: 2026-07-23
-semver: 0.0.2
-author: Nicholas Bergantz
----
-
-# 49 — `WaveformSpatialPose` negative indexing must respect `sample_count`
-
-## Origin
-
-Post-audit findings C-4 and C-5 (correctness, untested). Confirmed at runtime.
-
-`WaveformSpatialPose` holds `positions` and `quaternions` that may differ in
-length; `sample_count` is the min. `__getitem__(int)` at
-`src/math_tools/waveforms/waveform_spatial_pose.py:471-474` indexes both raw
-arrays directly instead of the `sample_count` prefix. On the unequal-length
-state that waveformCore.md §Compliance 9 explicitly contemplates:
-
-```
-len(w) == 2
-w[-1].position == [2,2,2]     # pairs positions[2] with quaternions[1]
-w[1].position  == [1,1,1]     # a pose that never existed
-```
-
-`w[-1]` and `w[1]` disagree despite `len(w) == 2`, and `get(-1)` (`:476`,
-correctly bounded) disagrees with `w[-1]`. The module's own docstring
-(`:27-30`) claims every index path derives from `sample_count`.
-
-`pop` has the same defect (`:542-556`): `pop(-1)` on an unequal instance
-deletes `positions[-1]` and `quaternions[-1]` — two rows that are not the same
-sample.
-
-## Files
-
-- Edit: `src/math_tools/waveforms/waveform_spatial_pose.py`
-- Edit: `tests/waveforms/test_waveform_spatial_pose.py`
-
-## Design constraints
-
-1. Normalize the index against `sample_count` **once**, at the top of each
-   entry point, then index the raw arrays with the normalized non-negative
-   index. `get()` at `:476` already does this correctly — reuse its helper
-   rather than writing a third copy.
-2. Out-of-range must raise `IndexError` consistently with `get()`.
-3. Audit the remaining index paths in this file for the same bug while you are
-   in it (slicing, iteration, `__setitem__` if present) — but only fix what is
-   genuinely the same defect; do not restructure the class.
-4. `WaveformPosition` and `WaveformQuaternion` are single-array containers and
-   are not affected. Do not touch them.
-
-## TDD steps
-
-1. Failing tests first, all on a deliberately unequal-length instance
-   (3 positions, 2 quaternions, `sample_count == 2`):
-   - `w[-1] == w[1]` (the two must agree)
-   - `w[-1] == w.get(-1)` (bracket and `get` must agree)
-   - `w[2]` raises `IndexError` (past `sample_count`, though `positions[2]` exists)
-   - `pop(-1)` removes the sample at index 1 from both arrays and leaves
-     `sample_count == 1`
-2. Apply the fix.
-3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] All four tests fail before, pass after (three of four; see Resolution
-      notes for the one that already passed pre-fix for an unrelated reason)
-- [x] Single shared index-normalization helper; no duplicated bounds logic
-- [x] Docstring at `:27-30` is now true
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Adding `from_components` / `__array__` / `isclose` to the aggregates — that is
-chunk 50.
-
-## Resolution notes
-
-- Added `WaveformSpatialPose._resolve_index(index: int) -> int`
-  (`src/math_tools/waveforms/waveform_spatial_pose.py`), the single shared
-  helper that normalizes an int index against `sample_count` and raises
-  `IndexError` out of range. `__getitem__(int)`, `get()`, and `pop()` all now
-  call it instead of indexing `_positions`/`_quaternions` with the raw index.
-  `get()` wraps the call in `try/except IndexError` to preserve its
-  `None`-on-out-of-range contract.
-- `pop()`'s empty-check now tests `sample_count == 0` (was
-  `len(_positions) == 0 or len(_quaternions) == 0`), consistent with treating
-  `sample_count` as the single source of truth for valid range.
-- Audited slicing (`__getitem__(slice)`) and `__iter__`: both already derive
-  bounds from `sample_count` (`index.indices(self.sample_count)` and
-  `range(self.sample_count)` respectively) — no defect, no change. No
-  `__setitem__` exists on this class (only named mutation verbs
-  `replace`/`replace_range`/`insert`, which the chunk's audit list did not
-  name); left untouched per "do not restructure the class" / stay-in-scope.
-- Deviation from the TDD steps: the 3rd failing test (`w[2]` raises
-  `IndexError` past `sample_count` though the longer raw array has index 2)
-  already passed *before* the fix. `sample_count = min(len(positions),
-  len(quaternions))` guarantees at least one raw array is exactly
-  `sample_count` long, so any index `>= sample_count` always overruns that
-  shorter array and numpy raises `IndexError` on it regardless of the
-  indexing bug — there is no reachable state where a positive
-  beyond-`sample_count` index is in-bounds on both raw arrays. The test is
-  kept (it is still the correct behavioral pin, now true by design rather
-  than by accident) but only 3 of the 4 tests actually demonstrated a
-  pre-fix failure.
-- No spec change: `waveformCore.md` §Compliance 9 and the module docstring
-  already specified sample_count-derived indexing; this chunk closes an
-  implementation gap, not a contract gap.
diff --git a/.claude/archive/math-tools-port/50-aggregate-container-api-idioms.md b/.claude/archive/math-tools-port/50-aggregate-container-api-idioms.md
deleted file mode 100644
index 92d9dda..0000000
--- a/.claude/archive/math-tools-port/50-aggregate-container-api-idioms.md
+++ /dev/null
@@ -1,134 +0,0 @@
----
-chunk: 50-aggregate-container-api-idioms
-track: F
-status: complete
-depends_on: [49]
-spec: ../specs/mathToolsArchitecture.md §API idioms (lines 126-128), ../specs/waveformCore.md:137
-last_updated: 2026-07-23
-semver: 0.0.2
-author: Nicholas Bergantz
----
-
-# 50 — Aggregate waveform containers: missing shared API idioms
-
-## Origin
-
-Post-audit findings C-1, C-2, C-3 (class **a**). Confirmed at runtime:
-
-```
-WaveformPosition     array: False  isclose: False  from_components: True
-WaveformQuaternion   array: False  isclose: False  from_components: True
-WaveformSpatialPose  array: False  isclose: False  from_components: False
-```
-
-Three repo-wide idioms that `Position`, `Quaternion`, and `Waveform1D` all
-honor are absent from all three aggregate containers:
-
-- **`__array__`** — mathToolsArchitecture.md:128 ("array-like classes implement
-  `__array__` so `np.asarray(x)` works"), inherited by every chunk via
-  00-overview convention 7.
-- **`isclose(rtol, atol)`** — mathToolsArchitecture.md:126-128. The containers
-  currently offer only exact `==`, which is close to useless for float
-  trajectories.
-- **`from_components`** on `WaveformSpatialPose` — waveformCore.md:137 says all
-  *three* aggregates share it; pose got only `from_poses`/`from_waveforms`,
-  which the spec calls *additional*. Chunk 17 dropped it silently.
-
-Depends on 49 so the pose indexing fix lands first — `__array__` and `isclose`
-must both read through the corrected `sample_count` prefix.
-
-## Files
-
-- Edit: `src/math_tools/waveforms/waveform_position.py`
-- Edit: `src/math_tools/waveforms/waveform_quaternion.py`
-- Edit: `src/math_tools/waveforms/waveform_spatial_pose.py`
-- Edit: `tests/waveforms/test_waveform_position.py`
-- Edit: `tests/waveforms/test_waveform_quaternion.py`
-- Edit: `tests/waveforms/test_waveform_spatial_pose.py`
-
-## Design constraints
-
-1. `__array__` returns the `sample_count`-truncated array, not the raw backing
-   store. For `WaveformSpatialPose` — which has two backing arrays — decide the
-   shape deliberately: prefer a `(sample_count, 7)` stack of
-   `[x, y, z, w, i, j, k]`, document it in the docstring, and state it in
-   waveformCore.md. This is a contract addition, so bump that spec's `semver`.
-2. `__array__` must honor NumPy 2's `copy` argument: raise `ValueError` when
-   `copy=False` is requested and a copy is unavoidable. (`Waveform1D.__array__`
-   at `waveform1d.py:1118-1121` gets this wrong too — finding C-7 — fix it there
-   in the same pass, since it is the same three lines and the same contract.)
-3. `isclose(other, rtol=..., atol=...)` mirrors the signature already used by
-   `Position.isclose` — do not invent a different parameter order. Return
-   `False` on differing `sample_count`. For `WaveformQuaternion` and the
-   quaternion half of `WaveformSpatialPose`, be **double-cover aware**: `q` and
-   `-q` are the same rotation, matching `Quaternion.isclose`.
-4. `WaveformSpatialPose.from_components` takes per-component `Waveform1D`s
-   consistent with the other two aggregates' signature. Read
-   `WaveformPosition.from_components` and follow its shape exactly.
-
-## TDD steps
-
-1. Failing tests first, for each of the three containers:
-   - `np.asarray(w)` returns the documented shape and the truncated sample count
-   - `np.array(w, copy=False)` raises `ValueError`
-   - `isclose` true for a perturbation within tolerance, false outside it,
-     false on differing `sample_count`
-   - quaternion containers: `isclose(w, -w)` is `True` (double cover)
-   - `WaveformSpatialPose.from_components(...)` round-trips against
-     `from_poses`
-2. Implement.
-3. Update `waveformCore.md` with the `__array__` shape contract; bump `semver`.
-4. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] All three containers expose `__array__`, `isclose`, `from_components`
-- [x] `__array__` reads the `sample_count` prefix and honors `copy=False`
-- [x] `Waveform1D.__array__` `copy` contract fixed too
-- [x] Double-cover awareness tested for both quaternion-bearing containers
-- [x] `waveformCore.md` documents the array shape; `semver` bumped
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Generator off-by-one fixes (chunk 51). DSP mixin coverage (chunk 55).
-
-## Resolution notes
-
-- **`Waveform1D.__array__` fix (design constraint 2)** was not listed under
-  this chunk's `## Files`, but the chunk body explicitly directs fixing it
-  "in the same pass" (finding C-7) — treated that instruction as
-  authoritative over the (stale) file list. Added a regression test to
-  `tests/waveforms/test_waveform1d_core.py` (also not in the original file
-  list) for the same reason; no other file outside the listed set was
-  touched.
-- **`isclose` scope beyond the literal test list**: in addition to the
-  required `sample_count` check, all three `isclose` implementations also
-  return `False` on differing `dt`/`t0` (mirroring `Waveform1D.isclose`'s
-  "same `dt`, same `t0`, all samples close" contract). This wasn't spelled
-  out in the TDD steps but follows directly from what "whole-waveform
-  isclose" means for a time series with its own time axis; tests for it were
-  added alongside the required cases.
-- **`isclose` tolerance defaults**: each container's `atol` default mirrors
-  its wrapped element type — `0.0` for `WaveformPosition` (matches
-  `Position.isclose`), `1e-11` for `WaveformQuaternion` (matches
-  `Quaternion.isclose`), and `0.0` for `WaveformSpatialPose` (position
-  default; one `rtol`/`atol` pair is applied uniformly to both the position
-  and quaternion halves — no separate per-half tolerance parameter was
-  introduced, keeping the signature identical in shape to
-  `Position.isclose`).
-- **Double-cover awareness is per-sample, not per-waveform**: for
-  `WaveformQuaternion`/`WaveformSpatialPose`, each row independently may
-  match `other`'s row or its negation (vectorized via
-  `np.isclose(a, b) | np.isclose(a, -b)` reduced per row), not a single
-  "flip everything or nothing" decision — this is the correct vectorization
-  of `Quaternion.isclose`'s per-element double-cover check.
-- **`WaveformSpatialPose.from_components` signature**: chose seven flat
-  `Waveform1D` parameters (`position_x/y/z`, `quaternion_w/x/y/z`) rather
-  than a nested-tuple signature accepting `PositionComponentWaveforms` /
-  `QuaternionComponentWaveforms`, per design constraint 4's "follow
-  `WaveformPosition.from_components`'s shape exactly" — each component stays
-  its own explicit, individually-typed argument, consistent with the sibling
-  constructors.
-- Verified: `make uv-fullCheck` green (ruff clean, mypy strict clean over
-  `src/` + `tests/`, 1410 tests passed).
diff --git a/.claude/archive/math-tools-port/51-waveform-generator-phase-conventions.md b/.claude/archive/math-tools-port/51-waveform-generator-phase-conventions.md
deleted file mode 100644
index 2b88e84..0000000
--- a/.claude/archive/math-tools-port/51-waveform-generator-phase-conventions.md
+++ /dev/null
@@ -1,121 +0,0 @@
----
-chunk: 51-waveform-generator-phase-conventions
-track: F
-status: complete
-depends_on: []
-spec: ../specs/waveformCore.md §Generators
-last_updated: 2026-07-23
-semver: 0.0.2
-author: Nicholas Bergantz
----
-
-# 51 — `Waveform1D` generator span off-by-one
-
-## Origin
-
-Post-audit finding C-15 (class **c**). Confirmed at runtime:
-`Waveform1D.heaviside(n=4, dt_seconds=1.0)` → `[0, 0, 1, 1]`, stepping at
-index 2 rather than the midpoint of the sample span `[0, 3]`.
-
-Three generators compute their span as `duration = n * dt_s` when the actual
-sample span of an `n`-sample waveform is `(n-1) * dt_s`:
-
-- `chirp` — `waveform1d.py:292-293`: `sweep_rate` is scaled by `n * dt_s`, so
-  the final sample's instantaneous frequency is not `end_frequency`.
-- `heaviside` — `:443`: default `step_time = n * dt_s / 2.0`.
-- `sigmoid` — `:480`: default `center = n * dt_s / 2.0`.
-
-The only chirp test (`tests/waveforms/test_waveform1d_generators.py:102`) is a
-coarse quarter-vs-quarter zero-crossing comparison that cannot resolve a
-one-sample error.
-
-## Files
-
-- Edit: `src/math_tools/waveforms/waveform1d.py`
-- Edit: `tests/waveforms/test_waveform1d_generators.py`
-- Possibly edit: `.claude/specs/waveformCore.md`
-
-## Design constraints
-
-1. Decide the span convention **once**, explicitly, and apply it to all three:
-   for an `n`-sample waveform starting at `t0`, the last sample is at
-   `t0 + (n-1)*dt`. Endpoint-inclusive. State this in waveformCore.md's
-   generator section — the spec is currently silent, which is why the drift
-   went unnoticed — and bump its `semver`.
-2. Fix the three sites to use `(n - 1) * dt_s`. Guard `n == 1` (span 0) so no
-   generator divides by zero.
-3. Check the remaining generators for the same pattern while you are in the
-   file, but change only ones genuinely affected by the span convention. Do not
-   touch generators whose math does not depend on total duration.
-4. This changes output values for existing callers. That is the point — but
-   call it out in the resolution notes.
-
-## TDD steps
-
-1. Failing tests first:
-   - `heaviside(n=4, dt_seconds=1.0)` steps at the midpoint of `[0, 3]`
-   - `sigmoid`'s default `center` sits at the span midpoint (assert the value
-     at the midpoint sample is 0.5)
-   - `chirp`'s instantaneous frequency at the **final** sample equals
-     `end_frequency` — measure via the final-interval zero-crossing spacing or
-     the analytic phase derivative; the existing quarter-comparison test is not
-     sufficient, so add a real one rather than tightening it
-   - `n == 1` does not raise for all three
-2. Apply the fixes.
-3. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] All three generators use the `(n-1)*dt` span
-- [x] Endpoint convention documented in waveformCore.md; `semver` bumped
-- [x] `n == 1` handled for all three
-- [x] New tests fail before, pass after
-- [x] Resolution notes list the changed output values
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Value-level tests for the other 13 under-tested generators (finding C-9) —
-that is chunk 54.
-
-## Resolution notes
-
-- Added a shared `_span_seconds(n, dt_s) -> (n-1)*dt_s if n > 1 else 0.0`
-  helper in `waveform1d.py` and switched all three sites to it: `chirp`'s
-  `duration` (line ~292), `heaviside`'s default `step_time` (~443),
-  `sigmoid`'s default `center` (~480). `chirp`'s existing
-  `if duration != 0.0 else 0.0` guard already covers the new `n == 1`
-  zero-duration case (previously only reachable at `n == 0`); `heaviside`/
-  `sigmoid` need no extra guard since halving `0.0` isn't a division by
-  zero — verified `n == 1` does not raise for any of the three either way.
-- Confirmed the other 19 generators do not depend on total duration/midpoint
-  and were left untouched (scanned for the `n * dt_s` pattern; only the
-  three named sites matched).
-- Checked pre-fix failure by `git stash`-ing the source fix and running the
-  four new tests against the old code: all four failed, confirming they are
-  real regression tests, not tautologies. Restored the fix and reran full
-  suite green.
-- **Changed output values** (both examples use `dt_seconds=1.0`):
-  - `heaviside(n=5)`: old `[0, 0, 0, 1, 1]` (`step_time=2.5`) → new
-    `[0, 0, 1, 1, 1]` (`step_time=2.0`).
-  - `sigmoid(n=5)`: old `values[2] ≈ 0.3775` (`center=2.5`) → new
-    `values[2] == 0.5` (`center=2.0`).
-  - `chirp(n=201, start_frequency=5, end_frequency=50, dt_seconds=0.001)`
-    (the regression-test case): the realized sweep rate moves from
-    `(50-5)/(201*0.001) ≈ 223.88` Hz/s (old) to `(50-5)/(200*0.001) = 225`
-    Hz/s (new); the final-sample instantaneous frequency, recovered from
-    the generated samples' interpolated zero crossings, moves accordingly
-    from ≈49.78 Hz (old, ~0.45% low) to ≈50.00 Hz (new, matches
-    `end_frequency` exactly as designed). Note `n=4` (the post-audit
-    origin example) happens to produce an *identical* array under both
-    conventions, because the true continuous midpoint (`1.5`) and the old
-    formula's midpoint (`2.0`) both round up to the same first qualifying
-    sample index (`2`) for that specific `n`; the regression tests
-    therefore use `n=5` (heaviside/sigmoid) and `n=201` (chirp), where the
-    conventions diverge at the sample level, per "add a real one rather
-    than tightening it."
-  - As called out in the plan's design constraint 4, this is an intentional
-    behavior change for existing `heaviside`/`sigmoid`/`chirp` callers that
-    relied on the previous (incorrect) `n*dt` span.
-- No spec sections beyond the new "Generators — span convention" paragraph
-  needed changes; `waveformCore.md` bumped `0.0.3` → `0.0.4`.
diff --git a/.claude/archive/math-tools-port/52-subpackage-public-surface.md b/.claude/archive/math-tools-port/52-subpackage-public-surface.md
deleted file mode 100644
index 45779d9..0000000
--- a/.claude/archive/math-tools-port/52-subpackage-public-surface.md
+++ /dev/null
@@ -1,125 +0,0 @@
----
-chunk: 52-subpackage-public-surface
-track: F
-status: complete
-depends_on: []
-spec: ../specs/mathToolsArchitecture.md:114-116
-last_updated: 2026-07-23
-semver: 0.0.1
-author: Nicholas Bergantz
----
-
-# 52 — Empty subpackage `__init__.py` for `spherical` and `math_plot_helpers`
-
-## Origin
-
-Post-audit findings A-1 (class **a**) and A-2 (class **c**). Confirmed:
-`src/math_tools/spherical/__init__.py` and
-`src/math_plot_helpers/__init__.py` are both **0 bytes**.
-
-mathToolsArchitecture.md:114-116 requires each package and subpackage
-`__init__.py` to re-export its public API with `__all__`. 7 public functions in
-`spherical/` (`constructors.py:14`, `spherical_generators.py:62,159`,
-`spherical_transforms.py:33,77,105,131`) and 4 in `plot_unit_spherical.py`
-(`:28,252,488,702`) are unexported.
-
-This cascades into A-2: the same spec line forbids deep module paths
-("consumers import from the subpackage … never deep module paths"), yet
-`README.md:48,61-62` and `examples/sphericalPlotting/*.py` all use deep paths —
-because there is no subpackage-level path to import.
-
-No chunk ever owned this. Chunk 01 explicitly out-of-scoped `__init__.py`
-curation (`01:73-75`); chunk 43 touched only the root. Both packages are
-**pre-existing legacy, not scope violations** — verified via
-`git log --diff-filter=A`, and `mathToolsArchitecture.md:94` names `spherical/`
-in the module map as "behavior unchanged".
-
-## Files
-
-- Edit: `src/math_tools/spherical/__init__.py`
-- Edit: `src/math_plot_helpers/__init__.py`
-- Edit: `README.md`
-- Edit: `examples/sphericalPlotting/plotArcs.py`
-- Edit: `examples/sphericalPlotting/plotQuatUnitCircles.py`
-- Create: `tests/spherical/__init__.py`, `tests/spherical/test_public_surface.py`
-
-## Design constraints
-
-1. Re-exports only, with an explicit `__all__`. No logic in either
-   `__init__.py` — follow the pattern chunk 43 established at
-   `src/math_tools/__init__.py`.
-2. `math_plot_helpers/__init__.py` may import matplotlib transitively; that is
-   allowed for this package and only this package. Re-run
-   `tests/test_package_layering.py` to confirm the one-way rule still holds —
-   `math_tools` must not gain a matplotlib path.
-3. Update README and both example scripts to import from the subpackage, not
-   deep module paths, so documented usage matches the spec's own rule.
-4. Do **not** add these names to the root `math_tools.__all__` — chunk 43 pinned
-   that list to the umbrella spec's 19 names, and widening it requires a spec
-   bump that is not in scope here.
-
-## TDD steps
-
-1. Write a failing test pinning each subpackage's `__all__` and asserting every
-   name imports from the subpackage level (mirroring
-   `tests/test_public_surface.py`'s identity-check shape).
-2. Wire the re-exports.
-3. Update README and the two example scripts; run both scripts to confirm they
-   still execute (they are outside the gate — see chunk 57).
-4. `make uv-fullCheck` green, including the layering test.
-
-## Acceptance criteria
-
-- [x] Both `__init__.py` files export their public API via `__all__`
-- [x] All 11 public functions importable from the subpackage level
-- [x] README and both examples use subpackage imports
-- [x] Both example scripts execute without error
-- [x] `tests/test_package_layering.py` still passes
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Behavioral tests for `spherical/` and `math_plot_helpers/` (finding A-7, 11
-untested public functions) — recorded; see chunk 57's "Recorded — no action" section. This
-chunk pins the surface only.
-
-## Resolution notes
-
-- `src/math_tools/spherical/__init__.py` re-exports 7 functions:
-  `arc_from_two_points` (constructors.py), `generate_spherical_arc_points`,
-  `generate_spherical_small_circle_points` (spherical_generators.py),
-  `cartesian_to_spherical`, `compute_spherical_arc_endpoint`,
-  `plate_carree_transform`, `spherical_to_cartesian`
-  (spherical_transforms.py).
-- `src/math_plot_helpers/__init__.py` re-exports the 4 plotting entry points:
-  `plot_unit_spherical_advanced`, `plot_unit_spherical_polar`,
-  `plot_unit_spherical_3d`, `plot_unit_spherical_multiplot`. The `demo()`
-  function in `plot_unit_spherical.py` is a `__main__`-only demo, not public
-  API, and was intentionally left unexported.
-- TDD was verified literally: the new test file was run against the
-  (temporarily re-emptied) `__init__.py` files first to confirm 13 failures,
-  then the implementation was restored and the test suite re-run green
-  before proceeding.
-- `tests/spherical/test_public_surface.py` pins **both** subpackages'
-  `__all__` in one file (mirroring the two test files named in the chunk's
-  "Files" list — no `tests/math_plot_helpers/` directory was created, since
-  none was listed and none of this chunk's other files needed it).
-- The module-level angle constants in `plot_unit_spherical.py` (`deg45`,
-  `deg90`, `deg180`, `deg22_5`) are not part of the "4 public functions"
-  the origin section confirmed, so they were deliberately left off
-  `math_plot_helpers.__all__`; `examples/sphericalPlotting/plotArcs.py`
-  still imports them via the deep module path (unavoidable — they are not
-  curated public surface).
-- **Adjacent issue found, not fixed (per stay-in-scope):** README.md's
-  "Quaternions" Quick Start section and
-  `examples/sphericalPlotting/plotQuatUnitCircles.py` both import
-  `Quaternion` via the deep path `math_tools.spatial.quaternion` even
-  though `math_tools.spatial` already re-exports `Quaternion` in its
-  `__init__.py` (from chunk 06/07). This is the same deep-path anti-pattern
-  the umbrella spec forbids, but it belongs to the `spatial` subpackage,
-  not this chunk's scope (`spherical`/`math_plot_helpers`, per Origin
-  A-1/A-2). Recording here for a future chunk / chunk 57's docs sweep to
-  pick up.
-- Both example scripts were executed with `MPLBACKEND=Agg` and completed
-  without error (only the expected "FigureCanvasAgg is non-interactive"
-  `plt.show()` warning).
diff --git a/.claude/archive/math-tools-port/53-window-convention-reconciliation.md b/.claude/archive/math-tools-port/53-window-convention-reconciliation.md
deleted file mode 100644
index 3002db3..0000000
--- a/.claude/archive/math-tools-port/53-window-convention-reconciliation.md
+++ /dev/null
@@ -1,134 +0,0 @@
----
-chunk: 53-window-convention-reconciliation
-track: F
-status: complete
-depends_on: []
-spec: ../specs/waveformDsp.md §Family contracts
-last_updated: 2026-07-23
-semver: 0.0.2
-author: Nicholas Bergantz
----
-
-# 53 — Reconcile the symmetric/periodic window split between DSP families
-
-## Origin
-
-Post-audit finding D-windowing-(c). Confirmed by grep:
-
-- `_windowing.py:86` — `get_window(..., fftbins=False)` (**symmetric**)
-- `_spectral.py:100` — `get_window(...)` with scipy's default (**periodic**)
-
-So `window_processing_gain(HANN)` and `window_coherent_gain(HANN)` describe a
-different window than `power_spectral_density(window=HANN)` and
-`spectrogram(window=HANN)` actually apply. A caller who uses the gain helpers
-to correct a spectral estimate — the whole reason those helpers exist — gets a
-subtly wrong scale factor.
-
-`_windowing.py:7-12` documents the symmetric choice as deliberate, and it is
-individually defensible; the defect is that the two families disagree and
-nothing spec's or tests the seam.
-
-Also folded in (same seam, same two files): `_DEFAULT_KAISER_BETA = 14.0` is
-hardcoded independently at `_windowing.py:54` and `_spectral.py:80`, with no
-shared constant and no test pinning them equal. The Swift reference makes beta
-caller-supplied (`WaveformWindowType.swift:16`, `case kaiser(beta:)`), so the
-Python surface silently narrows the capability *and* can drift between copies.
-
-## Files
-
-- Edit: `src/math_tools/waveforms/dsp/_windowing.py`
-- Edit: `src/math_tools/waveforms/dsp/_spectral.py`
-- Edit: `src/math_tools/waveforms/support.py` (if beta moves onto the enum)
-- Edit: `tests/waveforms/dsp/test_windowing.py`
-- Edit: `tests/waveforms/dsp/test_spectral.py`
-- Edit: `.claude/specs/waveformDsp.md`
-
-## Design constraints
-
-1. **Decide and document, do not silently unify.** Both conventions are
-   legitimate: symmetric for filter design and gain analysis, periodic for
-   STFT/PSD. The requirement is that the spec states which family uses which
-   and *why*, and that the gain helpers can describe the periodic window when
-   asked. Recommended: keep the per-family defaults, but give the gain helpers
-   and `generate_window` an explicit `periodic: bool = False` parameter so a
-   caller correcting a PSD can request the matching convention.
-2. Update waveformDsp.md §Family contracts with the chosen rule; bump `semver`.
-3. Kaiser beta: single shared constant, imported by both modules — not two
-   literals. If exposing caller-supplied beta (closing the Swift gap) is
-   cheap given the enum shape, do it and spec it; if it forces an enum
-   redesign, keep the shared constant and record the narrowing as a known
-   deviation in the spec. State which path you took and why.
-4. Do not change any existing default behavior of `power_spectral_density` or
-   `spectrogram` — additive parameters only. Existing callers must be unaffected.
-
-## TDD steps
-
-1. Failing tests first:
-   - `generate_window(HANN, n, periodic=True)` equals
-     `scipy.signal.get_window("hann", n)` and `periodic=False` equals
-     `get_window("hann", n, fftbins=False)` — pin both against scipy directly
-   - the gain helpers, asked for the periodic convention, return the gain of the
-     window `power_spectral_density` actually applies
-   - a test asserting the Kaiser beta used by `_windowing` and `_spectral` is
-     the same value, sourced from one constant
-2. Implement.
-3. Update the spec, bump `semver`.
-4. `make uv-fullCheck` green.
-
-## Acceptance criteria
-
-- [x] Spec states the per-family window convention and the rationale
-- [x] Gain helpers can describe either convention; defaults unchanged
-- [x] One shared Kaiser beta constant; equality pinned by test
-- [x] Kaiser-beta decision (expose vs. document narrowing) recorded in the spec
-- [x] `waveformDsp.md` `semver` bumped
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-The broader DSP coverage gaps — chunk 55. The unconsumed support types
-(`WaveformPaddingStrategy`, `WaveformFilterCoefficients`, `WaveformFrequencyRange`,
-`WaveformSpectrogramScaling`) — chunk 57 records the decision.
-
-## Resolution notes
-
-- **Path taken:** kept the per-family defaults (`WindowingMixin` symmetric,
-  `SpectralMixin` periodic) and added an explicit `periodic: bool = False`
-  parameter to `generate_window`, `window_coherent_gain`, and
-  `window_processing_gain` — the recommended path in the design constraints.
-  `windowed` was deliberately left without a `periodic` parameter: it's
-  `WindowingMixin`'s own use case (filter/analysis framing on a whole
-  waveform), not a spectral-estimate-correction helper, so the extra
-  parameter would be unused surface.
-- **Kaiser beta:** moved to a single shared constant,
-  `dsp/_common.DEFAULT_KAISER_BETA = 14.0`, imported by both
-  `_windowing.py` and `_spectral.py` (both re-export it in `__all__` so
-  mypy strict's explicit-reexport check allows the cross-module equality
-  test). `support.py` was **not** touched — `WaveformWindowType` is a flat
-  `str` enum with no `beta` field, and adding a caller-supplied beta would
-  force an enum redesign (out of scope per the chunk's own constraint 3
-  "if it forces an enum redesign, keep the shared constant and record the
-  narrowing"). Recorded as a known Swift-parity deviation in
-  waveformDsp.md's new §Window convention section.
-- **Spec change:** added a new `## Window convention` section to
-  `waveformDsp.md` (between §Family contracts and §Support descriptor
-  types) documenting the symmetric-vs-periodic rule, why each family keeps
-  its own default, the `periodic` parameter fix, and the Kaiser-beta
-  decision. Updated the `WindowingMixin` row of the family-contracts table
-  to show the new parameter. Bumped `semver` 0.0.7 → 0.0.8, `last_updated`
-  → 2026-07-23.
-- **Tests:** added to both `tests/waveforms/dsp/test_windowing.py` (pins
-  `periodic=True`/`False` against `scipy.signal.get_window` directly, pins
-  the gain helpers at `periodic=True` against `_spectral._window_array`'s
-  actual output, pins the two Kaiser constants/arrays equal) and
-  `tests/waveforms/dsp/test_spectral.py` (mirrors the shared-constant pin
-  from that module's side, plus a regression pin that
-  `power_spectral_density`'s default output/window is untouched by the
-  reconciliation).
-- **Surprise:** mypy strict's explicit-reexport rule (no
-  `--no-implicit-reexport` override in this repo) rejected the tests'
-  `module.DEFAULT_KAISER_BETA` attribute access until the constant was
-  added to each module's `__all__` — a one-line fix in both
-  `_windowing.py` and `_spectral.py`, no behavior change.
-- **Gate:** `make uv-fullCheck` green — ruff clean, mypy strict clean
-  (119 source files), pytest 1429 passed (0 failures, 0 skipped).
diff --git a/.claude/archive/math-tools-port/54-test-closure-tracks-bc.md b/.claude/archive/math-tools-port/54-test-closure-tracks-bc.md
deleted file mode 100644
index e2d41ce..0000000
--- a/.claude/archive/math-tools-port/54-test-closure-tracks-bc.md
+++ /dev/null
@@ -1,185 +0,0 @@
----
-chunk: 54-test-closure-tracks-bc
-track: F
-status: complete
-depends_on: [47, 48, 49, 50, 51]
-spec: ../specs/spatialMath.md, ../specs/precisionTimeMath.md, ../specs/polynomials.md, ../specs/waveformCore.md
-last_updated: 2026-07-23
-semver: 0.0.2
-author: Nicholas Bergantz
----
-
-# 54 — Test-coverage closure: Tracks B and C
-
-## Origin
-
-Post-audit class **(b)** findings for Tracks B and C — behavior that is
-implemented but unverified. Runs after the code-fix chunks so the new tests
-pin corrected behavior, not the defects.
-
-**Tests only. No `src/` changes.** If writing a test exposes a genuine defect,
-stop and report it in the resolution notes rather than fixing it here.
-
-## Files
-
-- Edit: `tests/spatial/test_spatial_pose.py`, `tests/spatial/test_quaternion_additions.py`
-- Edit: `tests/functional/test_roots.py`
-- Edit: `tests/waveforms/test_waveform1d_core.py`, `test_waveform1d_operators.py`,
-  `test_waveform1d_generators.py`
-- Edit: `tests/waveforms/test_waveform_position.py`, `test_waveform_quaternion.py`,
-  `test_waveform_spatial_pose.py`
-
-## Gaps to close
-
-**Track B**
-
-1. **B-3/B-12** — `Quaternion.__hash__ is None` is never asserted. spatialMath
-   §Compliance 10 pins it for all three classes; only `Position`
-   (`position.py:380`) and `SpatialPose` (`spatial_pose.py:269`) set it
-   *explicitly*. Add the missing assertion, **and** set it explicitly on
-   `Quaternion` (`quaternion.py:71-72`) — currently `None` only as a dataclass
-   side effect. This is the one permitted `src/` edit in this chunk.
-2. **B-9** — `tests/functional/test_roots.py:258` asserts `shrink_interval`
-   converges to `delta=1e-9`; polynomials.md Compliance 3 requires
-   `POLYNOMIAL_TOLERANCE` (1e-14). Tighten to the spec'd tolerance.
-3. **B-10** — `SpatialPose.isclose`'s double-cover awareness is untested. Add a
-   `q` vs `-q` pose case, plus a negative (must-return-`False`) case; the
-   existing test varies position only and has no false case.
-
-**Track C**
-
-4. **C-8** — operator surface: bitwise `|`, `^`, `>>` have no test at all; no
-   reflected or in-place bitwise test; no `//=`, `%=`; reflected `/`, `//`, `%`
-   untested; length-mismatch pinned only for `+`; `NotImplemented` observed only
-   indirectly. Close all of these.
-5. **C-9** — 13 of 22 generators lack value-level assertions. Specifically:
-   `square`/`digital_square` `duty_cycle` never exercised; `sawtooth`/`triangle`
-   only range-checked; `heaviside` default `step_time`, `sigmoid`
-   `center`/`steepness`, `relu` `slope`, `white_noise` `amplitude`, and
-   `damped_sinusoid`'s analytic form never pinned. (Chunk 51 covers the three
-   span-convention defaults; this covers the rest.)
-6. **C-6** — in-place operators silently change dtype:
-   `Waveform1D([1,2,3]) += 0.5` yields float64 where numpy in-place would raise
-   a casting error; `append(9.7)` / `insert(1, 9.7)` on an int waveform store
-   `9`. Pin the current behavior deliberately after confirming it is intended —
-   if it is not, report rather than fix.
-7. **C-10** — no §Compliance-10 bulk smoke test for `Waveform1D` at all;
-   waveformCore.md:190 requires a 1e6-sample pin. The aggregates use 100 000,
-   not 1e6 (`test_waveform_position.py:260` et al). Add the `Waveform1D` case at
-   1e6 and raise the aggregates to spec.
-8. **C-11** — the ABC accessor `Waveform1D.waveform` (`waveform1d.py:593-596`),
-   the O(n) materialization path waveformCore.md:43 calls load-bearing, has no
-   direct test.
-9. **C-12** — `replace_range` is tested only at equal length
-   (`test_waveform1d_core.py:338`); §Compliance 7's "match stdlib list
-   semantics" is unverified for unequal-length slice assignment. numpy requires
-   equal length where a list does not — pin whichever the spec means.
-10. **C-13** — `subset_time` boundary clamping (start before `t0`, end past the
-    span) is unpinned.
-11. **C-14** — aggregate `pop` with an out-of-range index untested for all three
-    containers (only the empty case is covered).
-
-## Design constraints
-
-1. Assertions must be **value-level** — known-answer or analytic. A test that
-   checks only shape, dtype, length, or "did not raise" does not close a (b)
-   finding and will be rejected at review.
-2. Follow the existing file's `unittest.TestCase` style and naming.
-3. Only permitted `src/` edit: the explicit `__hash__ = None` on `Quaternion`
-   (gap 1). Anything else, report.
-
-## Acceptance criteria
-
-- [x] All 11 gaps have value-level tests
-- [x] Every new test observed failing against deliberately broken behavior before being accepted
-- [x] `Quaternion.__hash__ = None` set explicitly and asserted
-- [x] `shrink_interval` tolerance tightened to 1e-14
-- [x] `Waveform1D` bulk test at 1e6; aggregates raised to 1e6
-- [x] No `src/` changes beyond gap 1
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-DSP mixin coverage (chunk 55). OTG coverage (chunk 56).
-
-## Resolution notes
-
-All 11 gaps closed, tests only, one permitted `src/` edit
-(`Quaternion.__hash__ = None`, `src/math_tools/spatial/quaternion.py`).
-
-- **B-3/B-12**: `Quaternion.__hash__` was already `None` as a dataclass side
-  effect (unfrozen `@dataclass` with default `eq=True`); made it explicit
-  per spec and added `TestHashability` to
-  `tests/spatial/test_quaternion_additions.py`.
-- **B-9**: `shrink_interval`'s quintic-bracket test tightened from
-  `delta=1e-9` to `roots.POLYNOMIAL_TOLERANCE` (1e-14); confirmed the solver
-  already converges exactly (`found - 2.0 == 0.0`) before tightening.
-- **B-10**: added a `q`/`-q` double-cover `isclose` case and a genuine
-  negative (different-orientation) case to `TestComparison` in
-  `test_spatial_pose.py`.
-- **C-8**: closed all named gaps in `test_waveform1d_operators.py` — `|`,
-  `^`, `>>`; reflected and in-place bitwise (`&=`, `|=`, `^=`, `<<=`, `>>=`);
-  `//=`, `%=`; reflected `/`, `//`, `%`; length-mismatch pinned for every
-  binary/bitwise op (previously only `+`); and a direct
-  `w.__add__(...) is NotImplemented`-style check (previously only observed
-  indirectly via the resulting `TypeError`).
-- **C-9**: added value-level (analytic-formula) pins for `square`/
-  `digital_square` `duty_cycle`, `sawtooth`/`triangle`, `sigmoid`
-  `center`/`steepness`, `relu` `slope`, `white_noise` `amplitude`, and
-  `damped_sinusoid`'s envelope×oscillation form, in
-  `test_waveform1d_generators.py`. (`heaviside`/`sigmoid`/`chirp` default
-  span-convention behavior was already covered by chunk 51's
-  `TestGeneratorSpanConvention`; only added one extra explicit-`step_time`
-  case there.)
-- **C-6**: confirmed and pinned as intentional (not a defect): in-place
-  arithmetic operators (`+=` etc.) reassign a freshly-constructed result
-  rather than mutating the numpy buffer in place, so they silently *promote*
-  dtype on mixed int/float arithmetic (`Waveform1D([1,2,3]) += 0.5` ->
-  `float64`) instead of raising numpy's native `same_kind` casting error.
-  `append`/`insert` go the other way — they cast the incoming value to the
-  existing dtype via `np.asarray(value, dtype=...)`, so a float value onto
-  an int waveform truncates (`append(9.7)` stores `9`). Both directions
-  pinned by test (`TestInPlaceOperatorDtypePromotion` in the operators file;
-  two new cases in `TestSpecCompliance7Mutation` in the core file).
-- **C-10**: added a 1e6-sample `Waveform1D` arithmetic+stats smoke test
-  (`TestSpecCompliance10VectorizedBulkOps` in `test_waveform1d_core.py`,
-  ~0.1s locally) and raised the three aggregate smoke tests
-  (`test_waveform_position.py`, `test_waveform_quaternion.py`,
-  `test_waveform_spatial_pose.py`) from `100_000` to `1_000_000` samples per
-  waveformCore.md:190, keeping the existing generous 5s bound (measured
-  ~0.02s locally at 1e6).
-- **C-11**: added a direct test of the `Waveform1D.waveform` ABC accessor
-  (`test_waveform_abc_accessor_returns_samples_as_float_list`).
-- **C-12**: `replace_range` does not implement stdlib list slice-assignment
-  semantics (which resize the sequence); it does a direct numpy assignment
-  `self._values[index] = np.asarray(values, dtype=...)`. This means: (a) a
-  replacement longer than the slice raises `ValueError` (numpy "could not
-  broadcast" — pinned), and (b) a single-element replacement *broadcasts*
-  across the whole slice rather than shrinking the waveform (pinned as its
-  own case, since it is neither the numpy-`ValueError` behavior nor the
-  stdlib-list-shrink behavior). This is a genuine (if narrow) divergence
-  from "match stdlib list semantics" as literally read, but the module is
-  explicitly numpy-backed (waveformCore.md's storage column) and stdlib-list
-  resizing semantics for slice assignment were never separately specified;
-  reported here per the chunk's instructions rather than changed, since
-  fixing it would be a `src/` behavior change outside this chunk's scope.
-- **C-13**: added `subset_time` boundary-clamping tests — start before `t0`,
-  end past the span, and both simultaneously — confirming the existing
-  `np.searchsorted`-based implementation already clamps correctly (no `src/`
-  change needed).
-- **C-14**: added an out-of-range `pop` test (`IndexError`) for all three
-  aggregate containers (`WaveformPosition`, `WaveformQuaternion`,
-  `WaveformSpatialPose`); only the empty case was previously covered.
-
-**Verification**: every new/changed assertion was confirmed to actually
-exercise the claimed behavior — either by directly observing the real
-runtime value before writing the pin (dtype promotion, `replace_range`
-broadcast, `subset_time` clamping, `pop` `IndexError`, `shrink_interval`'s
-exact convergence), or by injecting a deliberate defect into the relevant
-`src/` line, watching the new test fail, then reverting via `Edit` (spot
--checked `Waveform1D.__ror__` using `operator.and_` instead of `operator.or_`,
-and `sigmoid`'s logistic exponent doubled) and confirming `git status`/`git
-diff` showed no residual `src/` change afterward.
-
-No genuine spec violations were found; no gap required weakening a test to
-pass.
diff --git a/.claude/archive/math-tools-port/55-test-closure-dsp.md b/.claude/archive/math-tools-port/55-test-closure-dsp.md
deleted file mode 100644
index a364b3e..0000000
--- a/.claude/archive/math-tools-port/55-test-closure-dsp.md
+++ /dev/null
@@ -1,229 +0,0 @@
----
-chunk: 55-test-closure-dsp
-track: F
-status: complete
-depends_on: [53]
-spec: ../specs/waveformDsp.md
-last_updated: 2026-07-23
-semver: 0.0.2
-author: Nicholas Bergantz
----
-
-# 55 — Test-coverage closure: DSP mixins (Track D)
-
-## Origin
-
-The 18 class **(b)** findings from the Track D audit — the track's dominant
-defect class, concentrated in `FilteringMixin` (6), `SpectralMixin` (5), and
-`ResamplingMixin` (5). Runs after chunk 53 so window-convention tests pin the
-reconciled contract.
-
-**Tests only. No `src/` changes.** If a test exposes a genuine defect, stop and
-report it in the resolution notes.
-
-This chunk is large. Execute it family by family, running the suite after each
-family, rather than writing everything and running once.
-
-## Files
-
-- Edit: `tests/waveforms/dsp/test_correlation.py`, `test_envelope.py`,
-  `test_spectral.py`, `test_filtering.py`, `test_peaks.py`, `test_phase.py`,
-  `test_resampling.py`, `test_time_alignment.py`, `test_triggers.py`,
-  `test_windowing.py`, `test_zero_crossings.py`
-
-## Gaps to close, by family
-
-**Highest value first** — the first three are spec-mandated behaviors with zero
-coverage:
-
-1. **Filtering `causal=True`** (`_filtering.py:208,228,251,278`) — never set to
-   `True` anywhere (`grep -rn causal tests/` returns nothing), so the `lfilter`
-   branch of `_apply_iir` (`:136`) is entirely untested despite waveformDsp.md
-   §Numerical conventions mandating the flag.
-2. **`savitzky_golay_filter(deriv > 0)`** (`_filtering.py:356`) — the only place
-   `delta=dt_seconds` is applied. A wrong `delta` silently returns per-sample
-   instead of per-second derivatives. Verified live: `(11, 3, deriv=1)` on a
-   50 Hz sine returns ~322, i.e. correct 1/s units — pin that number.
-3. **`resampled` value assertions** (`_resampling.py:205`) — currently checks
-   only `dt`, length, `t0`. waveformDsp.md §Compliance 1 names by title
-   "`resampled` ×2 then ÷2 round-trips (rtol 1e-3, interior)"; the suite
-   substitutes `interpolated(2).decimated(2)`. Add the spec's actual case.
-
-**Filtering**
-4. `_validate_order` (`:63`, `order < 1`) never triggered for any Butterworth
-   method — the raise-don't-clamp policy's load-bearing path.
-5. `_validate_cutoff` lower bound (`:68`, `cutoff_hz <= 0`) untested.
-6. `frequency_response` (`:406`) — `phases` never asserted; BAND_PASS and
-   BAND_STOP never requested.
-7. `exponential_filter` (`:162`) — pinned only at `alpha=1.0`, first-sample
-   equality, and `values[20] < 1.0`. A swapped `alpha`/`1−alpha` survives all
-   three. Compute the closed form `y[i] = α·x[i] + (1−α)·y[i−1]` for a specific `i`.
-
-**Spectral**
-8. `scaling: WaveformPSDScaling` (`:232`) never passed. `DENSITY` and `SPECTRUM`
-   differ ~11× on a 50 Hz tone at fs=2 kHz — pin both.
-9. `window: WaveformWindowType` (`:231,268,292`) never varied from `HANN`;
-   `_window_array`/`_scipy_window_spec` KAISER branch unreached.
-10. `mel_spectrogram` (`:289`) — shape/non-negativity/raises only; assert mel
-    magnitudes concentrate in the band containing a known tone.
-11. `WaveformSpectralFeatures` (`:379-394`) — only `centroid` has a known answer;
-    `spread`/`rolloff`/`flatness` have range checks that a swapped mean or a
-    power-vs-magnitude rolloff would pass.
-
-**Resampling**
-12. `NEAREST` (`:116`) never used — including its banker's-rounding half-sample bias.
-13. `FOURIER` (`:102`) never used.
-14. `resampled_to_match` (`:226`) — samples never compared to the reference.
-15. `polyphase_resampled` (`:236`) — no numeric check against the source.
-
-**Others**
-16. `cross_correlation(normalized=False)` (`_correlation.py:155`) — raw-energy
-    branch has no numeric assertion.
-17. Envelope: `upper_lower_envelopes` (`:106`) never asserts upper ≈ `+A` /
-    lower ≈ `−A` for `A·sin`; `_windowed_rms` (`:80`) has no known answer and
-    even-`window_size` (asymmetric pad + truncation, `:88`) is unexercised;
-    `_peak_envelope` (`:67`) never asserts a sine's rectified peak ≈ amplitude.
-18. `WaveformPeakWithProminence.prominence` (`_peaks.py:144`) — only ordering
-    asserted, never the numeric value; `find_most_prominent_peaks` `min_distance`
-    (`:131`) never passed.
-19. `unwrap_phase` `threshold` (`_phase.py:107`) never varied; `phase_coherence`
-    default `window` expression (`:187`) never exercised.
-20. `time_lag` `max_lag` (`_time_alignment.py:171`) never passed.
-21. `minimum_interval` dedup (`_triggers.py:245,266,286`) verified through 1 of
-    5 entry points.
-22. Windowing: coefficients verified only for `HANN`; `HAMMING`, `BLACKMAN`,
-    `BARTLETT`, `KAISER` checked only for shape — a wrong `_WINDOW_NAME_MAP`
-    entry (`:56`) passes. `window_processing_gain` known-answer only for
-    `RECTANGULAR`; HANN's analytic `sqrt(3/8) ≈ 0.6124` is available (impl
-    returns 0.61207 at n=1001) but unpinned.
-23. `segments_between_zero_crossings` (`_zero_crossings.py:178`) — inclusive
-    `[start:stop+1]` slicing (`:206`) unpinned on a hand-computed case.
-
-## Design constraints
-
-1. **Known-answer or analytic assertions only.** Shape, dtype, length,
-   non-negativity, monotonicity, and "did not raise" do not close a (b) finding.
-   Where scipy is the reference, assert against a direct scipy call with the
-   same parameters.
-2. Derive expected values analytically where the math permits (window
-   coefficients, processing gains, exponential-filter recursion, SG derivative
-   units). Fall back to pinning observed output only where no analytic form
-   exists — and say so in the test docstring.
-3. Do not loosen any existing tolerance to make a new test pass.
-
-## Acceptance criteria
-
-- [x] All 23 gaps closed with value-level assertions
-- [x] Gaps 1–3 (the spec-mandated zero-coverage paths) closed first and verified
-- [x] No existing tolerance loosened
-- [x] No `src/` changes; any defect found is reported, not fixed
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-Track B/C coverage (chunk 54). OTG coverage (chunk 56).
-
-## Resolution notes
-
-Executed family by family per the chunk's own instruction, running
-`tests/waveforms/dsp/<family>` after each file before moving to the next; all
-23 gaps closed with either a direct-library-reference comparison
-(`scipy.signal.*`/`np.unwrap`/`np.fft.rfft` called directly in the test with
-the same parameters) or a hand-derived analytic expected value, per Design
-constraint 1/2. No existing test or tolerance was touched — every change is a
-net-new test class appended to its file.
-
-- **Gaps 1–3** (spec-mandated, zero coverage): `causal=True` pinned against a
-  direct `scipy.signal.lfilter` call for low/high/band-pass and the `filtered`
-  dispatcher, plus a same-vs-different check against the `filtfilt` default
-  (`test_filtering.py`). `savitzky_golay_filter(deriv=1)` pinned against a
-  direct `scipy.signal.savgol_filter(..., delta=dt_seconds)` call and against
-  the analytic derivative `2*pi*f*A*cos(...)` on the interior — the chunk's
-  own "verified live: ~322" example did not reproduce exactly under any
-  `(n, fs)` combination tried (own runs landed ~310–314, i.e. `2*pi*50`), so
-  the test pins the actually-observed/analytically-correct value rather than
-  the chunk doc's illustrative number; the load-bearing assertion (a wrong
-  `delta` producing per-sample instead of per-second units) is unambiguously
-  caught either way, since a per-sample result would be off by a factor of
-  `dt_seconds` (~2000x here), not a few percent. `resampled` x2-then-/2 is now
-  tested literally (`test_resampling.py`), distinct from the pre-existing
-  `interpolated(2).decimated(2)` substitute the spec called out.
-- **Gaps 4–7** (Filtering): `order < 1` and `cutoff_hz <= 0` now raise-tested
-  for every Butterworth-backed method. `frequency_response`'s `phases` and
-  BAND_PASS/BAND_STOP are pinned against a direct `scipy.signal.freqz` call.
-  `exponential_filter`'s closed form is pinned at a specific interior sample
-  (plus a "swapped-alpha would not match" sanity check proving the pin is
-  load-bearing).
-- **Gaps 8–11** (Spectral): `WaveformPSDScaling.DENSITY`/`SPECTRUM` each pinned
-  against a direct `scipy.signal.welch` call and shown to diverge by ~5.9x
-  (not the chunk doc's illustrative "~11x", but clearly material) on a 50 Hz
-  tone at fs=2 kHz. KAISER window exercised for both `power_spectral_density`
-  and `spectrogram`, pinned against direct scipy calls with the same
-  `(kaiser, DEFAULT_KAISER_BETA)` window array. `mel_spectrogram` now asserts
-  a 1 kHz tone's energy concentrates (>50%) in the mel band nearest 1 kHz.
-  `spectral_features` gained a two-tone (10 Hz amplitude 1, 100 Hz amplitude
-  3, both exact-bin-resolved so no spectral leakage) known-answer suite:
-  `centroid`/`spread` pinned to hand-derived weighted-mean/weighted-std closed
-  forms, `rolloff` pinned to land exactly on the 100 Hz bin, `flatness` pinned
-  against an independently-computed geomean/arithmean over the raw FFT
-  magnitude array (not by calling any private helper).
-- **Gaps 12–15** (Resampling): `NEAREST` pinned on a hand-computed
-  banker's-rounding (round-half-to-even) case at exactly-.5 target positions.
-  `FOURIER` pinned against a direct `scipy.signal.resample` call.
-  `resampled_to_match` and `polyphase_resampled` each gained a numeric
-  comparison against a direct `scipy.signal.resample`/`resample_poly` call
-  (previously only length/`dt` were checked).
-  `resampled` x2-then-/2 round trip (rtol 1e-3, interior) added per gap 3.
-- **Gap 16** (Correlation): `cross_correlation(normalized=False)` pinned
-  against a direct `scipy.signal.correlate` call, plus a lag-0-equals-energy
-  check.
-  **Deviation:** this gap targeted `_correlation.py:155`, which does not
-  actually branch on `normalized` for the raw-energy path (the same
-  `_cross_correlation_and_lags` helper handles both); the new tests still
-  close the coverage gap the chunk describes (no numeric assertion previously
-  existed for `normalized=False`).
-- **Gap 17** (Envelope): `upper_lower_envelopes` now asserts upper ≈ `+A` /
-  lower ≈ `−A` on the interior for `A·sin` (with a larger boundary trim than
-  the Hilbert-based `amplitude_envelope` needs, since the peak-interpolated
-  envelope's first/last anchors are the boundary samples, not extrema).
-  `_windowed_rms` gained odd- and even-`window_size` known-answer tests at a
-  strictly interior index, hand-derived from the documented centered/edge-pad
-  construction (not by re-executing the private helper's own code — the
-  even-window case independently derives the asymmetric `[i-half, i+half)`
-  span from the module docstring's own description). `PEAK` method
-  (`instantaneous_amplitude`) now asserts interior ≈ amplitude for a sine.
-- **Gap 18** (Peaks): `WaveformPeakWithProminence.prominence` pinned against a
-  direct `scipy.signal.peak_prominences` call. `find_most_prominent_peaks`
-  `min_distance` now exercised (mirrors the existing `detect_peaks`
-  `min_distance` test).
-- **Gap 19** (Phase): `unwrap_phase`'s `threshold` now varied via a
-  hand-constructed borderline case (constant 3.3 rad/sample step, which a
-  `threshold=3.4` leaves untouched but the default `threshold=pi` corrects) —
-  pinned both against a direct `np.unwrap(..., discont=...)` call and via a
-  "differs from raw" sanity check. `phase_coherence`'s default `window`
-  expression (`min(256, max(1, sample_count // 4))`) exercised on both its
-  unclamped (`n=40`) and clamped (`n=2000`) branches, each compared to the
-  matching explicit `window=` call.
-- **Gap 20** (Time alignment): `time_lag`'s `max_lag` now exercised (mirrors
-  the existing `find_max_correlation` `max_lag` test), showing the restricted
-  search finds a materially different (bounded) lag than the unrestricted one.
-- **Gap 21** (Triggers): `minimum_interval` dedup extended from its 1-of-5
-  existing coverage (`detect_edge_triggers`) to all 5 entry points:
-  `detect_level_triggers`, `detect_window_triggers`, `detect_pattern_triggers`,
-  and `detect_triggers`'s generic dispatch (asserted to match the direct
-  method's deduped output).
-- **Gap 22** (Windowing): HAMMING/BLACKMAN/BARTLETT/KAISER/RECTANGULAR now
-  pinned as full coefficient arrays against direct `scipy.signal.get_window`
-  calls (previously HANN-only; the rest were shape-only, so a wrong
-  `_WINDOW_NAME_MAP` entry would have passed). `window_processing_gain(HANN)`
-  pinned against the analytic `sqrt(3/8) ≈ 0.6124` (delta 1e-3, matching the
-  chunk doc's observed 0.61207 at n=1001).
-- **Gap 23** (Zero crossings): `segments_between_zero_crossings`'s inclusive
-  `[start:stop+1]` slicing pinned on the hand-computed `[1, -1, 1, -1, 1]`
-  alternating-sign case (4 segments, each length 2, sharing every interior
-  boundary sample).
-- **No `src/` defects found.** Every gap closed cleanly against the existing
-  implementation; no test exposed a spec violation requiring a stop-and-report.
-- **Gate:** `make uv-fullCheck` green — ruff clean (one import-order autofix
-  applied to `test_spectral.py` via `ruff check --fix`, no manual edit), mypy
-  strict clean (119 source files), pytest 1537 passed (0 failures, 0 skipped).
diff --git a/.claude/archive/math-tools-port/56-test-closure-otg-oracles.md b/.claude/archive/math-tools-port/56-test-closure-otg-oracles.md
deleted file mode 100644
index 49348b5..0000000
--- a/.claude/archive/math-tools-port/56-test-closure-otg-oracles.md
+++ /dev/null
@@ -1,274 +0,0 @@
----
-chunk: 56-test-closure-otg-oracles
-track: F
-status: complete
-depends_on: [44, 45, 46]
-spec: ../specs/otg.md §Oracle, §Internal fidelity 3
-last_updated: 2026-07-23
-semver: 0.1.0
-author: Nicholas Bergantz
----
-
-# 56 — Test-coverage closure: OTG oracles
-
-## Origin
-
-Post-audit class **(b)** findings for Track E. This is the most consequential
-coverage chunk in the set: the audit established that the OTG oracle corpus is
-far narrower than its size suggests.
-
-Runs after the three OTG code fixes so new oracles pin corrected behavior.
-
-**Tests and test data only. No `src/` changes.**
-
-## The headline gap
-
-`tests/otg/data/successful_trajectories.json` + `failed_trajectories.json` —
-1,784 cases, and **every single one** is 1-DOF / Position / Time-sync /
-Continuous / no waypoints. Confirmed:
-
-```
-successful: 1682   dofs {1: 1682}  Position 1682  Time 1682  Continuous 1682
-failed:      102   dofs {1: 102}   Position 102   Time 102   Continuous 102
-```
-
-Combined with the 1-DOF fast path at `calculator_target.py:546`, the audit
-instrumented `PositionThirdOrderStep2.get_profile` and confirmed it is invoked
-**exactly 0 times across all 1,784 corpus cases**. The 2,744-line Step2 module —
-the largest, hardest file in the port, and the one chunk 44 just fixed a
-transcription defect in — has no oracle coverage. Its only tests are 3 boundary
-conditions × 3 scale factors.
-
-## Files
-
-- Edit: `tests/otg/test_otg_continuity.py`, `test_otg_driver.py`,
-  `test_otg_invariants.py`, `test_otg_comprehensive.py`
-- Edit: `tests/otg/test_calculator_target.py`
-- Edit: `tests/otg/steps/test_position_third_step2.py`
-- Create: multi-DOF corpus data under `tests/otg/data/`
-
-## Gaps to close
-
-1. **Multi-DOF corpus (E-4).** Generate a corpus that actually reaches Step2:
-   ≥2 DOF, so the 1-DOF fast path is bypassed. Verify reach by instrumenting
-   `PositionThirdOrderStep2.get_profile` and asserting a non-zero invocation
-   count — do not assume coverage, measure it, and record the count in the
-   resolution notes. This is the acceptance signal for the whole chunk.
-2. **Phase synchronization (E-5).** `_is_input_collinear`
-   (`calculator_target.py:154`) has **0% statement coverage (0/50)**, measured
-   by `sys.settrace` over all 222 passing OTG tests. `Synchronization.PHASE`
-   appears only as an enum-value assertion and a field assignment; it is never
-   driven through `calculate`. otg.md §Internal fidelity 3 requires this path.
-3. **Discrete duration (E-6).** `calculator_target.py:543` never exercised
-   end-to-end. Same for `minimum_duration` (never passed to `calculate`),
-   `Synchronization.TIME_IF_NECESSARY`, and `ControlInterface.VELOCITY` (never
-   driven through `calculate`/`update` — only `InputParameter.validate`).
-   `TargetCalculator.calculate` overall sits at **45% (89/198 statements)**.
-4. **Continuity across `update` cycles (E-7).** `test_otg_continuity.py:33`
-   never calls `update()` and never crosses a section boundary; all 5 cases call
-   `Otg.calculate`. The file's own docstring concedes it is "a self-consistency
-   check on the profile's internal bookkeeping, not a comparison against an
-   external oracle." Chunk 42 design constraint 3 and otg.md §Oracle 3 both
-   require continuity across consecutive `update` cycles *including at section
-   changes*. Add real cross-cycle continuity, asserting across a
-   `did_section_change` transition.
-5. **New target mid-trajectory (E-8).** No test pins it. The audit verified the
-   behavior works (retarget at cycle 11 of a 90-cycle move triggers exactly one
-   extra recalculation and converges to `-3.000000000000001`), but
-   `TestUpdateLoopReachesFinishedWithinBound` drives an unchanging input, and the
-   `new_calculation` assertion (`:109-110`) asserts the *absence* of
-   recalculation, never its presence on a genuine mid-flight change.
-6. **Intra-cycle limit violations (E-9).** `test_otg_invariants.py:142` samples
-   `new_velocity`/`new_acceleration`/`new_jerk` only at control-cycle instants,
-   1-DOF, 50 cases — intra-cycle peaks are invisible. Sample the trajectory
-   densely *within* cycles. Also: invariant (2) is evaluated on the last
-   re-planned trajectory (after `pass_to_input` at `:163` re-plans every cycle),
-   not the originally planned one, which substantially weakens "at_time(duration)
-   hits the target". Assert against the originally planned trajectory.
-7. **Under-covered Step2 branches (E-10).** `check_root_udud` (`:1041`) at
-   **3% (1/29)** and live (reachable from `_time_vel`'s UDUD branch);
-   `_time_acc0_vel` 34%, `_time_acc1_vel` 44%, `_time_acc0_acc1` 48%. The
-   multi-DOF corpus (gap 1) should reach these — measure and report which
-   remain uncovered. `_time_none_smooth` (`:2415`, 0%) is dead in Swift too and
-   documented as such: **no action, recorded**.
-8. **Missing Swift case (E-11).** Swift `OTGComprehensiveTests.swift:312`
-   defines **5** `testBugFix_*` cases; the port lands **4**.
-   `testBugFix_NegativeTimeInterval_Case3` is silently absent, and both the
-   module docstring (`test_otg_comprehensive.py:12`) and chunk 42:134 claim all
-   4/all cases are ported. It matters: the only port of that input
-   (`test_otg_failure_fixes.py:169`) wraps every assertion in `if result >= 0:`,
-   so a regression to an error `Result` would assert nothing, whereas the
-   comprehensive contract requires unconditional success. The audit ran it —
-   it passes today (`result=0`, `dur=3.5809`, target hit, `maxv=6.279 ≤ 6.282`,
-   `maxa=9.128 ≤ 9.974`). Port it and fix both docstring claims.
-
-## Design constraints
-
-1. **Measure, don't assume.** Gaps 1, 2, 3, 7 are coverage claims — report
-   before/after statement coverage for `_is_input_collinear`,
-   `TargetCalculator.calculate`, `check_root_udud`, and Step2's
-   `get_profile` invocation count.
-2. Do not loosen any tolerance. The existing 1e-6 segment-time atol was
-   human-approved with a recorded rationale and stays as is.
-3. No `pytest.skip`, `xfail`, or `expectedFailure` in new tests. If a case
-   cannot be made to pass, report it as a defect — do not park it.
-4. Generated corpus data must be reproducible: commit the generator script or a
-   fixed seed alongside the data.
-
-## Acceptance criteria
-
-- [x] Multi-DOF corpus lands; Step2 `get_profile` invocation count > 0, measured and reported
-- [x] `_is_input_collinear` coverage > 0%, measured and reported
-- [x] Discrete-duration, `minimum_duration`, `TIME_IF_NECESSARY`, and VELOCITY interface each driven through `calculate`/`update`
-- [x] Continuity asserted across `update` cycles including a `did_section_change` transition
-- [x] Mid-trajectory retarget test pins the recalculation *and* convergence
-- [x] Limits checked intra-cycle, not only at cycle instants; invariant (2) against the originally planned trajectory
-- [x] `testBugFix_NegativeTimeInterval_Case3` ported; docstring and chunk 42 claims corrected
-- [x] `TargetCalculator.calculate` coverage materially above 45%; report the number
-- [x] No skips/xfails; no tolerance loosened
-- [x] `make uv-fullCheck` passes
-
-## Out of scope
-
-`_time_none_smooth` coverage — dead in Swift, recorded as no-action.
-
-## Resolution notes
-
-**Files touched.** `tests/otg/test_calculator_target.py`,
-`tests/otg/test_otg_continuity.py`, `tests/otg/test_otg_driver.py`,
-`tests/otg/test_otg_invariants.py`, `tests/otg/test_otg_comprehensive.py`,
-`tests/otg/steps/test_position_third_step2.py` (docstring-only coverage
-note, no new cases), `tests/otg/data/generate_multi_dof_corpus.py` (new),
-`tests/otg/data/successful_trajectories_multi_dof.json` (new, 450 cases),
-and `.claude/action-plan/42-otg-oracle-suites.md` (correcting its "all 4"
-`testBugFix_*` claim per gap 8's explicit instruction — the only `src/`-free,
-doc-only touch outside this chunk's own file). No `src/` files were changed.
-
-**Gap 1 — multi-DOF corpus (E-4).** `generate_multi_dof_corpus.py` combines
-1-DOF `successful_trajectories.json` cases (fixed seed `20260722`) into
-150×2-DOF + 150×3-DOF + 150×4-DOF cases (450 total, 1,350 of the 1,682
-source cases consumed) under default `Synchronization.TIME`, filtering to
-only combinations `Otg.calculate` itself verifies succeed at generation
-time (450/450 kept, 0 rejected in the committed run — re-running the
-generator against the unmodified source corpus reproduces the JSON
-byte-for-byte, verified). `TestMultiDofCorpusReachesStep2` drives all 450
-cases through `Otg.calculate` with `PositionThirdOrderStep2.get_profile`
-instrumented: **900 invocations across 450 cases**, all succeed (0
-errors) — this is the chunk's acceptance signal, and it was measured, not
-assumed.
-
-**Gap 2 — phase synchronization (E-5).** Two new tests drive
-`Synchronization.PHASE` through `calculate()` for real:
-`TestPhaseSynchronizationCollinear` (proportional rest-to-rest targets,
-`_is_input_collinear` returns `True`, 0 Step2 calls — phase sync reuses the
-limiting DOF's own timing) and `TestPhaseSynchronizationFallsBackToTime`
-(a current-velocity ratio that doesn't match the position-delta ratio,
-`_is_input_collinear` returns `False`, falls back to per-DOF `TIME` sync
-via Step2 — confirming otg.md's "phase synchronize when possible, else fall
-back to TIME" contract). Statement coverage of `_is_input_collinear`,
-measured via `sys.settrace` over the full OTG suite: **0% (0/61) before →
-59% (36/61) after**. The remaining uncovered lines are the
-velocity/acceleration-driven scale-vector fallback branches (used only
-when the PHASE-tagged DOFs' position deltas are ~0), the "no scale vector
-found → return False" trivial path, the `math.isinf(max_jerk)` branch, and
-the second loop's `continue` for a non-PHASE DOF mixed with PHASE DOFs —
-recorded, not chased further (design constraint 1 asks for >0% measured
-and reported, not 100%).
-
-**Gap 3 — discrete duration / minimum_duration / TIME_IF_NECESSARY /
-VELOCITY (E-6).** Four new test classes, each driven through
-`TargetCalculator.calculate` (three) or `Otg.calculate` (the VELOCITY
-case): `TestDiscreteDuration` (a non-multiple-of-`delta_time` natural
-optimum gets rounded up to the next multiple), `TestMinimumDuration` (a
-1-DOF move stretched to 2x its natural optimum lands exactly on
-`minimum_duration`, via a real Step2 solve — confirmed the 1-DOF fast path
-is bypassed whenever `minimum_duration is not None`), and
-`TestTimeIfNecessarySynchronization` (both branches: a zero-target-velocity
-DOF keeps its own short unstretched duration and just holds at the target
-early, non-zero-target-velocity forces a Step2 stretch to the synchronized
-duration), `TestVelocityControlInterface` (a pure velocity-interface move
-reaches the target velocity through `set_boundary_for_velocity` +
-`VelocityThirdOrderStep1`/`Step2`).
-`TargetCalculator.calculate` statement coverage, measured the same way:
-**41.8% (167/400) before → 58.5% (234/400) after** (absolute line counts
-differ from the original post-audit's own tooling — no `coverage.py` in
-this project's venv, so an ad hoc `sys.settrace` line-counter was used
-instead; the audit's own baseline numbers also predate chunks 44-46's own
-regression tests, which already moved some of these numbers before this
-chunk started). Materially above the pre-chunk 45% figure either way.
-
-**Gap 4 — cross-cycle continuity (E-7).**
-`TestUpdateCycleContinuity` drives a real `Otg.update()` control loop to
-`FINISHED` and asserts, every cycle: `output.new_*` matches an independent
-`trajectory.at_time(output.time)` query, and the cycle-to-cycle state jump
-is bounded. A single-section (no-waypoint) trajectory has exactly one real
-`did_section_change` transition — the cycle `output.time` first crosses
-`trajectory.duration` (`Trajectory._state_to_integrate_from`'s branch
-switch) — confirmed to coincide exactly with the `FINISHED` cycle; the test
-asserts this transition occurs exactly once, at the `FINISHED` cycle, and
-that the state at that transition matches the target within `1e-6`.
-
-**Gap 5 — mid-trajectory retarget (E-8).**
-`TestMidTrajectoryRetarget` (in `test_otg_driver.py`) mutates
-`inp.target_position` at cycle 11 of a run that finishes at cycle 86 (target
-6.0 → -3.0), and asserts `new_calculation` is `True` on exactly cycles `[1,
-11]` (the initial calculation plus exactly one recalculation, never more)
-and that the loop converges to the new target (`-3.000000000000002`,
-matching the audit's own empirical observation almost to the ULP) rather
-than the original one.
-
-**Gap 6 — intra-cycle limits + invariant (2) (E-9).** Each cycle in
-`TestRandomizedValidInputInvariants` now additionally samples
-`trajectory.at_time` at 11 points across the just-elapsed cycle interval
-(not just the single control-cycle instant) and checks velocity/
-acceleration limits there too (jerk is piecewise-constant per profile
-segment, so it has no intra-segment peak the cycle-instant sample could
-miss, unlike velocity/acceleration). Investigated the premise behind
-"`pass_to_input` re-plans every cycle": empirically, for these 50 seeded
-random cases, `Otg.update()`'s change-detection sees the caller's
-`pass_to_input`-updated `current_*` state as identical to the driver's own
-internally-updated cached copy (`otg.py:173`'s own `output.pass_to_input(
-self._current_input)`), so **no case recalculates more than once** — the
-post-loop `output.trajectory` was, in every observed case, already the
-originally-planned trajectory, not a re-planned one. This doesn't
-contradict the spec (no violation to report) — but per the gap's literal
-ask, and to make the test robust to any future change in that
-change-detection behavior, invariant (2) now explicitly snapshots
-(`copy.deepcopy`) the trajectory immediately after the first
-(`new_calculation`) cycle and asserts against that snapshot, rather than
-relying on the post-loop `output.trajectory` reference remaining
-unmutated.
-
-**Gap 7 — under-covered Step2 branches (E-10).** No new cases added to
-`test_position_third_step2.py`; the multi-DOF corpus (gap 1) reaches these
-branches through realistic synchronized multi-DOF inputs. Measured via
-`sys.settrace`, before → after: `check_root_udud` 82% → 98% (1/55 lines
-unreached — a `linecache`/`dis` measurement artifact inside a nested
-function, not chased further), `_time_acc0_vel` 39% → 99% (the one
-"uncovered" line is the `def` line itself), `_time_acc1_vel` 41% → 99%
-(same artifact), `_time_acc0_acc1` 98% → 98% unchanged (one substantive
-branch remains unreached: the `check_with_timing(..., ReachedLimits.
-ACC0_ACC1, ...)` success path at `position_third_order_step2.py:1267`;
-recorded, not pursued further — design constraint 1 asks for measurement
-and reporting, not 100%). `_time_none_smooth` (0%, dead in Swift) is out of
-this chunk's scope per its own "Out of scope" section, unchanged.
-
-**Gap 8 — `testBugFix_NegativeTimeInterval_Case3` (E-11).** Ported into
-`TestBugFixNegativeTimeInterval.test_case_3` with the file's unconditional-
-success contract (unlike `test_otg_failure_fixes.py`'s existing port of the
-same input, which wraps every assertion in `if result >= 0:`). Both the
-module docstring ("Ported (4 cases)" → "Ported (5 cases)") and
-`.claude/action-plan/42-otg-oracle-suites.md`'s "All 4 of the Swift file's
-`testBugFix_*` cases are ported case-for-case" claim were corrected in
-place (with a note explaining the correction, not a silent edit).
-
-**Gate.** `make uv-fullCheck`: `uv-lint` clean, `uv-typecheck` clean (mypy
-strict, 120 source files), `uv-test` 1,548 passed (0 failures, 0 errors,
-0 skips). Full `tests/otg` suite: 237 top-level tests / 90 subtests, all
-passing, ~14s.
-
-**Deviations from the plan as written.** None functionally; the chunk 42
-doc correction (gap 8) was made as a small in-place edit with an
-explanatory note rather than a rewrite, since it is itself an
-already-committed action-plan artifact and the instruction was to correct
-a specific factual claim, not restructure the file.
diff --git a/.claude/archive/math-tools-port/57-docs-and-convention-sweep.md b/.claude/archive/math-tools-port/57-docs-and-convention-sweep.md
deleted file mode 100644
index cce5a56..0000000
--- a/.claude/archive/math-tools-port/57-docs-and-convention-sweep.md
+++ /dev/null
@@ -1,266 +0,0 @@
----
-chunk: 57-docs-and-convention-sweep
-track: F
-status: complete
-depends_on: [44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56]
-spec: ../specs/templateConformance.md, ../specs/mathToolsArchitecture.md
-last_updated: 2026-07-23
-semver: 0.0.2
-author: Nicholas Bergantz
----
-
-# 57 — Docs and convention sweep (runs last)
-
-## Origin
-
-All class **(e)** docs/convention-drift findings from the audit, plus the
-governance-test gaps. Runs last so it can also reconcile documentation against
-whatever chunks 44–56 actually changed.
-
-## Files
-
-- Edit: `Makefile`, `pyproject.toml`, `README.md`
-- Edit: `.claude/CLAUDE.md`
-- Edit: `.claude/specs/templateConformance.md`
-- Edit: `.claude/action-plan/00-overview.md` and all chunk files (frontmatter only)
-- Edit: `.claude/action-plan/42-otg-oracle-suites.md`
-- Edit: `src/math_tools/hints.py`
-- Edit: `src/math_tools/waveforms/waveform_position.py`,
-  `waveform_quaternion.py`, `waveform_spatial_pose.py` (resolution-note comments only)
-- Edit: `tests/otg/test_otg_truth_table.py`, `test_otg_comprehensive.py` (docstrings only)
-- Edit: `tests/test_governance.py`
-
-## Gaps to close
-
-**Dead references**
-
-1. **A-3** — `templateConformance.md:27-29` lists `ci.yml` / `tag-on-prod.yml` /
-   `publish.yml` as "already conformant (verify, don't re-do)".
-   `.github/workflows/` contains only `ci-cd.yml`. Correct the spec to name the
-   file that exists.
-2. **A-4** — `Makefile:434-436` prints release instructions referencing
-   `tag-on-prod.yml` and "the publish-on-tag workflow". Neither exists;
-   `make release` hands the user a dead procedure. Fix the text to match
-   `ci-cd.yml`'s actual release path, or state plainly that release is manual.
-3. **A-13** — `README.md:40` says `pip install py_math_tools`, but the package
-   is unpublished (`pyproject.toml:57-59` point at `github.com/kopecn`) and the
-   real path is `make uv-sync`. templateConformance Gap 4.1 requires the README
-   describe what actually exists.
-4. **A-8** — `pyproject.toml:15`: `keywords = ["my_package", "python", "package"]`
-   — template boilerplate that survived Gap 4.
-
-**Stale claims in test and plan docs**
-
-5. **E-doc** — `tests/otg/test_otg_truth_table.py:121` and
-   `test_otg_comprehensive.py:29` both say "segment times atol 1e-8"; the
-   constant at `test_otg_truth_table.py:55` is `1e-6`.
-6. **E-doc** — `.claude/action-plan/42-otg-oracle-suites.md:37` design constraint 2
-   still says atol 1e-8, contradicting the same file's own Resolution at `:158-168`.
-7. **E-doc** — `42-otg-oracle-suites.md:14` says "32-case numeric truth table";
-   it is 31. (The audit re-parsed all 31 Swift cases and diffed every field —
-   0 mismatches, nothing dropped. The count in the doc is simply wrong.)
-8. **C-16** — chunks 15/16 resolution notes claim `normalize()`'s zero-magnitude
-   check uses "the same `atol=1e-12` tolerance" as `Position.is_unit`. The code
-   uses an exact `norms == 0.0` (`waveform_position.py:242`,
-   `waveform_quaternion.py:266`, `waveform_spatial_pose.py:423,430`). The
-   behavior is correct — it matches `Position.normalize`'s own exact
-   `magnitude == 0.0` (`position.py:354`) — the notes are wrong. Fix the notes.
-
-**Convention drift**
-
-9. **A-9** — `00-overview.md:33-34` defines chunk status as
-   `pending` → `in_progress` / `done`. All 44 existing chunk files use
-   `status: complete`, a value the convention does not define. Reconcile:
-   amend the convention to include `complete` (simpler, matches reality) and say
-   so in the overview.
-10. **A-10** — `templateConformance.md:104-109`: all six compliance boxes remain
-    `- [ ]` though chunks 01–03 are complete and five of six are satisfied.
-    Check off what is genuinely true; leave the rest unchecked.
-11. **A-11** — `.claude/CLAUDE.md` carries no frontmatter, while all 8 specs and
-    all 44 chunks correctly carry `last_updated` / `semver` /
-    `author: Nicholas Bergantz`. Add it.
-12. **A-12** — `src/math_tools/hints.py:30-32`: an
-    `if __name__ == "__main__":` block with a bare `assert isinstance(...)`.
-    Not spec'd, not tested, not reachable. Delete.
-
-**Governance-test gaps**
-
-13. **A-5** — half the template compliance checklist has no regression test.
-    `templateConformance.md:104-105` (no `pyMathTools` hits anywhere; `py.typed`
-    present in every public package) are never asserted;
-    `tests/test_governance.py:18-43` covers only items 107-108. A rename
-    regression or a dropped `py.typed` passes the gate silently. Add both
-    assertions.
-14. **A-6** — `examples/` is entirely outside the gate: `Makefile:37`
-    (`PY_EXAMPLES ?=`) is never set, so neither `uv-typecheck` (`Makefile:281`)
-    nor `uv-lint` scans it. Chunk 03's "both example scripts import-run without
-    error" was a one-time manual check with nothing guarding it — the exact
-    dead-import class of bug Gap 4.3 existed to fix. Evidence it has already
-    drifted: `examples/sphericalPlotting/plotArcs.py:1` and
-    `plotQuatUnitCircles.py:28` use `from typing import List`, which ruff's `UP`
-    rules (`pyproject.toml:85`) would flag if scanned. Wire `examples/` into
-    lint and typecheck, then fix what that surfaces.
-
-## Design constraints
-
-1. Docs only, plus the two mechanical code deletions (gap 12) and the
-   governance/gate wiring (gaps 13–14). No behavioral source changes.
-2. Gap 14 will surface lint/type errors in `examples/`. Fix those; if any fix
-   would change example *behavior*, stop and report instead.
-3. Reconcile every doc against the post-44–56 state of the repo, not the
-   pre-audit state.
-
-## Acceptance criteria
-
-- [x] All 14 gaps closed
-- [ ] `grep -rn "tag-on-prod\|publish.yml" Makefile .claude/` returns nothing
-      -- unchecked as literally written: `Makefile` and
-      `templateConformance.md` are clean (verified separately), but the
-      grep still matches this chunk file's own gap-description prose
-      (`.claude/action-plan/57-docs-and-convention-sweep.md`, describing
-      the dead references that were fixed) and this line's own text. See
-      Resolution notes.
-- [x] `examples/` covered by `uv-lint` and `uv-typecheck`; both clean
-- [x] `test_governance.py` asserts no-`pyMathTools` and `py.typed` presence
-- [x] `.claude/CLAUDE.md` has compliant frontmatter
-- [x] `make uv-fullCheck` passes
-
-## Resolution notes
-
-**All 14 gaps closed.** File-by-file:
-
-- **A-3** (`templateConformance.md`): "Already conformant" bullet corrected
-  to name `ci-cd.yml` (quality + compatibility checks on PRs to
-  `dev`/`prod`) instead of the nonexistent `ci.yml`/`tag-on-prod.yml`/
-  `publish.yml` scaffold.
-- **A-4** (`Makefile`): `release` target's printed procedure and preceding
-  comment rewritten to state plainly that no CI-driven publish path exists
-  (`ci-cd.yml` only runs quality/compat checks) and release is a manual,
-  human-run `twine upload`. Behavior unchanged — `make release` still
-  refuses and exits 1.
-- **A-13** (`README.md`): Installation section no longer claims
-  `pip install py_math_tools`; states the package is unpublished and points
-  at `make uv-sync`, linking to Development Workflows.
-- **A-8** (`pyproject.toml`): `keywords` replaced with real, descriptive
-  terms (`math`, `numpy`, `quaternion`, `spatial`, `waveform`,
-  `trajectory-generation`), replacing the `my_package`/`python`/`package`
-  boilerplate.
-- **E-doc atol** (`tests/otg/test_otg_truth_table.py:121`,
-  `tests/otg/test_otg_comprehensive.py:41`): both corrected from the stale
-  "atol 1e-8" to the actual "atol 1e-6" the constants/spec use.
-- **E-doc constraint 2** (`42-otg-oracle-suites.md:37`): design constraint
-  2 corrected from `atol 1e-8` to `atol 1e-6` to match the chunk's own
-  Resolution notes (the historical narrative documenting *why* it changed,
-  lines 92-169, was left untouched — only the current-tense
-  Deliverable/Files/Design-constraint text describing what the chunk
-  produces was corrected).
-- **E-doc "32-case"** (`42-otg-oracle-suites.md:14,24`): corrected to
-  "31-case" in the Deliverable and Files sections (same rationale: the
-  historical Resolution-notes narrative is left as-is).
-- **C-16** (deviation from the literal Files list): the false "same
-  `atol=1e-12`" claim about `normalize()`'s zero-magnitude check does not
-  exist anywhere in `src/math_tools/waveforms/waveform_position.py`,
-  `waveform_quaternion.py`, or `waveform_spatial_pose.py` (grepped for it;
-  0 hits). It exists only in `.claude/action-plan/15-waveform-position.md`
-  and `16-waveform-quaternion.md`'s own "Resolution notes" sections — the
-  chunk's Files list appears to have mislabeled the file type for this
-  item. Fixed at the actual location instead: both chunk files' resolution
-  notes now correctly state that `are_all_unit` uses `atol=1e-12` (parity
-  with `Position.is_unit`) while the zero-magnitude `ValueError` in
-  `normalize()` uses an exact `== 0.0` check (parity with
-  `Position.normalize()`'s own exact check), not `atol=1e-12`. Bumped both
-  chunks' frontmatter (semver 0.0.1 → 0.0.2) since their body text changed.
-  `waveform_spatial_pose.py`/chunk 17 was checked and carries no such claim
-  — nothing to fix there.
-- **A-9** (`00-overview.md`): convention item 5 amended to specify
-  `complete` (not `done`) as the terminal status, matching all 57 existing
-  chunk files. Reconciled the doc to reality per the gap's own
-  recommendation rather than rewriting 44 chunk files' status fields.
-- **A-10** (`templateConformance.md` compliance checklist): checked off
-  5 of 6 boxes after independently re-verifying each (grep for
-  `pyMathTools` → 0 hits; `py.typed` in all 9 public package dirs;
-  `make uv-fullCheck` passes; `.claude/CLAUDE.md` links all 8 specs;
-  `README.md` has no "Boilerplate" text). The 6th
-  (`test_package_layering.py` "passes and fails if matplotlib is added")
-  was also checked, since `test_math_tools_does_not_import_matplotlib`
-  is a real AST-scan assertion, not a vacuous one.
-- **A-11**: `.claude/CLAUDE.md` given minimal frontmatter
-  (`last_updated`/`semver`/`author`), matching the gap's literal ask.
-- **A-12**: the dead `if __name__ == "__main__":` block deleted from
-  `src/math_tools/hints.py`; its now-unused `q_one` import removed too
-  (would otherwise trip ruff F401).
-- **A-5** (`tests/test_governance.py`): added
-  `TestNoPreRenamePackageName` (scans `src/`, `tests/`, `examples/`,
-  `Makefile`, `pyproject.toml` for the pre-rename `pyMathTools` string;
-  excludes itself and `__pycache__`) and
-  `TestPublicPackagesShipPyTyped` (walks every `__init__.py` under `src/`
-  that defines `__all__` — the mechanical definition of "public package"
-  used elsewhere in this repo, e.g. distinguishing the private
-  `otg/steps/` from public packages — and asserts a sibling `py.typed`).
-  Both pass against the current tree (6/6 governance tests green).
-- **A-6** (`examples/` gate wiring): `Makefile`'s `PY_EXAMPLES ?=` default
-  changed to `PY_EXAMPLES ?= examples`. This surfaced real lint/type
-  errors exactly as the gap predicted: unused `typing.List` imports,
-  unsorted imports, 3 genuinely-unused constants (`deg45`/`deg180`/
-  `deg22_5`) in `plotArcs.py`, a too-long docstring line, a missing `-> None`
-  return annotation, an `arcs` list typed too narrowly for what
-  `arc_from_two_points` actually returns (widened to the `UnitSphericalArcABC`
-  base it's declared to return, matching `plot_unit_spherical_multiplot`'s
-  own parameter type), and 3 `from_unit_x_to_vector(list[int])` calls
-  needing `np.ndarray` per that method's signature. All fixes are
-  mechanical (typing/import hygiene, no numeric or control-flow change);
-  verified by running both example scripts end-to-end under `Agg` backend
-  post-fix — both complete without error, matching pre-fix behavior.
-
-**Deviation from the literal acceptance grep.** The plan's acceptance
-criterion `grep -rn "tag-on-prod\|publish.yml" Makefile .claude/` cannot
-return zero hits as literally written, because this chunk file
-(`.claude/action-plan/57-docs-and-convention-sweep.md`) necessarily quotes
-those strings while describing the A-3/A-4 gaps it fixed (and now also
-quotes the acceptance-criterion line itself). Verified the substantive
-intent instead: `grep -rn "tag-on-prod\|publish.yml" Makefile
-.claude/specs/templateConformance.md` returns nothing — the two files that
-actually needed correcting are clean.
-
-**No spec-semver bump was needed on `mathToolsArchitecture.md`** — nothing
-in its content was found stale by this sweep. `templateConformance.md` was
-bumped 0.0.2 → 0.0.3 (A-3 correction + compliance-checklist checkoffs);
-`.claude/action-plan/00-overview.md` bumped 0.1.0 → 0.1.1 (status
-convention); `42-otg-oracle-suites.md` bumped 0.0.2 → 0.0.3;
-`15-waveform-position.md` and `16-waveform-quaternion.md` each bumped
-0.0.1 → 0.0.2.
-
-**Gate.** `make uv-fullCheck`: ruff clean (`src`, `tests`, `examples`),
-mypy strict clean (122 source files, up from 116 pre-sweep since
-`examples/` is now scanned), 1550 passed (up from 1548 — the 2 new
-governance tests), exit 0.
-
-## Recorded — no action
-
-These audit findings are deliberately not being fixed. Recorded so the decision
-is not relitigated:
-
-- **B-6** — `Position`/`SpatialPose` operators hardcode `Position.from_vector`
-  while constructors are `cls: type[T]`-generic, so subclasses degrade to the
-  base type on arithmetic (`position.py:245,257,320,334,364`;
-  `spatial_pose.py:192,206,212,226,253`). No subclasses exist in-repo and none
-  are planned; fixing it touches every operator. Revisit if a subclass appears.
-- **B-4/B-5** — `SpatialPose.inverse` and `UnivariatePolynomial.derivative` are
-  methods where the spec's notation implies properties. Cosmetic; changing them
-  is a breaking API change for no behavioral gain.
-- **A-7** — `spherical/` and `math_plot_helpers/` have zero behavioral tests
-  (11 public functions). Pre-existing legacy, explicitly "behavior unchanged"
-  per `mathToolsArchitecture.md:94`; no chunk ever owned them. Chunk 52 pins
-  their public surface. A test suite for them is separate scoped work.
-- **D-cross-cutting** — `WaveformPaddingStrategy`,
-  `WaveformFilterCoefficients`, `WaveformFrequencyRange` (`support.py:158,238,354`)
-  and `WaveformSpectrogramScaling` (`support.py:174`) are spec'd support types
-  that no DSP method consumes. Either the spec's YAGNI rule is violated or
-  consuming methods are missing. Deciding which is a spec question, not a fix —
-  raise it in the next spec review.
-- **D-spectral-(c)** — `spectrogram` uses legacy `scipy.signal.spectrogram`
-  where waveformDsp.md names `scipy.signal.ShortTimeFFT`. Chunk 21 permitted
-  either, so spec and code disagree but chunk and code do not. Migrating is a
-  behavioral change needing its own chunk.
-- **E-10** — `_time_none_smooth` (`position_third_order_step2.py:2415`, 0%
-  coverage) is dead in Swift too and documented as such.
diff --git a/.claude/findings/2026-08-26-spherical-spatial-packaging.md b/.claude/findings/2026-08-26-spherical-spatial-packaging.md
new file mode 100644
index 0000000..32ca643
--- /dev/null
+++ b/.claude/findings/2026-08-26-spherical-spatial-packaging.md
@@ -0,0 +1,373 @@
+---
+version: 1.0
+type: findings
+name: spherical-spatial-packaging-defects
+purpose: Reproduced defect evidence, measurements, and implementation material displaced from the specs during the 2026-08-26 normalization
+scope: project
+status: open
+applies_to: src/math_tools/spherical/, src/math_tools/spatial/, src/math_tools/waveforms/, requirements.txt, Makefile, README.md
+last_updated: 2026-09-24
+semver: 0.1.2
+author: Nicholas Bergantz
+---
+
+# Findings — spherical geometry, spatial math, packaging
+
+Companion to [sphericalGeometry.md](../specs/sphericalGeometry.md),
+[spatialMath.md](../specs/spatialMath.md),
+[waveformCore.md](../specs/waveformCore.md), and
+[templateConformance.md](../specs/templateConformance.md).
+
+This artifact holds what those specs must not: current-defect evidence,
+reproductions, measured values, source locations, and implementation material.
+The specs state the durable expected outcomes; this states what was observed on
+2026-08-26 and what an implementer needs in hand.
+
+Nothing here is normative. Recording an observation does not authorize a
+requirement.
+
+## Source
+
+Eight findings produced by an audit pass on 2026-08-26 and then presented to
+the human for decisions. All eight were independently reproduced before any
+spec was drafted. Two additional defects were found during that reproduction
+and are marked as such. None of these findings is human-authorized; they are
+observations, and the decisions taken on them are recorded separately.
+
+## F1 — `arc_from_two_points` bearing uses transposed colatitude terms
+
+**Location:** `src/math_tools/spherical/constructors.py:84`
+
+**Observed:** the `x` component is written
+`cos θ₁ · sin θ₂ − sin θ₁ · cos θ₂ · cos Δφ`; substituting `lat = π/2 − θ` into
+the standard initial-bearing formula gives `sin θ₁ · cos θ₂ − cos θ₁ · sin θ₂ · cos Δφ`.
+The two terms are transposed.
+
+| input `(φ₁,θ₁) → (φ₂,θ₂)` | requested endpoint | actual endpoint |
+| --- | --- | --- |
+| `(0.5, 0.8) → (1.2, 1.0)` | `(1.2000, 1.0000)` | `(1.3506, 0.6944)` |
+| `(0.0, 0.01) → (π/2, 1.0)` | `(1.5708, 1.0000)` | `(2.3516, 0.9930)` |
+
+**Why it survived review:** the transposed form is not wrong everywhere.
+Measured over 200 random pairs per family, correct and transposed agree
+*exactly* on the equator, on any `θ₁ = θ₂` pair, and on the `Δφ = π`
+antimeridian pair. They disagree on all 200 of `Δφ = π/2`, and differ by
+exactly `π` (opposite bearings) at `Δφ = 0`. Equal-colatitude pairs are the
+easiest examples to write by hand, which is why hand-checked spot tests pass.
+
+**Corrected form validated:** round-trip through
+`compute_spherical_arc_endpoint` over 4,000 seeded random cases, worst chordal
+error **4.1e-13**.
+
+## F1a — near-pole bearing regression vector (compliance item withdrawn)
+
+A "pole-start bearing" compliance item was drafted requiring the constructed
+arc to reach the requested target azimuth for start points down to
+`abs(sin θ₁) ≥ 1e-6`. It was withdrawn from the spec: it restated the
+constructor round-trip item without adding an observable, its "at any distance
+from a pole" wording contradicted its own lower bound, and target azimuth is
+undefined when the *target* is at a pole — an endpoint the item left unbounded.
+
+The vector it was built from is still worth exercising, with both endpoints
+held away from the poles. The near-pole start row of the F1 table above is that
+vector: `(0.0, 0.01) → (π/2, 1.0)`, requested `(1.5708, 1.0000)`, actual on the
+defective code `(2.3516, 0.9930)`. The round-trip item covers it, since
+`abs(sin 0.01) = 0.0099 ≥ 1e-6`.
+
+## F2 — arc generator builds a reversed local-north tangent
+
+**Location:** `src/math_tools/spherical/spherical_generators.py:217`
+
+**Observed:** `north_tangent = cross(east, start_point)`, which equals `−n̂`.
+The initial direction is therefore `−cos(orient)·n̂ + sin(orient)·ê`.
+
+From the equator with `orient = 0` and `arc_length = π/4`, generated points
+travel **south** to polar `2.3562` (`3π/4`), while
+`compute_spherical_arc_endpoint` correctly predicts `0.7854` (`π/4`).
+
+`generate_spherical_small_circle_points:112` already uses the correct
+`cross(center, east)` form — the two functions in the same module disagree.
+
+**Corrected form validated:** `cross(start_point, east)`, with the pole
+threshold shared with `compute_spherical_arc_endpoint`, agrees with the
+endpoint function to worst chordal **2.1e-14** over 4,000 seeded arcs at
+`num_points=33`.
+
+**Why it survived review:** `tests/spherical/` contains only
+`test_public_surface.py`, which pins exports and identity. No geometry test
+exists for the subpackage.
+
+## F2a — pole-threshold mismatch (found during reproduction, not reported)
+
+`compute_spherical_arc_endpoint:189` tests `abs(sin(theta_start)) < 1e-10`.
+The generator's branch tests `abs(z_start) < 0.999`, i.e. colatitude within
+~2.56° of a pole — a band roughly 8 orders of magnitude wider.
+
+Measured consequence of leaving them mismatched: raising only the generator's
+threshold to `1e-6` while the endpoint function stays at `1e-10` produces a
+chordal error of **1.075 radians** across the whole intervening band. A
+proposal to widen one side as a fix was evaluated and rejected on this
+measurement.
+
+## F2b — near-pole conditioning limit (found during reproduction)
+
+After both fixes, agreement is not machine-precision arbitrarily close to a
+pole. `compute_spherical_arc_endpoint` recovers `Δazimuth` through a quotient
+whose denominator is `sin(θ_start)·sin(θ_end)`; that division loses
+significance as `sin(θ_start) → 0`. The generator rotates a Cartesian vector
+and does not. The residual is the endpoint function's conditioning.
+
+Measured worst-case chordal disagreement, shared threshold at `1e-10`:
+
+| `abs(sin(polar_start))` | worst chordal error |
+| --- | --- |
+| `1e-4` | 1.4e-13 |
+| `1e-5` | 5.8e-12 |
+| `1e-6` | 1.3e-10 |
+| `1e-7` | 7.0e-10 |
+| `1e-8` | 9.9e-09 |
+| `1e-9` | 3.4e-08 |
+| `1.1e-10` | 4.2e-07 |
+| below threshold | exact (shared pole convention) |
+
+The spec states the resulting bands as normative outcomes. Narrowing the
+sliver would require reformulating the endpoint function's `Δazimuth`
+computation — not requested, not authorized.
+
+## F2c — azimuth range split defeats naive comparison
+
+`compute_spherical_arc_endpoint` normalizes to `[0, 2π)`; the generators
+return raw `arctan2` output in `(-π, π]`. For `orient = -2.0` a correct
+implementation yields `4.283185…` and `-2.0` — exactly `2π` apart. Any
+equality or `assertAlmostEqual` comparison fails on correct code. Verified
+live.
+
+## F2d — a monotonicity test has no power against F2
+
+A monotone-traversal check was drafted as a compliance item on the reasoning
+that a tangent sign error produces fold-back at the midpoint. Measured against
+the live F2 defect: **0 of 200** random arcs produced any fold-back. A sign
+flip reverses direction without folding the path. The item was replaced with a
+midpoint-agreement check, which does discriminate.
+
+## F3 — `angular_distance` saturates for non-unit quaternions
+
+**Location:** `src/math_tools/spatial/spatial_pose.py:242`
+
+Clips an unnormalized dot product. Two quaternions separated by 60° and scaled
+by 3 report **0.0** rather than `1.047198`. Clipping does not sanitize an
+unnormalized dot — it saturates it.
+
+## F3a — `Quaternion.angle` has the same defect (found during review)
+
+**Location:** `src/math_tools/spatial/quaternion.py:317`
+
+`2.0 * arccos(clip(self.w, -1.0, 1.0))` reads a raw `w` with no norm division.
+A 60° rotation scaled by 5 reports **0.0°**.
+
+`Quaternion.axis` was checked and is already scale-invariant.
+
+Authorized by the human on 2026-08-26 to become normative for `angle` only;
+`axis` and `interpolate` explicitly left unchanged.
+
+## F4 — zero-magnitude normalization yields NaN
+
+| Location | Observed |
+| --- | --- |
+| `quaternion.py:684` (`from_axis_angle`) | `quaternion(0.8775825618903728, nan, nan, nan)` — finite `w`, three NaN |
+| `quaternion.py:293` (`normalized`) | `quaternion(nan, nan, nan, nan)` |
+| `quaternion.py` (`inverse`) | `1.0 / q` on the zero quaternion is NaN |
+
+The `from_axis_angle` case is the worse of the two: a plausible-looking finite
+`w` makes the result read as valid at a glance.
+
+`Position.normalize()` already raises `ValueError` on the zero vector, so the
+sibling contract exists and `Quaternion` diverges from it.
+
+## F5 — the foundation dependency pin is mutable
+
+`requirements.txt:22` currently pins `pyFoundationTools @ git+https://github.com/kopecn/py-foundationTools.git@dev`.
+
+`dev` is a branch, so the same requirements file can resolve to different commits over time. This violates [templateConformance.md](../specs/templateConformance.md) §Pin immutability and prevents a clean environment from being reproducible from the declared dependency source alone.
+
+The prior dead-branch reference has been replaced, and every test-running Makefile path now installs `requirements.txt` before the editable package. The remaining defect is limited to replacing `dev` with a remotely reachable release tag or full commit SHA that supplies the required foundation import surface.
+
+## F7 — waveform insertion rejects indices `list.insert` clamps
+
+**Locations:** `waveform1d.py:812`, `waveform_position.py:324`,
+`waveform_quaternion.py:352`, `waveform_spatial_pose.py:620` — all bare
+`np.insert`.
+
+`np.insert` raises `IndexError` outside `[-n, n]`; `list.insert` clamps.
+Measured on a 3-sample waveform, `insert(99, x)` raises on all four classes,
+where `[0,1,2].insert(99, 9)` appends.
+
+None of the four `insert` methods carries a docstring, unlike `pop()` beside
+each, which documents its `IndexError`.
+
+## F8 — spatial deserializers rely on assertions
+
+| Location | `from_dict(<non-dict>)` raises |
+| --- | --- |
+| `position.py:149` | `AssertionError` |
+| `spatial_pose.py:118` | `AssertionError` |
+| `quaternion.py:829` | `AttributeError` (no `isinstance` check at all) |
+
+Under `python -O` the asserts are stripped and `Position.from_dict` degrades to
+`AttributeError` — verified live. Two duplicate assert-based numeric coercers
+exist: `Position._from_float` (`position.py:53`) and `Quaternion.from_float`
+(`quaternion.py:47`).
+
+---
+
+# Material for the implementation plan
+
+Displaced from the specs during normalization. This is plan input, not
+contract.
+
+## Index-clamping recipe (F7)
+
+Clamp before delegating to the array helper, in each of the four `insert`
+methods:
+
+```python
+n = len(self._values)
+if index < 0:
+    index = max(0, n + index)
+else:
+    index = min(index, n)
+```
+
+`WaveformSpatialPose.insert` clamps **once** and applies the same index to
+both parallel arrays, so `len(positions) == len(quaternions)` is preserved. A
+per-array clamp would desynchronize them.
+
+## Shared deserializer helper (F8)
+
+New private module `src/math_tools/spatial/_serde.py`, replacing
+`Position._from_float` and `Quaternion.from_float`. Private: leading
+underscore, no `__all__` entry, no public-surface change.
+
+While editing the three `from_dict` methods, unify their signatures:
+`Position` and `SpatialPose` use `from_dict(cls: type[T], obj: Any) -> T`;
+`Quaternion.from_dict(cls, obj: Any) -> Quaternion` hardcodes the return type
+and breaks subclass covariance. `Quaternion` adopts the `TypeVar` form.
+
+## Docstring edit targets (spherical)
+
+`spherical_generators.py` describes `orient` as a right-hand-rule rotation
+about the radial vector at lines 169–171, 181–182, 202, 209, and 226 — replace,
+do not append. Line 227 already reads "orient=0 points north, positive orient
+rotates towards east", so the file contradicts itself; the compass wording is
+the one that stays. The module docstring (lines 7–36) documents θ and φ but
+never defines `orient` at all.
+
+`arc_from_two_points`' docstring claims the `isPositive=False` arc "reaches
+toward (azimuth2, polar2)". It does not.
+
+Suggested check after the edit:
+`grep -niE "right.hand|thumb|fingers curl" src/math_tools/spherical/` returns
+nothing.
+
+## Shared-constant check (spherical)
+
+`spherical_generators.py:132` carries an unrelated, legitimate
+`axis_norm > 1e-10` (a Rodrigues axis-degeneracy guard in the small-circle
+loop). A bare `grep 1e-10` cannot distinguish it from a pole literal, so the
+conformance check must be line-scoped to lines involving `sin(`.
+
+## Test material
+
+- Regression case for F1: `(0.5, 0.8) → (1.2, 1.0)`.
+- Non-discriminating control worth asserting as such: a `θ₁ = θ₂` pair, which
+  both the correct and transposed formulas pass.
+- Mandatory case for F2c: `orient = -2.0`, which exposes a naive `==`.
+- Literal scale cases: 60°/scale-3 for `angular_distance`, 60°/scale-5 for
+  `Quaternion.angle`.
+- `tests/spherical/` currently holds only `test_public_surface.py`; geometry
+  test files do not yet exist.
+- Gate: `make uv-fullCheck`.
+
+## Downstream consumers to re-check after the spherical fixes
+
+`examples/sphericalPlotting/plotArcs.py` chains
+`compute_spherical_arc_endpoint` into `arc_from_two_points`. Note it is **not**
+a discriminating check: its inputs land on `Δφ = -π/2` with `θ₂ = 0`, where
+both bearing formulas return 0.
+
+`src/math_plot_helpers/plot_unit_spherical.py:878-892` holds demo arcs whose
+expected directions are only consistent with the compass reading of `orient`.
+
+## Recorded, not actioned
+
+- `Makefile` `uv-sync-release` installs `requirements-release.txt`, which does
+  not exist; the target fails if run. Human decision 2026-08-26: leave it,
+  report only.
+- `Quaternion` keeps `fromNumpyQuaternion` / `to_unitSphericalSmallCircle` as
+  permanent aliases with no `DeprecationWarning` and no sunset path.
+- The Tier-2 ABC docstring `UnitSphericalArcABC.orient` ("Rotated orientation
+  about the origin->start vector") carries the right-hand-rule wording that
+  conflicts with the compass convention. Fixing it is a py-foundationTools
+  change; worth filing upstream.
+
+## Test vectors and verification procedure
+
+Displaced from spec compliance sections, which state outcomes rather than the
+inputs that demonstrate them.
+
+### Waveform insertion (F7)
+
+Differential vector against stdlib. On a 3-sample waveform, for
+`i ∈ {-99, -4, -3, -1, 0, 1, 2, 3, 4, 99}`, the resulting order matches the
+identical `list.insert` call on `[0, 1, 2]` and nothing raises. Boundary
+illustrations:
+
+```
+[1, 2, 3].insert(99, 9)   → [1, 2, 3, 9]
+[1, 2, 3].insert(-99, 0)  → [0, 1, 2, 3]
+```
+
+`WaveformSpatialPose` is additionally checked for equal parallel-array lengths
+after a clamped insertion.
+
+### Spherical geometry
+
+- Randomized items use an explicitly seeded generator (`np.random.default_rng`
+  with a literal seed) so failures reproduce.
+- Constructor round-trip coverage must include a pair with `Δφ ∉ {0, π}` and
+  `θ₁ ≠ θ₂`. Coincident-value families do not discriminate the contracted
+  formula from the transposed one (F1), so a suite built only from
+  equal-colatitude or antimeridian pairs passes against the defect.
+- Generator/endpoint agreement is exercised in both accuracy bands: the
+  guaranteed band and the near-pole sliver.
+- Pole agreement is exercised with at least one negative `orient`, which is
+  where the azimuth-range split (F2c) makes a naive equality comparison fail
+  on correct code.
+- `POLE_EPS` conformance is checked line-scoped to bearing-resolving code, not
+  by a bare literal grep — see the `spherical_generators.py:132` caveat above.
+
+### Spatial math
+
+- Scale invariance: literal cases 60°/scale-3 for `angular_distance` and
+  60°/scale-5 for `Quaternion.angle`, plus scale factors below 1.
+- Deserializer suite runs twice, once under `python -O`.
+
+### Packaging
+
+Pin and install-path conformance is verified against a **fresh** environment.
+An existing working environment is not evidence: it can hold an install of a
+ref that is no longer remotely reachable, which is precisely what masked F5.
+
+## Implementation notes displaced from spec prose
+
+- **Scale invariance (F3, F3a):** divide by the operand norms, or normalize,
+  *before* the range-limiting step. Clipping an unnormalized dot product or a
+  raw `w` component to `[-1, 1]` saturates rather than sanitizes.
+- **Near-pole bands (F2b):** the bound originates in
+  `compute_spherical_arc_endpoint`'s `Δazimuth` recovery, whose denominator
+  carries a factor of `sin(θ_start)`. The generator rotates a Cartesian vector
+  and does not share the conditioning.
+- **`assert` on deserializer paths (F8):** prohibited, because assertions are
+  stripped under `python -O`, turning a rejected payload into a silently
+  constructed object. The spec states the equivalent outcome (behaviour
+  identical with assertions disabled) rather than the mechanism ban.
diff --git a/.claude/settings.json b/.claude/settings.json
new file mode 100644
index 0000000..61eb5e1
--- /dev/null
+++ b/.claude/settings.json
@@ -0,0 +1,7 @@
+{
+  "permissions": {
+    "allow": [
+      "Bash(make *)"
+    ]
+  }
+}
diff --git a/.claude/specs/mathToolsArchitecture.md b/.claude/specs/mathToolsArchitecture.md
index 6bac934..42159fe 100644
--- a/.claude/specs/mathToolsArchitecture.md
+++ b/.claude/specs/mathToolsArchitecture.md
@@ -3,19 +3,17 @@ version: 1.0
 type: umbrella-architecture
 name: mathToolsArchitecture
 purpose: Layering, package layout, dependency policy, and shared conventions for py-MathTools
-spec: MathToolsArchitecture
 scope: project
-status: accepted
-applies_to: src/, tests/, pyproject.toml
-last_updated: 2026-07-11
-semver: 0.0.2
+applies_to: src/, tests/, pyproject.toml, requirements.txt
+last_updated: 2026-09-24
+semver: 0.1.1
 author: Nicholas Bergantz
 ---
 
 # py-MathTools Architecture
 
-> Umbrella spec. Each module's behavioral contract lives in a sibling spec
-> (index at the bottom); this spec owns the layering, the package layout, the
+> Umbrella spec. Each module's behavioral contract lives in a sibling spec;
+> this spec owns the layering, the package layout, the
 > dependency policy, and the conventions every sibling inherits. On conflict
 > within this repo, this spec wins for structure; the sibling wins for its own
 > module's behavior.
@@ -43,11 +41,7 @@ Rules that follow:
 2. py-MathTools **never re-implements storage/data-carrier types** that
    foundation already generates; it interoperates with them via
    `to_dict`/`from_dict` (wire-format parity is the compatibility contract).
-3. Dependency direction is one-way: py-MathTools → pyFoundationTools. Nothing
-   in foundation may import this package. The foundation-side `XxxxMathLike`
-   modules referenced by `mathTypeTiers.md` do not exist yet; when foundation
-   adds them, tightening our base classes is a follow-on task in that repo's
-   cadence — not assumed here.
+3. Dependency direction is one-way: py-MathTools → pyFoundationTools. Nothing in foundation may import this package.
 
 ## Dependency policy (differs from foundation)
 
@@ -70,9 +64,7 @@ per the template BKM (see [templateConformance.md](templateConformance.md)).
 
 ## Packages and layering
 
-Two top-level snake_case packages under `src/` (replacing `pyMathTools` and
-`pyMathToolsPlotHelpers` — see the rename contract in
-[templateConformance.md](templateConformance.md)):
+Two top-level snake_case packages under `src/`:
 
 ```
 math_plot_helpers  →  math_tools  →  pyFoundationTools  →  stdlib
@@ -87,11 +79,11 @@ No reverse imports. `matplotlib` never appears in `math_tools`.
 src/math_tools/
   __init__.py            # curated public re-exports (see Public surface)
   py.typed
-  hints.py               # shared type aliases (migrated from pyMathTools/hints.py)
+  hints.py               # shared type aliases
   errors.py              # exception hierarchy (see Error semantics)
   precision_time/        # PrecisionTimeInterval, PrecisionTimestamp   → precisionTimeMath.md
   spatial/               # Position, Quaternion, SpatialPose           → spatialMath.md
-  spherical/             # migrated spherical arc/circle utilities (behavior unchanged)
+  spherical/             # unit-sphere arcs/circles/transforms       → sphericalGeometry.md
   waveforms/             # Waveform1D + aggregates                     → waveformCore.md
     dsp/                 # DSP mixin per family                        → waveformDsp.md
     support.py           # DSP descriptor dataclasses/enums            → waveformDsp.md
@@ -99,8 +91,7 @@ src/math_tools/
   otg/                   # online trajectory generation (Ruckig port)  → otg.md
 ```
 
-`src/math_plot_helpers/` holds the migrated plotting module(s); rename-only,
-no behavioral change in this effort.
+`src/math_plot_helpers/` holds the plotting module(s).
 
 ## Shared conventions (inherited by every sibling spec)
 
@@ -135,11 +126,8 @@ no behavioral change in this effort.
 - **Error semantics:** see below.
 - **Testing:** `unittest.TestCase` style run under pytest (repo convention,
   `tests/test*.py`); tests mirror the package layout
-  (`tests/spatial/test_position.py`, …). TDD per chunk. Gate:
-  `make uv-fullCheck`.
-- **Docstrings:** every public symbol; module docstrings state conventions
-  (e.g. the ISO spherical convention doc in the existing `spherical/` module
-  stays canonical).
+  (`tests/spatial/test_position.py`, …).
+- **Docstrings:** every public symbol; module docstrings reference the governing convention where needed. [sphericalGeometry.md](sphericalGeometry.md) is authoritative for the ISO spherical convention.
 
 ## Error semantics
 
@@ -171,18 +159,6 @@ class PolynomialSolveError(MathToolsError): ...         # unsolvable/ill-posed r
 4. **Swift stubs are not ported:** `Waveform1D+Custom`, the empty
    `SpatialWaveforms/Operators/*+Arithmetic` files, and the empty
    `PrecisionTime/Extensions` files define no behavior.
-5. **Serialization file I/O helpers** (Swift's CSV/JSON `load/save`) are not
-   part of this effort; wire interop is `to_dict`/`from_dict` (foundation's
-   `DataModelHelper` owns file I/O patterns).
-
-## Sibling spec index
-
-| Spec | Contract |
-|---|---|
-| [templateConformance.md](templateConformance.md) | template migration: packaging, Makefile/CI parity, rename, governance |
-| [precisionTimeMath.md](precisionTimeMath.md) | `PrecisionTimeInterval`, `PrecisionTimestamp` |
-| [spatialMath.md](spatialMath.md) | `Position`, `Quaternion`, `SpatialPose` |
-| [waveformCore.md](waveformCore.md) | `Waveform1D` + aggregate waveform containers |
-| [waveformDsp.md](waveformDsp.md) | DSP families, scipy mapping, support types |
-| [polynomials.md](polynomials.md) | polynomial type + analytic root solvers |
-| [otg.md](otg.md) | online trajectory generation (Ruckig port) |
+5. **No serialization file I/O helpers.** Wire interop is
+   `to_dict`/`from_dict`; foundation's `DataModelHelper` owns file I/O
+   patterns.
diff --git a/.claude/specs/otg.md b/.claude/specs/otg.md
index 186e485..38d8997 100644
--- a/.claude/specs/otg.md
+++ b/.claude/specs/otg.md
@@ -3,12 +3,10 @@ version: 1.0
 type: specification
 name: otg
 purpose: Behavioral contract for the online trajectory generation (OTG / Ruckig-port) subsystem
-spec: OTG
 scope: project
-status: accepted
 applies_to: src/math_tools/otg/, tests/otg/
-last_updated: 2026-07-22
-semver: 0.0.5
+last_updated: 2026-09-24
+semver: 0.0.6
 author: Nicholas Bergantz
 ---
 
@@ -21,7 +19,7 @@ author: Nicholas Bergantz
 > (1) identical results on the truth-table oracles, (2) identical public
 > semantics, (3) code structure mirroring the Swift files so the two ports
 > stay diffable. Numeric kernel: `functional/roots.py`
-> ([polynomials.md](polynomials.md)) — the OTG chunks MUST NOT reimplement
+> ([polynomials.md](polynomials.md)) — the OTG subsystem MUST NOT reimplement
 > root solving.
 
 ## Module layout (mirrors the Swift files 1:1)
@@ -51,14 +49,6 @@ math_tools/otg/
     velocity_third_order.py    # VelocityThirdOrderStep1/Step2
 ```
 
-**Chunking hints (sized for one-session execution):**
-`position_third_order_step1.py` and `position_third_order_step2.py` are
-separate modules AND separate chunks (combined they are ~2,750 Swift lines —
-never one chunk; split further along Swift function boundaries if needed,
-preserving diffability). `profile.py` (~715 Swift lines),
-`calculator_target.py` (~780), and the `Otg` driver each get their own
-chunk.
-
 Only the `__init__.py` re-exports are public; `steps/`, `block/bound/brake`,
 and `calculator_target` are private (`_`-free filenames but excluded from
 `__all__`; they mirror Swift `internal`).
@@ -130,35 +120,7 @@ invalid.
 3. `TargetCalculator.synchronize` reproduces the Swift block-interval
    synchronization (including `Block`/`Interval` blocked-interval logic and
    the discrete-duration path).
-4. Float64 throughout; comparisons use the Swift port's exact epsilon
-   constants (`EPS16`, `POLYNOMIAL_*` from `functional/roots.py` — never
-   fresh literals). Swift `Double` division silently yields `inf`/`nan` on
-   a zero denominator (IEEE 754); Python's `/` raises `ZeroDivisionError`
-   instead. Where a step solver's own algebra can produce a legitimate
-   zero denominator at a degenerate root (e.g.
-   `steps/position_third_order_step1.py`'s `_time_all_none_acc0_acc1`, a
-   `t == 0` quartic root when the polynomial's constant term is zero), the
-   division is routed through an IEEE-754-semantics helper
-   (`_ieee754_div`) instead of the bare `/` operator, reproducing Swift's
-   silent nan/inf propagation (which `Profile.check`'s precision
-   comparisons then naturally reject) rather than crashing. This is NOT a
-   blanket rule to wrap every division in the OTG port — only sites where
-   a real Swift Double division-by-zero has been shown (by a failing
-   test) to be reachable. The same total-vs-partial-function divergence
-   applies to `sqrt`: Swift `Double`'s `sqrt` of a negative argument is
-   `nan` (never traps), Python's `math.sqrt` raises `ValueError`. A
-   negative-discriminant `sqrt` is the *generic* way a Step2 time-
-   synchronization solver's algebra signals "no real solution at this
-   prescribed duration" — reachable from ordinary usage (any
-   below-time-optimal duration), not a rare degenerate root — so
-   `steps/position_third_order_step2.py` routes every `sqrt` call through
-   an `_ieee754_sqrt` helper file-wide, unlike `_ieee754_div`'s
-   deliberately per-site scoping (see that file's module docstring and
-   `_ieee754_sqrt`'s docstring for the reachability trace that motivated
-   the broader scope, and `39-otg-position-third-step2.md`'s Resolution
-   notes). Future step-solver chunks should default to `_ieee754_div`'s
-   narrower, failing-test-driven scoping and only widen it the way this
-   file did if a similar cascade is demonstrated.
+4. Float64 throughout; comparisons use the Swift port's exact epsilon constants (`EPS16`, `POLYNOMIAL_*` from `functional/roots.py`) rather than fresh literals. Reachable divisions that may have a zero denominator use `_ieee754_div` so Python reproduces Swift `Double`'s `inf`/`nan` propagation instead of raising `ZeroDivisionError`; the helper is applied only at demonstrated reachable sites. `steps/position_third_order_step2.py` routes its synchronization-solver square roots through `_ieee754_sqrt`, because a negative discriminant represents no real solution at the prescribed duration and SHALL yield `nan` rather than raise `ValueError`.
 5. Pure Python + stdlib `math` in the per-cycle path (no numpy — scalar
    loops over DOFs, matching Swift; performance is explicitly a non-goal
    until measured).
@@ -169,27 +131,17 @@ Two oracle tiers — the JSON corpus records **inputs only** (no durations, no
 kinematics, no Result codes), so it can classify but not pin numbers; the
 numeric golden lives in a hardcoded Swift test array.
 
-1. **Classification corpus:** copy `successful_trajectories.json`
-   (~1,680 cases) and `failed_trajectories.json` (~100 cases) from
-   `spmMathTools/spm/Tests/spmMathToolsTests/OTGTests/truthTables/` into
-   `tests/otg/data/` unmodified. `test_otg_truth_table.py` asserts:
+1. **Classification corpus:** `tests/otg/data/` contains unmodified `successful_trajectories.json` (~1,680 cases) and `failed_trajectories.json` (~100 cases) from the Swift truth-table source. `test_otg_truth_table.py` asserts:
    successful cases → `calculate` returns a non-error `Result`
    (`Result >= 0`); failed cases → an error `Result` (`Result < 0` — the
    JSON's free-text error strings are NOT mapped to specific codes).
-2. **Numeric oracle:** port the 31-case hardcoded truth table from
-   `OTGTruthTableTests.swift` (each case: input state/limits +
-   `expectedDuration` + `expectedTimeIntervals`, the 7 profile segment
-   times) into `tests/otg/data/otg_numeric_truth.json`, transcribed
-   verbatim from the Swift literals. Assertions per case: trajectory
+2. **Numeric oracle:** `tests/otg/data/otg_numeric_truth.json` contains the 31 cases from `OTGTruthTableTests.swift`, transcribed verbatim with input state, limits, `expectedDuration`, and the seven `expectedTimeIntervals`. Assertions per case: trajectory
    duration rtol 1e-6; `Profile.t` segment times against
    `expectedTimeIntervals` atol 1e-6 (this pins branch selection, not just
    the coincidentally-summable duration; capped at 1e-6 rather than 1e-8
    because the Swift literals themselves are recorded to only 6 decimal
    places — a tighter atol cannot be satisfied by any correct port).
-3. **Ported suites:** the Swift `OTGComprehensiveTests`, `OTGContinuityTests`
-   (position/velocity/acceleration continuity across cycle boundaries and
-   section changes), and `OTGFailureFixTests` regression cases are ported
-   test-for-test.
+3. **Reference suites:** the test set covers the cases from Swift `OTGComprehensiveTests`, `OTGContinuityTests` (position/velocity/acceleration continuity across cycle boundaries and section changes), and `OTGFailureFixTests`.
 4. **Invariant tests:** for randomized (seeded) valid inputs — output never
    exceeds max velocity/acceleration/jerk beyond 1e-9; `at_time(duration)`
    hits the target state within 1e-8; `FINISHED` is reached within
diff --git a/.claude/specs/polynomials.md b/.claude/specs/polynomials.md
index 3a18bde..5452002 100644
--- a/.claude/specs/polynomials.md
+++ b/.claude/specs/polynomials.md
@@ -3,12 +3,10 @@ version: 1.0
 type: specification
 name: polynomials
 purpose: Behavioral contract for the univariate polynomial type and the analytic root solvers
-spec: Polynomials
 scope: project
-status: accepted
 applies_to: src/math_tools/functional/, tests/functional/
-last_updated: 2026-07-23
-semver: 0.0.4
+last_updated: 2026-09-24
+semver: 0.0.5
 author: Nicholas Bergantz
 ---
 
@@ -97,38 +95,8 @@ Rules:
    ascending convention).
 3. Pure `math`-module scalar code — **no numpy** in this module (called
    per-cycle by OTG; keep it allocation-light).
-4. Degenerate leading coefficients degrade exactly as Swift does (cubic with
-   `a ≈ 0` within tolerance solves the quadratic, etc.) -- with one accepted
-   deviation from the literal Swift source: `solve_cubic`'s leading-
-   coefficient degeneracy check (`Roots.swift:37`'s `abs(a) < .ulpOfOne`) is
-   an **absolute** threshold, which is wrong across the coefficient scales
-   this module sees. A coefficient like `a = 1e-10` against `b, c, d` of
-   order 1 is negligible, but `1e-10 >> ulpOfOne`, so the literal port took
-   the cubic branch, whose `1/a**3` scaling amplifies rounding error until
-   the solve collapses (confirmed: `solve_cubic(1e-10, 2.0, -3.0, -2.0)`
-   returned `[]` instead of the root near `2.0`). `roots.py` instead uses a
-   **scale-relative** threshold:
-   `abs(a) <= 1e-6 * max(abs(b), abs(c), abs(d))` (constant
-   `_CUBIC_LEADING_COEFF_EPS`). `1e-6` is chosen empirically as the
-   crossover where the closed-form cubic formula's error (which grows as
-   `a` shrinks, due to the `1/a**3` scaling) exceeds the quadratic
-   fallback's error (which shrinks as `a` shrinks, `O(a)` by dropping the
-   cubic term) -- pinned by the decade sweep in
-   `TestSolveCubicNearZeroLeadingCoefficient` (`tests/functional/test_roots.py`),
-   `a` from `1e-4` to `1e-14` against `b, c, d` of order 1-5.
-5. **Accepted deviation from the literal Swift source:** `solve_cubic`'s
-   `halfq` (the depressed-cubic resolvent term `R`) is scaled by `inva *
-   invaa` (`1/a³`), not `Roots.swift:70`'s literal `invaa * invaa` (`1/a⁴`).
-   The standard resolvent `R = (2A³ − 9AB + 27C) / 54` (`A=b/a, B=c/a,
-   C=d/a`) scales as `1/a³`; the Swift source's `1/a⁴` is a latent scaling
-   bug, inert at both of its call sites (`PositionThirdOrderStep2.swift`,
-   `PolynomialUnivariateFunction.swift`) because they always pass a monic
-   cubic (`a == 1`, where `1/a³ == 1/a⁴`). It is not inert for general
-   coefficients: Compliance 2b (below) requires agreement with `np.roots`
-   for randomized non-monic cubics, which the literal `1/a⁴` scaling fails
-   for any `a != 1`. This is the one intentional arithmetic correction in
-   this otherwise line-by-line port; it is called out inline in
-   `roots.py`'s `solve_cubic`.
+4. Degenerate leading coefficients use the scale-relative threshold `abs(a) <= 1e-6 * max(abs(b), abs(c), abs(d))`, exposed internally as `_CUBIC_LEADING_COEFF_EPS`, before degrading a cubic to the quadratic solver.
+5. `solve_cubic` scales the depressed-cubic resolvent term `halfq` by `inva * invaa` (`1/a³`). This intentionally corrects the Swift source's `1/a⁴` expression and is required for non-monic cubic agreement with Compliance 2b.
 
 ## Compliance requirements (test-checkable)
 
diff --git a/.claude/specs/precisionTimeMath.md b/.claude/specs/precisionTimeMath.md
index 4e00aab..1f40148 100644
--- a/.claude/specs/precisionTimeMath.md
+++ b/.claude/specs/precisionTimeMath.md
@@ -1,14 +1,12 @@
 ---
-version: 1.0
+version: 1.1
 type: specification
 name: precisionTimeMath
 purpose: Behavioral contract for the Tier-3 PrecisionTimeInterval and PrecisionTimestamp math types
-spec: PrecisionTimeMath
 scope: project
-status: accepted
 applies_to: src/math_tools/precision_time/, tests/precision_time/
-last_updated: 2026-07-11
-semver: 0.0.2
+last_updated: 2026-09-24
+semver: 0.0.4
 author: Nicholas Bergantz
 ---
 
@@ -69,10 +67,13 @@ noted; `NotImplemented` for foreign types so Python falls back correctly):
 - `==`, `<`, `<=`, `>`, `>=` (total ordering on signed total), `__hash__`.
 - `bool(x)` is `not x.is_zero`.
 
-**Serialization**: `to_dict` inherited from the ABC; `from_dict` accepts the
-ABC wire shape `{"seconds", "attoseconds", "sign"}` — exactly what
-`foundationTypes` `PrecisionTimeIntervalType.to_dict()` emits (wire-format
-interop is the Tier-1↔Tier-3 contract).
+**Serialization**: `to_dict` and `from_dict` are both implemented on this
+class (the Tier-2 ABC declares them abstract and, per `mathTypeTiers.md`, must
+stay free of concrete wire mappings — there is nothing to inherit). Both use
+the ABC wire shape `{"attoseconds", "seconds", "sign"}` (`sign` as its string
+value) — exactly what `foundationTypes` `PrecisionTimeIntervalType.to_dict()`
+emits, so payloads round-trip through either carrier (wire-format interop is
+the Tier-1↔Tier-3 contract).
 
 ## `PrecisionTimestamp`
 
@@ -110,8 +111,10 @@ epoch), `days_since_epoch: int`, `seconds_of_day: int`,
   rendering of Swift's `Result<ComparisonResult, ComparisonValidationError>`
   in `PrecisionTimestamp+Comparable.swift`.
 
-**Serialization**: ABC `to_dict` (camelCase optional keys); `from_dict`
-accepts the same wire shape (parity with `PrecisionTimestampType`).
+**Serialization**: `to_dict` and `from_dict` are both implemented on this
+class (camelCase optional keys `referenceFrame`/`timescale`/`uncertainty`
+emitted only when present); the wire shape matches `PrecisionTimestampType`
+for round-trip parity.
 
 ## Compliance requirements (test-checkable)
 
@@ -124,4 +127,7 @@ accepts the same wire shape (parity with `PrecisionTimestampType`).
 7. `timestamp - timestamp` across the epoch (one pre-1970 operand) is exact.
 8. `compare_validated` raises `TimestampComparisonError` on differing timescale (both set), differing frame (both set), and overlapping uncertainty (both set, delta ≤ combined — pin the boundary case delta == combined as raising); returns -1/0/1 otherwise. `can_compare` is True when either side's metadata is `None` and ignores uncertainty.
 9. `as_datetime`/`from_datetime` round-trips to microsecond precision, including a pre-epoch instant.
-10. mypy strict clean; all classes pass `isinstance(x, <ABC>)`.
+10. mypy strict clean; all classes structurally conform to their Tier-2
+    `<ABC>`. The ABC is a non-runtime_checkable `typing.Protocol`, so
+    conformance is verified by member presence (`hasattr` over
+    `<ABC>.__abstractmethods__`), not `isinstance`.
diff --git a/.claude/specs/spatialMath.md b/.claude/specs/spatialMath.md
index 5467715..0ea3250 100644
--- a/.claude/specs/spatialMath.md
+++ b/.claude/specs/spatialMath.md
@@ -1,14 +1,12 @@
 ---
-version: 1.0
+version: 1.1
 type: specification
 name: spatialMath
 purpose: Behavioral contract for the Position, Quaternion, and SpatialPose math types
-spec: SpatialMath
 scope: project
-status: accepted
 applies_to: src/math_tools/spatial/, tests/spatial/
-last_updated: 2026-07-11
-semver: 0.0.2
+last_updated: 2026-09-24
+semver: 0.1.2
 author: Nicholas Bergantz
 ---
 
@@ -24,40 +22,65 @@ author: Nicholas Bergantz
 | Class | Module | Subclasses | Storage |
 |---|---|---|---|
 | `Position` | `spatial/position.py` | `PositionABC` | `np.ndarray` shape `(3,)` float64 |
-| `Quaternion` | `spatial/quaternion.py` (migrated existing class) | `QuaternionABC` (already) | `numpy-quaternion` (already) |
+| `Quaternion` | `spatial/quaternion.py` | `QuaternionABC` | `numpy-quaternion` |
 | `SpatialPose` | `spatial/spatial_pose.py` | `SpatialTransformABC` | composed `Position` + `Quaternion` |
 
-`Quaternion` is the **existing, tested implementation** (~90 tests). Its
-math behavior is authoritative and unchanged, but one structural edit is
-REQUIRED: the pinned foundation branch deleted
-`foundationTypes.mathTypes.quaternionABC` — the base class re-parents to
-`foundation_abc.math.spatialABCs.QuaternionABC`. The old ABC also carried
-`DataModelHelper`; the new one is `ABC`-only, so serialization tests that
-assert `DataModelHelper` inheritance update their base-class assertions
-(`to_dict`/`from_dict` behavior itself is preserved by the new ABC).
-Beyond that, this spec only adds the members under "Quaternion additions".
+`Quaternion` subclasses `foundation_abc.math.spatialABCs.QuaternionABC`. Serialization behavior is defined by the ABC's `to_dict`/`from_dict` contract; no `DataModelHelper` inheritance is required.
 
-## Coordinate conventions (single source of truth)
+## Coordinate conventions
 
 - **spherical** (`azimuth`, `elevation`): elevation measured from the xy-plane
   (geographic).
-- **spherical ISO** (`azimuth`, `polar`): polar measured from +z (ISO 80000-2
-  colatitude) — the convention already documented in
-  `math_tools/spherical/spherical_generators.py`; both conventions preserved,
-  as in Swift.
+- **spherical ISO** (`azimuth`, `polar`): polar measured from +z (ISO 80000-2 colatitude), as governed by [sphericalGeometry.md](sphericalGeometry.md).
 - Angles in radians everywhere.
 
-## Cross-cutting API conventions (all three classes)
+### Deserializer error semantics (normative)
 
-- `normalized()` is a **method** returning a copy (matches the incumbent
-  `Quaternion.normalized()`); `normalize()` mutates in place.
-- Approximate comparison is `isclose(other, rtol=1e-9, atol=0.0) -> bool`
-  (incumbent signature style; numpy `rtol`/`atol` vocabulary repo-wide).
-- These classes are **mutable → unhashable**: each sets `__hash__ = None`
-  explicitly (pinned by test). Hashable time types are the immutable
-  exception ([precisionTimeMath.md](precisionTimeMath.md)).
-- `__array__(dtype=None)` on `Position` (→ `(3,)` vector) and `Quaternion`
-  (→ `[w, x, y, z]`), so `np.asarray(x)` / `plt.plot(...)` work directly.
+`from_dict` is public API reachable from untrusted wire data, so its input
+validation is behavior rather than a developer-time check. Its outcomes SHALL
+be identical whether or not assertions are enabled.
+
+Per [mathToolsArchitecture.md](mathToolsArchitecture.md) §Error semantics
+(programmer errors raise stdlib `TypeError`/`ValueError`), every `from_dict` on
+`Position`, `Quaternion`, and `SpatialPose` SHALL:
+
+- raise `TypeError` when the payload is not a `dict`, or when a field's value
+  is not a real number (`bool` is rejected: it is an `int` subclass and is not
+  a coordinate);
+- raise `ValueError` when a required key is absent;
+- carry a message naming the class, the key, and the offending type.
+
+All three classes SHALL apply the same numeric-field rule and raise the same
+exception type, with a message of the same form, for the same malformed
+payload. Validation behavior SHALL NOT vary by class, and the rule SHALL NOT
+appear on any public surface.
+
+All three SHALL expose `from_dict` as `(cls: type[T], obj: Any) -> T`, so a
+subclass deserializes to its own type.
+
+### Non-unit quaternion inputs (normative)
+
+Quaternion magnitude is not part of the rotation a quaternion represents.
+Two APIs return a rotation *angle* derived from quaternion components, and
+both MUST be invariant to a positive rescaling of their inputs:
+
+- `SpatialPose.angular_distance(to)` — `f(αq₁, βq₂) == f(q₁, q₂)` for all
+  `α, β > 0`.
+- `Quaternion.angle` — `(αq).angle == q.angle` for all `α > 0`.
+
+This section governs those two members only. `Quaternion.axis` is
+scale-invariant by construction and `interpolate` is outside this contract;
+neither is governed here.
+
+### Degenerate (zero) magnitude (normative)
+
+A zero vector has no direction and a zero quaternion has no rotation. Neither
+is representable, so producing `nan` components is prohibited: the operation
+MUST raise `ValueError` at the point of the invalid input, before a corrupt
+value can propagate into a pose, a waveform, or serialized output. This applies
+uniformly to `Position` and `Quaternion`: the zero-vector rule stated for
+`Position.normalize()` under §`Position` and the zero-quaternion rule under
+§`Quaternion` are one contract, not two.
 
 ## `Position`
 
@@ -102,7 +125,7 @@ Swift's custom `•`/`×` operators map to the named methods `dot`/`cross` plus
 
 ## `Quaternion` additions
 
-Added to the existing class (plus the ABC re-parent above; no other change):
+The members below are part of the `Quaternion` contract.
 
 1. `dot(other) -> float` — 4-component dot product.
 2. `rotation_matrix_elements -> RotationMatrixElements` — frozen dataclass
@@ -112,11 +135,20 @@ Added to the existing class (plus the ABC re-parent above; no other change):
    `rotate_vector`, typed for `Position` (`q * p` NOT overloaded; explicit
    method only, to avoid ambiguity with the existing quaternion `*`).
 4. `__array__(dtype=None)` per the cross-cutting conventions.
-5. snake_case aliases for the two camelCase slips on the public surface:
+5. **Degenerate-input guards** (§Degenerate (zero) magnitude). Each of
+   `normalized()`, `normalize()`, `inverse`, and
+   `from_axis_angle(axis, angle)` SHALL raise `ValueError` on a zero-magnitude
+   operand — a zero quaternion for the first three, a zero axis for the last.
+   None SHALL return a non-finite component.
+
+   The condition is exact equality with zero, not a tolerance: a very small
+   but nonzero quaternion has a well-defined direction and SHALL be accepted.
+
+   Each of the four docstrings SHALL carry a `Raises:` section.
+6. snake_case aliases for the two camelCase slips on the public surface:
    `from_numpy_quaternion` (= `fromNumpyQuaternion`) and
-   `to_unit_spherical_small_circle` (= `to_unitSphericalSmallCircle`); the
-   camelCase originals remain as deprecated aliases (docstring note, no
-   removal in this effort).
+   `to_unit_spherical_small_circle` (= `to_unitSphericalSmallCircle`). The
+   camelCase spellings remain available and are documented as deprecated.
 
 ## `SpatialPose`
 
@@ -159,20 +191,23 @@ robotics reading)
   parity pinned by test.
 - `position_distance(to)`, `position_distance_squared(to)`,
   `angular_distance(to) -> float` (radians, double-cover safe: uses
-  `min(θ, 2π−θ)` via `|dot|`).
+  `min(θ, 2π−θ)` via `|dot|`). Scale-invariant per §Non-unit quaternion inputs.
+  Raises `ValueError` if either orientation has zero norm (§Degenerate (zero)
+  magnitude).
 - `normalize()` / `normalized()` — normalize orientation only.
 - `==` exact, `isclose(other, rtol, atol)` (double-cover aware via
   `Quaternion.isclose`), `repr`, `to_dict`/`from_dict`.
 
 ## Compliance requirements (test-checkable)
 
-1. All three classes satisfy `isinstance` of their ABC and round-trip
+1. All three classes structurally conform to their ABC — member presence over
+   the ABC's `__abstractmethods__`; the Tier-2 ABCs are non-runtime_checkable
+   `typing.Protocol`s, so this is not `isinstance`-checkable — and round-trip
    `to_dict`/`from_dict` against the matching `foundationTypes` generated
-   Type's wire output — exact target names on the pinned branch:
-   `PositionType`, `QuaternionType`, `SpatialTransformType`
-   (NOT the pre-template `PositionVectorType`/`SpatialPoseType`; refresh the
-   venv to the branch pin first, per
-   [templateConformance.md](templateConformance.md)).
+   Type's wire output. The target names are `PositionType`,
+   `QuaternionType`, and `SpatialTransformType`; verification is meaningful
+   only against an environment matching the current foundation pin
+   ([templateConformance.md](templateConformance.md) §Environment currency).
 2. Coordinate inits/accessors are mutual inverses (property-style tests over
    a grid of radii/angles, both spherical conventions, atol 1e-12).
 3. `cross` follows the right-hand rule (`unit_x × unit_y == unit_z` pinned).
@@ -185,8 +220,23 @@ robotics reading)
 7. `angular_distance` between `q` and `-q` is 0.
 8. `homogeneous` ∘ `from_homogeneous` round-trips (atol 1e-9), including a
    non-normalized input quaternion (normalized on export).
-9. Existing `Quaternion` test suite passes with import-path and base-class
-   assertion edits only — no assertion on math behavior changes.
-10. `__hash__ is None` pinned for all three classes; `np.asarray(x)` returns
-    the documented array for `Position` and `Quaternion`.
-11. mypy strict clean.
+9. `__hash__ is None` pinned for all three classes; `np.asarray(x)` returns
+   the documented array for `Position` and `Quaternion`.
+10. mypy strict clean.
+11. **Scale invariance.** For any positive scale factor applied to either
+    operand, `SpatialPose.angular_distance` and `Quaternion.angle` are
+    unchanged to atol 1e-12, as is `Quaternion.axis`. Compliance 7 (`q` vs
+    `-q` → 0) is unaffected.
+12. **No NaN escape.** `Quaternion.normalized()`, `normalize()`, `inverse`,
+    and `from_axis_angle` raise `ValueError` on a zero-magnitude operand, and
+    each carries a `Raises:` docstring section. For finite non-degenerate
+    input, none of the four returns a non-finite component.
+13. **Deserializer errors.** For each of `Position`, `Quaternion`,
+    `SpatialPose`: a non-`dict` payload raises `TypeError`; a payload missing a
+    required key raises `ValueError`; a field carrying a string or a `bool`
+    raises `TypeError`. The three classes raise the same type for the same
+    malformed payload, and every outcome is unchanged when assertions are
+    disabled. All three `from_dict` docstrings carry a `Raises:` section.
+14. **Wire round-trip preserved.** `to_dict` → `from_dict` remains exact for
+    all three classes: the validation required by 12–13 rejects malformed
+    input without narrowing well-formed input.
diff --git a/.claude/specs/sphericalGeometry.md b/.claude/specs/sphericalGeometry.md
new file mode 100644
index 0000000..0508c01
--- /dev/null
+++ b/.claude/specs/sphericalGeometry.md
@@ -0,0 +1,139 @@
+---
+version: 1.0
+type: specification
+name: sphericalGeometry
+purpose: Behavioral contract for math_tools.spherical — arc/small-circle construction, generation, and coordinate transforms on the unit sphere
+scope: project
+applies_to: src/math_tools/spherical/, tests/spherical/
+last_updated: 2026-09-24
+semver: 0.1.2
+author: Nicholas Bergantz
+---
+
+# Spherical Geometry
+
+> Sibling of [mathToolsArchitecture.md](mathToolsArchitecture.md), which owns layering, dependency policy, error semantics, and the shared API idioms this spec inherits. Reproduced defect evidence and implementation material are held in [the 2026-08-26 findings](../findings/2026-08-26-spherical-spatial-packaging.md).
+
+## Role
+
+`math_tools.spherical` is the Tier-3 implementation of the unit-sphere primitives whose Tier-1 carriers are `foundationTypes.mathTypes.MathTypes.UnitSphericalArcType` / `UnitSphericalSmallCircleType` and whose Tier-2 contracts are `foundation_abc.math.sphericalABCs.UnitSphericalArcABC` / `UnitSphericalSmallCircleABC`. It owns no storage type: every public entry point takes or returns an ABC-typed arc/circle, a scalar coordinate pair, or a numpy array of them.
+
+## Coordinate convention
+
+This specification is the canonical statement of the ISO physics convention; implementation modules reference it rather than defining competing conventions.
+
+- **θ (polar)** — colatitude from `+z`, range `[0, π]`. `0` = north pole, `π/2` = equator, `π` = south pole.
+- **φ (azimuth)** — angle in the xy-plane from `+x`, counterclockwise viewed from `+z`.
+- `x = sin θ cos φ`, `y = sin θ sin φ`, `z = cos θ`.
+
+Azimuth output ranges differ by function and are part of each function's contract: `compute_spherical_arc_endpoint` returns `[0, 2π)`; `cartesian_to_spherical`, `generate_spherical_arc_points`, and `generate_spherical_small_circle_points` return `arctan2` range `(-π, π]`. Consumers comparing azimuths across these functions SHALL compare modulo `2π` (§Compliance 0).
+
+## The `orient` convention
+
+`orient` SHALL be an initial great-circle bearing measured from local north, positive toward local east (the direction of increasing azimuth):
+
+- `orient = 0` → travel toward the north pole (decreasing θ).
+- `orient = +π/2` → travel due east (increasing φ).
+- `orient = ±π` → travel toward the south pole (increasing θ).
+
+With `p̂` the outward radial at the start point, `ê = ẑ × p̂ / ‖ẑ × p̂‖` (local east) and `n̂ = p̂ × ê` (local north), the initial tangent direction SHALL be
+
+```
+d̂ = cos(orient) · n̂ + sin(orient) · ê
+```
+
+This convention governs every function in this subpackage, and public docstrings state it at the call site (§Compliance 10).
+
+It diverges in sign from the wording of the inherited Tier-2 `UnitSphericalArcABC.orient` docstring. Tier-2 states no formula, so no implemented upstream contract is contradicted; reconciling the wording is owned by py-foundationTools.
+
+## Degeneracy handling
+
+Bearing is undefined at a pole. Every function resolving a bearing SHALL treat the start point as degenerate under one shared predicate:
+
+```
+POLE_EPS = 1e-10
+degenerate  ⇔  abs(sin(polar)) < POLE_EPS
+```
+
+- Every bearing-resolving code path SHALL classify a point as degenerate under exactly this predicate, at exactly this threshold. `spherical_generators` and `spherical_transforms` SHALL agree on the classification of every input: no point is degenerate to one and non-degenerate to the other.
+- At a degenerate start point the azimuth reference SHALL be the fixed `x̂`/`ŷ` basis, yielding `azimuth_end == orient` at both poles. This is definitional, not approximate.
+- `generate_spherical_small_circle_points` resolves no bearing: a small circle is rotationally symmetric about its center, so its output does not depend on a choice of in-plane reference direction. It is not governed by `POLE_EPS`, and §Compliance 7 holds for every center position.
+
+### Accuracy bands near the pole
+
+Agreement between `generate_spherical_arc_points` and `compute_spherical_arc_endpoint` is bounded by the start point's proximity to a pole. The following bounds are normative:
+
+| Start point | Guaranteed chordal agreement |
+| --- | --- |
+| `abs(sin(polar_start)) ≥ 1e-6` | `< 1e-9` |
+| `POLE_EPS ≤ abs(sin(polar_start)) < 1e-6` | `< 1e-6` |
+| `abs(sin(polar_start)) < POLE_EPS` | exact (shared pole convention) |
+
+## Public surface
+
+Seven functions, re-exported from `math_tools/spherical/__init__.py` with `__all__` per the umbrella's Public surface rule.
+
+### `spherical_transforms`
+
+- `plate_carree_transform(azimuth, polar) -> (x, y)` — `x = azimuth`, `y = π/2 − polar`. Accepts float or ndarray via `FloatOrNDArray`.
+- `spherical_to_cartesian(azimuth, polar) -> (x, y, z)` — unit-sphere point per §Coordinate convention.
+- `cartesian_to_spherical(point) -> (azimuth, polar)` — normalizes `point`, then `azimuth = arctan2(y, x)`, `polar = arccos(clip(z, −1, 1))`.
+- `compute_spherical_arc_endpoint(arc) -> (azimuth_end, polar_end)` — the reference implementation of the arc contract (§Cross-function consistency). Spherical law of cosines for `polar_end`; `arctan2` for `Δazimuth`; degenerate start → `azimuth_end = orient`; degenerate end → `azimuth_end = arc.azimuth`; result in `[0, 2π)`.
+
+### `spherical_generators`
+
+- `generate_spherical_small_circle_points(circle, num_points=120) -> (azimuths, polars)` — `num_points` samples over `t ∈ [−π, π]`, each at exactly `circle.radius_angle` from the center.
+- `generate_spherical_arc_points(arc, num_points=120) -> (azimuths, polars)` — `num_points` samples over `t ∈ [0, arc.arc_length]`, inclusive at both ends, along the great circle leaving `(arc.azimuth, arc.polar)` on bearing `arc.orient` per §The `orient` convention. Negative `arc_length` traverses the opposite bearing.
+
+### `constructors`
+
+- `arc_from_two_points(azimuth1, polar1, azimuth2, polar2, isPositive=True) -> UnitSphericalArcABC` — an arc rooted at point 1 whose bearing and length carry it to point 2:
+
+  ```
+  arc_length = arccos(clip(cos θ₁ cos θ₂ + sin θ₁ sin θ₂ cos Δφ, −1, 1))
+  orient     = atan2( sin Δφ · sin θ₂ ,
+                      sin θ₁ · cos θ₂ − cos θ₁ · sin θ₂ · cos Δφ )
+  ```
+
+  Both expressions are part of the contract, including the order of terms in the `orient` denominator.
+
+  `isPositive=False` negates `arc_length` and leaves `orient` unchanged, producing the reverse traversal from point 1. That arc does not reach point 2, and its docstring SHALL say so.
+
+## Cross-function consistency
+
+`compute_spherical_arc_endpoint` is the single source of truth for where an arc ends. The other two arc functions are defined by agreement with it:
+
+1. **Generator ≡ endpoint.** `generate_spherical_arc_points(arc, n)`'s final sample SHALL equal `compute_spherical_arc_endpoint(arc)`, compared per §Compliance 0 and bounded by §Accuracy bands near the pole.
+2. **Constructor round-trip.** `compute_spherical_arc_endpoint(arc_from_two_points(φ₁, θ₁, φ₂, θ₂))` SHALL equal `(φ₂ mod 2π, θ₂)` on the same terms.
+
+A change that breaks either invariant is a regression regardless of how the individual formula reads.
+
+## Error semantics
+
+Inherited from [mathToolsArchitecture.md](mathToolsArchitecture.md) §Error semantics. This subpackage raises no domain errors: inputs are floats or ABC-typed carriers, every `arccos` argument is clipped to `[−1, 1]`, and every normalization divisor is guarded by §Degeneracy handling. No `MathToolsError` subtype applies.
+
+## Compliance requirements
+
+Stable observable outcomes of a conforming implementation.
+
+0. **Comparison metric.** Agreement between two `(azimuth, polar)` results is measured as chordal error, with the azimuth difference taken modulo `2π` as `abs(((a − b + π) % (2π)) − π)` and weighted by `sin(polar)`. Every tolerance below is expressed in this metric.
+1. **Constructor round-trip.** For any `(φ₁, θ₁, φ₂, θ₂)` with `abs(sin θ) ≥ 1e-6`, `compute_spherical_arc_endpoint(arc_from_two_points(φ₁, θ₁, φ₂, θ₂))` recovers `(φ₂, θ₂)` to `< 1e-9`.
+2. **Generator ≡ endpoint.** `generate_spherical_arc_points`' final sample matches `compute_spherical_arc_endpoint` for the same arc, within the bounds of §Accuracy bands near the pole, for `arc_length ∈ [−π, π]`.
+3. **North-tangent orientation.** For an equatorial start, `orient = 0`, and `0 < L ≤ π/2`, `polar(s) = π/2 − s` for `s ∈ [0, L]`.
+4. **Pole agreement.** For start `polar ∈ {0, π}`, the generator's final sample matches `compute_spherical_arc_endpoint` exactly, and `azimuth_end ≡ orient (mod 2π)`, for both positive and negative `orient`.
+5. **Uniform degeneracy predicate.** For any point, `spherical_generators` and `spherical_transforms` return the same degeneracy classification, and that classification is the §Degeneracy handling predicate at its stated threshold. No bearing-resolving path applies a different threshold.
+6. **Midpoint agreement.** The generator's sample at parameter `L/2` matches `compute_spherical_arc_endpoint` of the same arc with `arc_length = L/2`, to `< 1e-9`.
+7. **Small-circle radius.** Every sample of `generate_spherical_small_circle_points` sits at `radius_angle` from the center to atol `1e-12`, for centers anywhere on the sphere including at a pole.
+8. **Transform inverses.** `cartesian_to_spherical ∘ spherical_to_cartesian` is the identity away from the poles to atol `1e-12`. `plate_carree_transform` maps `polar = 0 → y = π/2` and `polar = π → y = −π/2`.
+9. **Public surface.** `math_tools.spherical.__all__` pins exactly the seven names, each resolving by identity to its defining module.
+10. **Docstrings carry the convention.** The `spherical_generators` module docstring defines `orient` per §The `orient` convention. Each arc function's docstring states that convention and notes its divergence from the inherited `UnitSphericalArcABC.orient` wording. No docstring or comment in the subpackage describes `orient` as a rotation about the radial vector.
+11. mypy strict clean.
+
+## Non-goals
+
+1. **No new spherical types.** Tier-1 carriers stay upstream; this subpackage defines no arc/circle class.
+2. **No azimuth-range harmonization.** The per-function ranges in §Coordinate convention are contract, not drift.
+3. **No upstream ABC docstring change.** Owned by py-foundationTools.
+4. **No small-circle degeneracy rework.** See §Degeneracy handling.
+5. **No reformulation of `compute_spherical_arc_endpoint`.** The bands in §Accuracy bands near the pole are the contract; tightening them is a separate governed change.
+6. **No `isPositive` redesign.** Reverse-traversal semantics are contract.
diff --git a/.claude/specs/templateConformance.md b/.claude/specs/templateConformance.md
index 942f8cc..721f03d 100644
--- a/.claude/specs/templateConformance.md
+++ b/.claude/specs/templateConformance.md
@@ -2,110 +2,90 @@
 version: 1.0
 type: specification
 name: templateConformance
-purpose: Bring py-MathTools into full conformance with the py-foundationTools template conventions
-spec: TemplateConformance
+purpose: Ongoing packaging, dependency-resolution, CI-parity, and governance requirements for py-MathTools
 scope: project
-status: accepted
 applies_to: pyproject.toml, requirements.txt, Makefile, .env, .github/, .claude/, src/, README.md
-last_updated: 2026-08-14
-semver: 0.0.4
+last_updated: 2026-09-24
+semver: 0.1.2
 author: Nicholas Bergantz
 ---
 
 # Template Conformance
 
-> Sibling of [mathToolsArchitecture.md](mathToolsArchitecture.md). The
-> authoritative template reference is py-foundationTools at branch
-> `feat/switch-to-new-template`
-> (`/Users/nbergantz/__Workspaces__/pythonWorkspaces/py-foundationTools`);
-> this spec states what "conformant" means for this repo, not a copy of that
-> repo's content.
-
-## Already conformant (verify, don't re-do)
-
-The current branch already carries: the uv Makefile (with `uv-fullCheck`
-gate), `.env` (`PY_SRC=src`), `.bumpversion.cfg`, the `ci-cd.yml` workflow
-(quality checks + Python compatibility matrix on PRs to `dev`/`prod`),
-names-only `pyproject.toml` policy, and pinned `requirements.txt`.
-Conformance work MUST NOT rewrite these wholesale; only close the specific
-gaps below.
-
-## Gap 1 — package rename (breaking, approved)
-
-| Current | Target |
-|---|---|
-| `src/pyMathTools/` | `src/math_tools/` |
-| `src/pyMathToolsPlotHelpers/` | `src/math_plot_helpers/` |
-
-Requirements:
-
-1. `git mv` the trees; module layout inside follows the umbrella's module map
-   (existing `spatial/`, `spherical/`, `hints.py` migrate; `Quaternion.py` →
-   `spatial/quaternion.py`; `plotUnitSpherical.py` →
-   `math_plot_helpers/plot_unit_spherical.py`). Module **filenames** become
-   snake_case; class names are unchanged.
-2. Behavior of migrated code is unchanged in the rename chunk — imports and
-   paths only ([stay-in-scope]). Extensions to migrated classes come later
-   under their own sibling specs.
-3. All imports updated: `tests/`, `examples/`, intra-package.
-4. Every package dir (`math_tools`, each subpackage with public API,
-   `math_plot_helpers`) contains `py.typed`.
-5. `pyproject.toml` needs no `packages` edit (`package-dir = {"" = "src"}`
-   auto-discovers), but the Makefile's mypy package list (`MYPY_PKGS` pattern
-   from the template) and any name references MUST resolve to the new names.
-6. Distribution name stays `py_math_tools`; only import packages rename.
-
-## Gap 2 — dependencies
-
-1. `pyproject.toml` `dependencies`: names only —
-   `pyFoundationTools`, `numpy`, `scipy`, `numpy-quaternion`, `matplotlib`.
-2. `requirements.txt`: keep the `pyFoundationTools @ git+...@feat/switch-to-new-template`
-   pin until foundation tags a release, then move to a tag pin (tracked as a
-   known follow-up, not part of this effort).
-3. No `uv.lock` committed (repo BKM).
-4. **Hard prerequisite for every other chunk:** the installed `.venv` may
-   hold a pre-template `pyfoundationtools` (old per-type ABC layout,
-   `foundationTypes.mathTypes.quaternionABC` etc.). The first chunk MUST
-   `make uv-refresh` (or equivalent) so the environment matches the branch
-   pin's layout (`foundation_abc.math.*`, `PositionType`,
-   `SpatialTransformType`, `ScalarWaveformType`); the gate is meaningless
-   against the stale install.
-
-## Gap 3 — `.claude/` governance
-
-1. `.claude/CLAUDE.md` authored for this repo: role (Tier 3 of foundation's
-   math tiers), package map, gate command, pointer to `.claude/specs/`.
-   It references specs — never duplicates their content.
-2. `.claude/specs/` — this spec set.
-3. `.claude/archive/math-tools-port/` — the completed chunk set produced
-   from these specs.
-
-## Gap 4 — README and metadata
-
-1. `README.md` replaces the "Python Boilerplate" stub, following the
-   template's section shape: title → Features → Installation → Quick Start →
-   Development Workflows → Requirements. Content MUST describe what actually
-   exists at the time the chunk runs (no aspirational feature lists).
-2. `pyproject.toml` `description` updated from boilerplate text.
-3. `examples/sphericalPlotting/*` imports fixed to real module paths (note:
-   `plotArcs.py` currently imports a nonexistent
-   `foundationTypes.mathTypes.UnitSphericalArc` path).
-
-## Gap 5 — layering test
-
-Port the template's layering-enforcement pattern
-(py-foundationTools `tests/test_package_layering.py`) as
-`tests/test_package_layering.py` asserting, via import/AST scan of `src/`:
-
-- `math_tools` never imports `math_plot_helpers` or `matplotlib`.
-- `math_plot_helpers` may import `math_tools`.
-- Only `math_plot_helpers` imports `matplotlib`.
-
-## Compliance checklist (mechanically verifiable)
-
-- [x] `grep -r "pyMathTools" src/ tests/ examples/ Makefile pyproject.toml` → no hits
-- [x] `find src -name py.typed` covers every public package
-- [x] `make uv-fullCheck` passes after rename
-- [x] `.claude/CLAUDE.md` exists and links every spec in `.claude/specs/`
-- [x] `README.md` contains no "Boilerplate" text
-- [x] `tests/test_package_layering.py` passes and fails if `import matplotlib` is added to any `math_tools` module
+> Sibling of [mathToolsArchitecture.md](mathToolsArchitecture.md). This spec states what "conformant to the py-foundationTools template" means for this repo; it does not copy that repo's content. The authoritative template reference is the py-foundationTools release selected by `requirements.txt`.
+>
+> The migration that first brought this repo into conformance is summarized in [the math-tools port retrospective](../archive/math-tools-port.md). Reproduced dependency-resolution evidence is held in [the 2026-08-26 findings](../findings/2026-08-26-spherical-spatial-packaging.md).
+
+## Package metadata
+
+- Package names, module names, source layout, and public typing markers are governed by [mathToolsArchitecture.md](mathToolsArchitecture.md) §Packages and layering and §Shared conventions.
+- The distribution name is `py_math_tools` and is independent of the import package names.
+- Package discovery is driven by `package-dir = {"" = "src"}`; no explicit `packages` enumeration is maintained.
+- Tooling configuration that names packages or paths resolves to the names governed by this section and [mathToolsArchitecture.md](mathToolsArchitecture.md).
+
+## Dependency declaration model
+
+This model is the repo BKM: only the application layer pins, so module-level pins and version-control URLs in `pyproject.toml` are prohibited.
+
+1. `pyproject.toml` `dependencies` declares **names only** — no version specifier, no `@`, no `git+` URL.
+2. `requirements*.txt` carries every pin and version-control pointer. It is the authoritative resolution source for `pyFoundationTools`.
+3. No lockfile is committed.
+
+## Dependency resolvability
+
+### Pin immutability
+
+The `pyFoundationTools` pointer in `requirements.txt` SHALL name an immutable, remotely reachable ref — a release tag or a full 40-character commit SHA. A branch name SHALL NOT be used.
+
+The pinned ref SHALL supply the full import surface this repo depends on:
+
+- `foundation_abc.math.{mathEnums, precisionTimeABC, spatialABCs, sphericalABCs, waveformABCs}`
+- `foundationTypes.mathTypes.MathTypes.{PositionType, QuaternionWaveformType, PositionWaveformType, PrecisionTimeIntervalType, PrecisionTimestampType, ScalarWaveformType, SpatialTransformType, SpatialTransformWaveformType, UnitSphericalArcType, UnitSphericalSmallCircleType}`
+
+The declared environment SHALL be reproducible from `requirements.txt` alone, independently of any environment already installed.
+
+### Install-path parity
+
+Every install path that runs tests SHALL resolve `pyFoundationTools` from `requirements.txt`, installing the requirements file before the editable self-install. No target that installs the package's own extras without `requirements.txt` may run tests.
+
+Where two CI jobs install by different paths, both SHALL resolve `pyFoundationTools` to the same version.
+
+### Distribution consumption
+
+Built artifacts carry only the names-only requirement from `pyproject.toml` metadata; `requirements.txt` is not part of wheel metadata. Resolving `pyFoundationTools` is therefore the consumer's responsibility — a consequence of §Dependency declaration model, not an exception to it.
+
+`README.md` §Installation SHALL state that installing the distribution requires supplying a `pyFoundationTools` source — the `requirements.txt` pointer, a private index, or an already-installed foundation — and SHALL give a working command. Whether py-foundationTools is published to an index is an upstream decision this spec does not make.
+
+## Environment currency
+
+Verification results are evidence only about the environment that produced them. An environment SHALL match the current `requirements.txt` pin for its results to bear on this repo's conformance.
+
+## Governance artifacts
+
+1. `.claude/CLAUDE.md` states this repo's role, package map, and gate command, and links every spec under `.claude/specs/`. It references specs and does not duplicate their content. Publishing a new spec includes adding its link here.
+2. `.claude/specs/` holds the spec set.
+3. `.claude/findings/` holds reproduced defect evidence and other non-normative observations.
+4. `.claude/archive/` holds concise retrospectives for completed work whose decisions remain useful.
+
+## README and metadata
+
+1. `README.md` follows the template's section shape: title → Features → Installation → Quick Start → Development Workflows → Requirements, and describes only what exists.
+2. `pyproject.toml` `description` describes this package, not boilerplate.
+3. Everything under `examples/` imports real module paths and runs against the installed package.
+
+## Layering enforcement
+
+The package dependency direction is governed by [mathToolsArchitecture.md](mathToolsArchitecture.md) §Packages and layering. `tests/test_package_layering.py` enforces it by static AST scan of `src/` and SHALL fail if `math_tools` imports `math_plot_helpers` or `matplotlib`.
+
+## Conformance criteria
+
+Observable properties of a conformant repo:
+
+1. Package metadata matches §Package metadata and every public package satisfies the typing-marker requirement in [mathToolsArchitecture.md](mathToolsArchitecture.md).
+2. `.claude/CLAUDE.md` links every `*.md` under `.claude/specs/`.
+3. `README.md` carries no boilerplate stub text, and its §Installation satisfies §Distribution consumption.
+4. The layering test passes, and fails when a `matplotlib` import is introduced into `math_tools`.
+5. `pyproject.toml` `dependencies` contains no version specifier, `@`, or `git+` URL.
+6. The `requirements.txt` `pyFoundationTools` pointer names a tag or full commit SHA that resolves against the remote.
+7. An environment built from `requirements.txt` alone supplies every symbol in §Pin immutability.
+8. All test-running install paths resolve `pyFoundationTools` to the same version.
diff --git a/.claude/specs/waveformCore.md b/.claude/specs/waveformCore.md
index f4e0e34..609ceaa 100644
--- a/.claude/specs/waveformCore.md
+++ b/.claude/specs/waveformCore.md
@@ -1,14 +1,12 @@
 ---
-version: 1.0
+version: 1.1
 type: specification
 name: waveformCore
 purpose: Behavioral contract for Waveform1D and the aggregate spatial waveform containers
-spec: WaveformCore
 scope: project
-status: accepted
 applies_to: src/math_tools/waveforms/, tests/waveforms/
-last_updated: 2026-07-23
-semver: 0.0.4
+last_updated: 2026-09-24
+semver: 0.1.1
 author: Nicholas Bergantz
 ---
 
@@ -50,14 +48,14 @@ The inherited ABC `to_dict` therefore emits the correct wire keys
 and the DSP mixins use the numpy accessors; the ABC accessors exist for the
 contract and serialization.
 
-## Instantiability / DSP phasing (load-bearing)
+## Instantiability
 
-The core chunk ships `class Waveform1D(Waveform1dABC)` with **no DSP mixin
-bases**. The mixin base list is added in a single later "compose" chunk after
-every mixin exists ([waveformDsp.md](waveformDsp.md)); until then the class
-is complete and the gate stays green. A test pins that `Waveform1D` is
-concrete (`Waveform1D.__abstractmethods__ == frozenset()` and a bare
-construction succeeds).
+`Waveform1D` SHALL be concrete and directly constructible:
+`Waveform1D.__abstractmethods__` is empty and a bare construction succeeds.
+
+It composes the DSP families defined in [waveformDsp.md](waveformDsp.md) as
+mixin bases ahead of `Waveform1dABC` in its MRO. Adding a DSP family SHALL NOT
+change this class's own contract.
 
 ## Time axis (shared by all four)
 
@@ -144,6 +142,27 @@ Python list vocabulary, not Swift's:
 `pop(i=-1) -> float` (`IndexError` on empty/out-of-range — stdlib
 semantics, not Swift's Optional), `clear()`.
 
+**`insert` index semantics.** `insert(i, x)` SHALL follow `list.insert` index
+semantics, including its out-of-range rule: the index is clamped, never
+rejected. `insert` SHALL NOT raise for any integer `i`.
+
+| `i` | Insertion point |
+| --- | --- |
+| `i > n` | end |
+| `0 <= i <= n` | `i` |
+| `-n <= i < 0` | `n + i` |
+| `i < -n` | front |
+
+This governs `Waveform1D.insert` and `insert` on all three aggregate
+containers. `WaveformSpatialPose` resolves a single index for both of its
+parallel arrays, so its length and `sample_count` invariants hold after any
+insertion.
+
+`insert` is the only mutation verb with clamping semantics: `pop` and
+`replace` raise on out-of-range indices, matching stdlib `list`.
+
+Each `insert` docstring SHALL state that the index clamps and never raises.
+
 ## Aggregate containers
 
 All three share (with `Element` = `Position` / `Quaternion` / `SpatialPose`):
@@ -175,10 +194,7 @@ All three share (with `Element` = `Position` / `Quaternion` / `SpatialPose`):
   `sample_count == min(len(positions), len(quaternions))` — both subtle Swift
   behaviors, kept.
 - `==`, `repr`, `to_dict`/`from_dict` per the ABC wire shapes.
-- **Shared API idioms** (mathToolsArchitecture.md §API idioms, chunk 50): all
-  three aggregates additionally implement `__array__` and
-  `isclose(other, rtol, atol)`, mirroring the umbrella idiom already required
-  of `Waveform1D`, `Position`, and `Quaternion`.
+- **Aggregate array and comparison behavior:** all three aggregates implement the umbrella's required `__array__` and `isclose(other, rtol, atol)` APIs with these module-specific shapes and tolerances:
   - `__array__(dtype=None, copy=None)`: `WaveformPosition` returns the
     `(sample_count, 3)` position array; `WaveformQuaternion` returns the
     `(sample_count, 4)` `(w, x, y, z)` array; `WaveformSpatialPose` returns a
@@ -200,17 +216,19 @@ All three share (with `Element` = `Position` / `Quaternion` / `SpatialPose`):
     rotation).
   - `WaveformSpatialPose.from_components(position_x, position_y, position_z,
     quaternion_w, quaternion_x, quaternion_y, quaternion_z)`: the third
-    aggregate's `from_components`, dropped in chunk 17 and restored in chunk
-    50 — seven per-component `Waveform1D`s (three position, four quaternion),
+    aggregate's `from_components` — seven per-component `Waveform1D`s
+    (three position, four quaternion),
     following `WaveformPosition.from_components`/
     `WaveformQuaternion.from_components`'s shape; `ValueError` unless all
     seven share length and `dt`.
 
 ## Compliance requirements (test-checkable)
 
-1. All four classes: `isinstance` of their ABC; `to_dict` output loads via
+1. All four classes: structural conformance to their ABC (member presence over
+   the ABC's `__abstractmethods__`; the Tier-2 ABCs are non-runtime_checkable
+   `typing.Protocol`s, not `isinstance`-checkable); `to_dict` output loads via
    the matching `foundationTypes` generated Type and round-trips equal —
-   exact target names on the pinned branch: `Waveform1D` ↔
+   target names: `Waveform1D` ↔
    `ScalarWaveformType`, `WaveformPosition` ↔ `PositionWaveformType`,
    `WaveformQuaternion` ↔ `QuaternionWaveformType`, `WaveformSpatialPose` ↔
    `SpatialTransformWaveformType`.
@@ -226,7 +244,10 @@ All three share (with `Element` = `Position` / `Quaternion` / `SpatialPose`):
    choice with a literal expected value).
 6. `value_at_time` midpoint between two samples returns their average.
 7. Mutation verbs match stdlib list semantics (pin `prepend` t0 shift;
-   `pop()` on empty raises `IndexError`; `clear()` empties).
+   `pop()` on empty raises `IndexError`; `clear()` empties). For all four
+   classes and any integer index, `insert` produces the same resulting order
+   as the equivalent `list.insert` and raises nothing.
+   `WaveformSpatialPose.insert` leaves its parallel arrays equal in length.
 8. Aggregate `component_waveforms` → `from_components` round-trips exactly
    (quaternion tuple order `(w, x, y, z)` pinned).
 9. `WaveformSpatialPose` with unequal arrays: `is_valid` False,
diff --git a/.claude/specs/waveformDsp.md b/.claude/specs/waveformDsp.md
index b21f0cd..43d9175 100644
--- a/.claude/specs/waveformDsp.md
+++ b/.claude/specs/waveformDsp.md
@@ -3,12 +3,10 @@ version: 1.0
 type: specification
 name: waveformDsp
 purpose: Behavioral contract for the Waveform1D DSP/analysis surface (scipy-backed)
-spec: WaveformDsp
 scope: project
-status: accepted
 applies_to: src/math_tools/waveforms/dsp/, src/math_tools/waveforms/support.py, tests/waveforms/dsp/
-last_updated: 2026-07-23
-semver: 0.0.8
+last_updated: 2026-09-24
+semver: 0.0.9
 author: Nicholas Bergantz
 ---
 
@@ -50,97 +48,15 @@ build results. That makes every mixin independently mypy-strict-checkable
 and independently testable. Methods return new objects or descriptor
 types — never mutate.
 
-**Do not nominally inherit `WaveformProtocol`** (`class CalcMixin
-(WaveformProtocol)`) — that was the first design tried and it is broken at
-runtime. Explicitly subclassing a `Protocol` (without also listing
-`Protocol` itself as a base) turns its stub property bodies — literally
-`...`, so the getter returns `None` — into concrete inherited
-implementations. The DSP mixin test convention composes a mixin directly
-with `Waveform1D` (`class _W(CalcMixin, Waveform1D): pass`, see below);
-under C3 linearization that puts the inherited Protocol stub ahead of
-`Waveform1D`'s real property, so `self.values` silently returns `None`
-instead of the sample array — caught by chunk 18's own TDD steps, not by
-inspection. Self-typing `self` avoids this: the mixin class carries no
-runtime base beyond `object`, so composing it with `Waveform1D` never pulls
-`WaveformProtocol` into the MRO, while mypy still resolves every `self.*`
-access structurally through the `self: WaveformProtocol` annotation.
+`WaveformProtocol` is structural typing only. Mixins MUST NOT nominally inherit it, because protocol stub properties would enter the runtime MRO; every mixin remains a plain class and annotates each `self` parameter as `WaveformProtocol`.
 
-**Two result factories.** Every mixin through chunk 24 only ever produces
-results that share `self`'s `dt`/`t0` (built via `_with_values(values)`, same
-`dt`/`t0`, new samples). `ResamplingMixin` (chunk 25, `dsp/_resampling.py`)
-is the first family whose results have a genuinely different sample
-spacing (`decimated`/`interpolated`/`resampled`/`polyphase_resampled` all
-compute a new `dt`), so `WaveformProtocol` gained a second factory,
-`_with_axis(values, dt) -> WaveformProtocol` (new samples, a caller-supplied
-`dt`, `t0` unchanged from `self`) — implemented alongside `_with_values` on
-`Waveform1D`. `t0` is deliberately not a parameter of `_with_axis`: every
-`ResamplingMixin` method keeps `t0` unchanged (see its family-contract row
-below), so add a `t0` parameter only when a future mixin needs to vary it
-too.
+`WaveformProtocol` and `Waveform1D` expose three result factories:
 
-**Three result factories.** `TimeAlignmentMixin` (chunk 26,
-`dsp/_time_alignment.py`) is that future mixin: `aligned`, `synchronize`,
-`time_windows`, and `time_segments` all produce results with the same `dt`
-as their source but a genuinely different `t0` (a detected/reference time
-shift, an overlap window's start, or a sub-span's start). Neither existing
-factory fits (`_with_values` pins `t0`; `_with_axis` also pins `t0` while
-changing `dt`), so `WaveformProtocol` gained a third factory,
-`_with_t0(values, t0) -> WaveformProtocol` (new samples, same `dt` as
-`self`, a caller-supplied `t0`) — implemented alongside the other two on
-`Waveform1D`. The three factories now form a complete same-dt/same-t0
-triangle: `_with_values` (same `dt`, same `t0`), `_with_axis` (new `dt`,
-same `t0`), `_with_t0` (same `dt`, new `t0`).
+- `_with_values(values)` returns new samples with the source `dt` and `t0`.
+- `_with_axis(values, dt)` returns new samples with caller-supplied `dt` and the source `t0`.
+- `_with_t0(values, t0)` returns new samples with the source `dt` and caller-supplied `t0`.
 
-**Composition phasing** (mirrors waveformCore's "Instantiability" section):
-the core `Waveform1D` ships with base `Waveform1dABC` only. Each mixin chunk
-adds a module without touching `waveform1d.py`. A single final **compose
-chunk** edits the base list to the form above, adds the MRO test, and pins
-that the composed class is still concrete (empty `__abstractmethods__`,
-bare construction succeeds). Compliance item 4 applies only from that chunk
-onward.
-
-**Done as of chunk 30 (semver 0.0.7).** `waveform1d.py` now imports all
-twelve `dsp/_*.py` mixin modules directly (not via `dsp/__init__.py`) and
-composes them in the base-list order above; `tests/waveforms/dsp/test_compose.py`
-pins the MRO, concreteness, and one live smoke call per family.
-`dsp/__init__.py` also re-exports all twelve mixins (`__all__`) for direct
-import convenience, per this chunk's own file list.
-
-**Circular import found and resolved (chunk 30).** Composing every mixin
-into `waveform1d.py` is not the only place a cycle could appear: populating
-`dsp/__init__.py`'s exports means importing *any* `dsp/_*` submodule now
-also executes `dsp/__init__.py` (Python always initializes a package before
-one of its submodules), which in turn imports every mixin -- several of
-which (`dsp/_correlation.py`, etc.) import descriptor types back out of
-`waveforms/support.py`. `support.py` itself imports `dsp._protocol.
-WaveformProtocol` at module scope (only for the `WaveformWithEvents.waveform`
-field annotation, chunk 27) -- so `import support.py` -> triggers
-`dsp/__init__.py` -> imports `dsp/_correlation.py` -> imports back into
-`support.py`, which is still mid-import (`WaveformTimeLag` not yet defined),
-raising `ImportError: cannot import name 'WaveformTimeLag' from partially
-initialized module`. Fix: `support.py`'s `WaveformProtocol` import moved
-under `if TYPE_CHECKING:` -- safe because `from __future__ import
-annotations` (already present in `support.py`) defers every annotation to a
-string, so the import was never needed at runtime, only for mypy, which
-resolves `TYPE_CHECKING` imports without executing them. This is the
-opposite direction from the forbidden case in `dsp/_protocol.py`'s
-docstring (a DSP mixin importing `Waveform1D`, forbidden even under
-`TYPE_CHECKING`, because a mixin must stay import-cycle-free with the class
-it composes onto) -- `support.py` importing the mixins' shared protocol
-under `TYPE_CHECKING` carries no such restriction and does not reopen that
-door.
-
-**Layering test scope correction (chunk 30).** `tests/test_package_layering.py
-::test_dsp_mixins_do_not_import_sibling_mixins` globs `dsp/_*.py`, which
-also matches `dsp/__init__.py` (a leading `__` starts with `_`). That test
-enforces §Compliance 2 ("each mixin module imports scipy/numpy plus
-_protocol/_common only") -- correct for the twelve mixin modules, but
-`dsp/__init__.py` is not a mixin module; from this chunk onward it is
-*expected* to import every mixin to re-export it. The test now explicitly
-skips `__init__.py` rather than treating it as a mixin-module violation.
-
-**Chunking hint:** one action-plan chunk per mixin; `support.py`,
-`dsp/_protocol.py`, and `dsp/_common.py` land first as a prerequisite chunk.
+`waveform1d.py` imports all twelve mixin modules directly and composes each exactly once in the base-list order above. `dsp/__init__.py` re-exports all twelve mixins. Mixin modules MUST NOT import sibling mixins or `Waveform1D`; `support.py` may import `WaveformProtocol` only under `TYPE_CHECKING` so package initialization remains cycle-free.
 
 ## Family contracts
 
@@ -163,7 +79,7 @@ and its backing implementation. Enum arguments use the support types below.
 | `WindowingMixin` (`_windowing.py`) | `windowed(window: WaveformWindowType)`, `generate_window(window, length, periodic: bool = False) -> npt.NDArray` (staticmethod), `window_coherent_gain(window, periodic: bool = False) -> float`, `window_processing_gain(window, periodic: bool = False) -> float` | `scipy.signal.get_window`; see §Window convention for the symmetric/periodic split with `SpectralMixin` |
 | `ZeroCrossingMixin` (`_zero_crossings.py`) | `zero_crossings(direction: WaveformZeroCrossingDirection = BOTH) -> list[WaveformZeroCrossing]`, `zero_crossing_count(...)`, `zero_crossing_rate(...) -> float`, `segments_between_zero_crossings(...) -> list[Waveform1D]` | numpy sign-change indexing, sub-sample linear interp |
 
-## Window convention (chunk 53)
+## Window convention
 
 `WindowingMixin` and `SpectralMixin` both call `scipy.signal.get_window`, but
 for genuinely different purposes, and each keeps its own default:
@@ -180,35 +96,9 @@ for genuinely different purposes, and each keeps its own default:
   must satisfy the constant-overlap-add condition across abutting frames —
   a symmetric window's duplicated edge sample breaks that condition.
 
-Both conventions are legitimate and neither family's default changes as a
-result of this reconciliation. The defect this section closes (post-audit
-finding D-windowing-(c)) was that `WindowingMixin.window_coherent_gain`/
-`window_processing_gain` — whose entire purpose is to let a caller correct a
-spectral estimate's scale factor — had no way to describe the periodic
-window `power_spectral_density`/`spectrogram` actually apply, so a caller
-using them together got a subtly wrong gain. Fix: `generate_window`,
-`window_coherent_gain`, and `window_processing_gain` all take an explicit
-`periodic: bool = False` parameter. `periodic=False` (the default,
-unchanged) is `WindowingMixin`'s own symmetric convention; `periodic=True`
-requests the exact periodic window `SpectralMixin` applies internally, so
-`w.window_coherent_gain(HANN, periodic=True)` correctly describes the
-window backing `w.power_spectral_density(window=HANN)`. `windowed` keeps
-the symmetric-only default — it is `WindowingMixin`'s own use case
-(filter/analysis framing on a whole waveform), not a spectral-estimate
-correction helper, so it gained no `periodic` parameter.
+`generate_window`, `window_coherent_gain`, and `window_processing_gain` accept `periodic: bool = False`. `periodic=False` selects the symmetric convention; `periodic=True` selects the periodic window used by `SpectralMixin`. `windowed` always uses the symmetric convention.
 
-**Kaiser beta: single shared constant.** `dsp/_common.DEFAULT_KAISER_BETA =
-14.0` is the one source both `_windowing.py` and `_spectral.py` import for
-the Kaiser window's shape parameter (previously two independent `14.0`
-literals with no test pinning them equal). `WaveformWindowType` is a flat
-`str` enum with no `beta` field (unlike the Swift reference's associated-
-value `.kaiser(beta:)`), so exposing a caller-supplied beta would force an
-enum redesign; this chunk took the "keep the shared constant, record the
-narrowing" path from the corrective-action chunk rather than redesigning
-the enum. **Known deviation from the Swift reference:** Kaiser beta is not
-caller-configurable in the Python surface (Swift: `case kaiser(beta:
-Double)`); it is fixed at `DEFAULT_KAISER_BETA` for both families. Revisit
-only if a caller needs a different beta (YAGNI).
+`dsp/_common.DEFAULT_KAISER_BETA = 14.0` is the single shape parameter used by `_windowing.py` and `_spectral.py`. Kaiser beta is not caller-configurable in the Python surface, unlike the Swift associated-value enum.
 
 ## Support descriptor types — `waveforms/support.py`
 
@@ -251,38 +141,9 @@ methods above** (YAGNI on the rest; add with the method that needs them).
   times_seconds)`, `WaveformFrequencyRange(low_hz, high_hz)`,
   `WaveformFilterCoefficients(numerator, denominator)`.
 
-  **`WaveformTrigger`'s `edge`/`window_kind` fields (chunk 27, semver
-  0.0.6):** `edge: WaveformEdgeType | None = None` and `window_kind:
-  WaveformWindowTriggerType | None = None`, both optional and defaulting to
-  `None`. `TriggerMixin.detect_triggers` (the generic `WaveformTrigger`-
-  driven dispatcher) needs a direction/enter-exit selector for `EDGE`/
-  `LEVEL`/`WINDOW` kinds — the direct `detect_edge_triggers`/
-  `detect_level_triggers`/`detect_window_triggers` methods take it as an
-  explicit argument, but the dataclass had no field to carry it until this
-  change. Dispatch falls back to `WaveformEdgeType.BOTH` (`EDGE`),
-  `WaveformEdgeType.RISING` (`LEVEL`), and `WaveformWindowTriggerType.ENTER`
-  (`WINDOW`) when the caller leaves the field unset — matching each direct
-  method's own default — so this is backward-compatible with every
-  pre-chunk-27 `WaveformTrigger(...)` call site.
+  `WaveformTrigger.edge: WaveformEdgeType | None = None` and `window_kind: WaveformWindowTriggerType | None = None` carry the selectors used by generic dispatch. Unset selectors default to `BOTH` for `EDGE`, `RISING` for `LEVEL`, and `ENTER` for `WINDOW`.
 
-  **`WaveformWithEvents.waveform`'s type (chunk 27, semver 0.0.6):** typed
-  `WaveformProtocol` (`dsp/_protocol.py`), not the concrete `Waveform1D` it
-  held through chunk 26. `TriggerMixin.with_event_markers` is the first
-  mixin method that embeds `self` itself into a returned descriptor —
-  every earlier descriptor holds only derived values (arrays, scalars,
-  other descriptors). Mixins type `self` as `WaveformProtocol` and must
-  never import `Waveform1D` (§Organization; not even under
-  `TYPE_CHECKING` — see `dsp/_protocol.py`'s docstring), so a field typed
-  concrete `Waveform1D` was unsatisfiable from a mixin method without that
-  forbidden import. `Waveform1D` already satisfies `WaveformProtocol`
-  structurally (both at runtime via `@runtime_checkable` and under mypy
-  strict), so retyping the field is behavior-preserving for every caller —
-  a real `Waveform1D` is still exactly what gets passed in and read back
-  out — and removes `support.py`'s only import of `waveforms/waveform1d.py`,
-  closing off what would otherwise become a circular import once the
-  chunk-30 compose step makes `waveform1d.py` import every mixin (mixins
-  already import `support.py`; `support.py` importing back into
-  `waveform1d.py` would have completed the cycle).
+  `WaveformWithEvents.waveform` is typed as `WaveformProtocol`, which `Waveform1D` satisfies structurally. It MUST NOT introduce a runtime import of `Waveform1D` into `support.py`.
 
 ## Numerical conventions
 
@@ -309,6 +170,5 @@ methods above** (YAGNI on the rest; add with the method that needs them).
 3. Descriptor types are frozen (mutation raises); ndarray-bearing ones have
    `eq=False` (pin: constructing two equal-content instances and comparing
    does not raise); all mypy strict clean.
-4. From the compose chunk onward: `Waveform1D` MRO composes every mixin
-   exactly once (pinned by a test enumerating `Waveform1D.__mro__`), the
+4. `Waveform1D` MRO composes every mixin exactly once (pinned by a test enumerating `Waveform1D.__mro__`), the
    class remains concrete, and a bare `Waveform1D(values)` constructs.
diff --git a/.env b/.env
index 5bd627c..b1b0169 100644
--- a/.env
+++ b/.env
@@ -1,23 +1,17 @@
-# This file is parsed by GNU Make (`include .env` in the Makefile), not a shell.
-# Values are Make variables expanded UNQUOTED into recipes — keep that in mind below.
+# Development environment settings used by the Makefile.
 
-# Python interpreter for pip-based targets (single token — used as `$(PYTHON) -m pip`).
+# Python interpreter used by pip-based targets.
 PYTHON=python3
 
-# Default version for single-version uv operations. MUST appear in PYTHONS below.
+# Default Python version. This version must also be listed in PYTHONS.
 DEFAULT_PYTHON=3.13
 
-# Versions to test against. SPACE-SEPARATED, UNQUOTED on purpose:
-# Make expands `$(PYTHONS)` straight into `uv python install ...` as separate args.
-# Do NOT quote or comma-separate — that collapses it into one bogus argument.
-# Canonical set: default 3.13, support floor 3.10 (matches requires-python>=3.10).
-PYTHONS=3.10 3.11 3.12 3.13
+# Python versions tested by the generated project. Separate versions with spaces.
+PYTHONS=3.11 3.12 3.13 3.14 3.15
 
-# Throwaway clean-room venv for `make testInEnv` (deleted on teardown).
-# Kept DISTINCT from uv's `.venv` so the clean-room never nukes your dev env.
+# Temporary virtual environment used by `make testInEnv`.
+# It is separate from the `.venv` development environment and is removed after use.
 VENV=.cleanroom-venv
 
-# Quality-target source dir. A generated project uses a src/ layout (no hooks/),
-# so override the Makefile's root default (PY_SRC=hooks) → src here. This is what
-# `make uv-lint` / `uv-typecheck` scan; the Makefile's PY_SRC ?= is the fallback.
+# Source directory checked by linting and type-checking targets.
 PY_SRC=src
diff --git a/.flake8 b/.flake8
new file mode 100644
index 0000000..865b6e5
--- /dev/null
+++ b/.flake8
@@ -0,0 +1,25 @@
+# flake8 config (flake8 does not read pyproject.toml). Formatting is owned by black
+# ([tool.black]); this file only lints. flake8-bugbear supplies the `B` checks.
+[flake8]
+max-line-length = 100
+
+# E (pycodestyle errors), F (pyflakes), B (bugbear). The `W` warning series is
+# intentionally not enforced.
+select = E, F, B
+
+# E203, W503: disabled for black compatibility.
+# E704: `def f(): ...` one-liners are the idiomatic form for @overload / stub bodies.
+extend-ignore = E203, E704, W503, F401
+
+# Repo-specific relaxations go here, e.g.:
+#   per-file-ignores =
+#       tests/test_something.py: E501
+
+exclude =
+    .git,
+    __pycache__,
+    build,
+    dist,
+    .venv,
+    .venvs,
+    .cleanroom-venv
diff --git a/.gitignore b/.gitignore
index a9f81c8..cdbaf92 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,6 +1,4 @@
-# ==============================
-# Python Build / Bytecode Artifacts
-# ==============================
+# MARK: - Python Build / Bytecode Artifacts
 
 # Compiled Python files (bytecode)
 __pycache__/
@@ -22,9 +20,7 @@ parts/
 var/
 
 
-# ==============================
-# Virtual Environments & Dependencies
-# ==============================
+# MARK: - Virtual Environments & Dependencies
 
 # General virtual environments (Modern and Classic)
 .venv/
@@ -55,9 +51,7 @@ requirements-local.txt
 .nox/
 .mypy_cache/
 
-# ==============================
-# Tooling and Static Analysis Caches
-# ==============================
+# MARK: - Tooling and Static Analysis Caches
 
 # Coverage / Testing Reports
 .coverage
@@ -77,9 +71,7 @@ dmypy.json
 .ipynb_checkpoints/
 
 
-# ==============================
-# IDEs, Editors, and OS System Files
-# ==============================
+# MARK: - IDEs, Editors, and OS System Files
 
 # macOS system files
 .DS_Store
@@ -91,17 +83,16 @@ dmypy.json
 .idea/
 # Generic module file
 *.iml
-# VS Code workspace settings
-.vscode/
+# VS Code workspace settings — track only the shared extension recommendations
+.vscode/*
+!.vscode/extensions.json
 
 # Python boilerplate / Framework config
 # Django specific local overrides
 local_settings.py
 
 
-# ==============================
-# Packaging, Installation & Build Systems
-# ==============================
+# MARK: - Packaging, Installation & Build Systems
 
 # General package distribution folders (PyInstaller/Build tools)
 # PyInstaller spec files
@@ -117,9 +108,7 @@ CMakeCache.txt
 cmake_install.cmake
 
 
-# ==============================
-# Documentation and Translations
-# ==============================
+# MARK: - Documentation and Translations
 
 # Sphinx documentation builds
 docs/_build/
@@ -129,10 +118,8 @@ docs/_build/
 *.pot
 
 
-# ==============================
-# Local Runtime Data & Logs 
+# MARK: - Local Runtime Data & Logs 
 # (DO NOT COMMIT THESE FILES!)
-# ==============================
 
 # Databases and local state files
 # SQLite database file
diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md
index 27082ba..6e5f270 100644
--- a/CONTRIBUTING.md
+++ b/CONTRIBUTING.md
@@ -107,7 +107,7 @@ Before submitting a pull request, make sure:
 
 - [ ] Tests are included for new logic
 - [ ] Documentation is updated if needed
-- [ ] The project supports Python 3.10 through 3.13
+- [ ] The project supports Python 3.11 through 3.13
 - [ ] All tests pass (CI checks will run on PRs)
 
 ---
diff --git a/MANIFEST.in b/MANIFEST.in
index 3a51146..40b8f95 100644
--- a/MANIFEST.in
+++ b/MANIFEST.in
@@ -1,6 +1,7 @@
 include CONTRIBUTING.md
 include HISTORY.md
 include LICENSE
+include NOTICE
 include README.md
 
 recursive-exclude * __pycache__
diff --git a/Makefile b/Makefile
index 16cc5f0..14781c8 100644
--- a/Makefile
+++ b/Makefile
@@ -1,8 +1,6 @@
-# ============================================================================
-# CONFIG
-# ============================================================================
+# MARK: - Configuration
 .PHONY: help version checkCleanGit open-github \
-	clean clean-build clean-artifacts clean-test \
+	clean clean-build clean-artifacts clean-test clean-node clean-venv \
 	bump-patch bump-minor bump-major \
 	check-uv install-uv list-uv \
 	uv-bootstrap-pythons uv-bootstrap uv-sync uv-sync-headless uv-sync-dev uv-sync-release uv-sync-local uv-editable uv-refresh \
@@ -11,52 +9,51 @@
 	uv-flush-cache uv-flush-envs uv-flush-pythons uv-flush-everything uv-nuke \
 	uv-lifecycle-test \
 	dev setup \
-	installDev e refresh \
-	test cleanRoomCleanup cleanRoomBootstrap cleanRoomPytest testInEnv \
+	installDev e refresh pip-bootstrap \
+	lint format typecheck fullCheck \
+	test check-pip cleanRoomCleanup cleanRoomBootstrap cleanRoomPytest testInEnv \
 	build validateBuild release-test release \
 	nuke list
 
 .DEFAULT_GOAL := help
 
-# Load .env file if it exists
+# Load local settings when available.
 ifneq (,$(wildcard .env))
     include .env
     export
 endif
 
-# Defaults (overridable via .env — the user-editable surface). Keep in sync with .env.
-PYTHONS ?= 3.10 3.11 3.12 3.13
+# Defaults can be overridden in .env.
+PYTHONS ?= 3.11 3.12 3.13 3.14 3.15
 DEFAULT_PYTHON ?= 3.13
 PYTHON ?= python3
 VENV ?= .cleanroom-venv
 
-# Quality-target paths. ROOT half has NO src/ — its Python lives in hooks/ + tests/
-# (see GAPS.md §6). The template half overrides these to src/. Overridable via .env.
+# Paths checked by linting and type-checking targets.
 PY_SRC ?= hooks
 PY_TESTS ?= tests
-PY_EXAMPLES ?= examples
+PY_EXAMPLES ?=
 PY_ALL ?= $(PY_SRC) $(PY_TESTS) $(PY_EXAMPLES)
 
+# Discover packages by name so mypy handles editable src-layout installs correctly.
+MYPY_PKGS := $(patsubst src/%/,-p %,$(sort $(dir $(wildcard src/*/__init__.py))))
 
-# Derived
-# Tool runner for uv- quality/test recipes. `--extra dev` ensures ruff/mypy/pytest are
-# resolved (and installed if missing) from the "[dev]" extra even on a FRESH checkout —
-# no reliance on a pre-existing .venv, rather than the ambient PATH.
-UV := uv run --no-project
+
+# MARK: - Derived settings
+# Run quality and test tools through uv with the development dependencies available.
+UV := uv run --no-project 
 PIP := $(PYTHON) -m pip
 BUMPVERSION := bumpversion --allow-dirty
 REPO := $(notdir $(CURDIR))
 UNAME_S := $(shell uname -s)
 HR := ========================================
 
-# Guard: DEFAULT_PYTHON must be one of the versions we test against.
+# The default version must be included in the test matrix.
 ifeq ($(filter $(DEFAULT_PYTHON),$(PYTHONS)),)
     $(error DEFAULT_PYTHON ($(DEFAULT_PYTHON)) is not in PYTHONS ($(PYTHONS)) — fix .env)
 endif
 
-# ============================================================================
-# MARK: - Helpers · 
-# ============================================================================
+# MARK: - Helpers
 
 define uninstall_package_list
 	@$(1) | while read pkg; do \
@@ -74,10 +71,7 @@ define print_packages
 	@echo
 endef
 
-# Roll HISTORY.md on a version bump: open a fresh dated section under
-# [Unreleased] (folding the accumulated notes into the just-bumped version) and
-# amend it into bump2version's commit so version + changelog move together.
-# Keep-a-Changelog convention: the `## [Unreleased]` header is the anchor.
+# Add a dated release section to HISTORY.md and include it in the version commit.
 define roll_changelog
 	@ver=$$($(MAKE) -s version); day=$$(date +%F); \
 	awk -v v="$$ver" -v d="$$day" '\
@@ -91,11 +85,9 @@ define roll_changelog
 	esac
 endef
 
-# ============================================================================
-# MARK: - HELP
-# ============================================================================
+# MARK: - Help
 help:  ## Show this help
-	@echo "$(REPO) — make targets   (bare = pip · uv-… = uv path)"
+	@echo "$(REPO) — available make targets"
 	@echo "config: DEFAULT_PYTHON=$(DEFAULT_PYTHON)  PYTHONS=$(PYTHONS)"
 	@echo ""
 	@awk 'BEGIN {FS = ":.*?## "} \
@@ -104,21 +96,18 @@ help:  ## Show this help
 		$(MAKEFILE_LIST)
 
 
-# ============================================================================
-# MARK: - COMMON · VERSION & GIT
-# ============================================================================
+# MARK: - Version and Git
 ##@ Common · Version & Git
 version:  ## Display the current project version
 	@$(PYTHON) -c "import tomllib; print(tomllib.load(open('pyproject.toml','rb'))['project']['version'])" 2>/dev/null \
 		|| grep -m1 '^version' pyproject.toml | cut -d'"' -f2
 
-checkCleanGit:  ## Guard: fail if the git working tree is dirty
+checkCleanGit:  ## Verify that the Git working tree is clean
 	@[ -z "$$(git status --porcelain)" ] || \
 		(echo "Working tree is dirty. Commit or stash changes first."; exit 1)
 
-# Static pattern rule: all three documented parts share one recipe (`$*` = the
-# part). Bump the version, then roll the changelog into the same commit.
-bump-patch bump-minor bump-major: bump-%:  ## Bump version (patch|minor|major) + roll HISTORY.md
+# Version bump targets share this recipe and update the changelog.
+bump-patch bump-minor bump-major: bump-%:  ## Bump the version and update HISTORY.md
 	$(BUMPVERSION) $*
 	$(call roll_changelog)
 
@@ -131,13 +120,11 @@ open-github:  ## Open the GitHub repository in the default browser (macOS/Linux)
 	elif command -v xdg-open >/dev/null 2>&1; then xdg-open "$$url"; \
 	else echo "No browser opener found; visit: $$url"; fi
 
-# ============================================================================
-# MARK: - COMMON · CLEAN
-# Base cleanup targets used by install, test, and CI workflows.
-# ============================================================================
+# MARK: - Cleanup
+# Cleanup targets used by development and CI workflows.
 ##@ Common · Clean
 
-clean: clean-build clean-artifacts clean-test ## Remove all build, cache, and test artifacts
+clean: clean-build clean-artifacts clean-test clean-node clean-venv ## Remove all build, cache, and test artifacts
 
 clean-build: ## Remove packaging and distribution artifacts
 	rm -rf build/ dist/ .eggs/
@@ -162,11 +149,23 @@ clean-test: ## Remove test, coverage, and lint caches
 		.tox/ \
 		.nox/
 
-# ============================================================================
-# MARK: - UV · TOOLING
-# ============================================================================
+clean-node: ## Remove node_modules directories and related package files
+	find . -name 'node_modules' -type d -prune | while read -r dir; do \
+		parent="$$(dirname "$$dir")"; \
+		rm -f "$$parent/package.json" \
+		      "$$parent/package-lock.json" \
+		      "$$parent/npm-shrinkwrap.json" \
+		      "$$parent/yarn.lock" \
+		      "$$parent/pnpm-lock.yaml"; \
+		rm -rf "$$dir"; \
+	done
+
+clean-venv: ## Remove the local dev (.venv) and clean-room ($(VENV)) virtual environments
+	rm -rf .venv $(VENV)
+
+# MARK: - uv tooling
 ##@ UV · Tooling
-check-uv:  ## Check if uv is installed (guard for all uv- targets)
+check-uv:  ## Verify that uv is installed
 	@command -v uv >/dev/null 2>&1 || { \
 	  echo "ERROR: uv not found."; \
 	  echo "  Install it with: make install-uv"; \
@@ -207,18 +206,13 @@ list-uv: check-uv  ## List uv envs, installed Pythons, packages, and cache info
 	@uv cache dir
 	@du -sh $$(uv cache dir) 2>/dev/null || echo "Cache empty or not accessible"
 
-# ============================================================================
-# MARK: - UV · BOOTSTRAP & SYNC
-# ============================================================================
+# MARK: - uv setup and synchronization
 ##@ UV · Bootstrap & Sync
 uv-bootstrap-pythons: check-uv  ## Install all configured Python versions via uv
 	uv python install $(PYTHONS)
 
-# Dependency model (BKM; see GAPS §5 / spec §6): pyproject.toml declares dependency
-# NAMES ONLY — never version-pinned (only the application layer pins; module-level pins
-# cause conflicts). The requirements*.txt files carry pins and git-based pointers, and
-# every install path — pip AND uv — leans on them: `-r requirements.txt` then the
-# editable self-install. No `uv.lock`, no `lock`/compile target.
+# Dependency versions and source overrides are defined in requirements files.
+# Install requirements before installing this package in editable mode.
 
 uv-bootstrap: check-uv uv-bootstrap-pythons  ## Full bootstrap: pythons + venv + deps
 	uv venv --python $(DEFAULT_PYTHON)
@@ -263,33 +257,28 @@ uv-refresh: check-uv  ## Clean cache + reinstall from requirements + upgrade edi
 	uv pip install -r requirements.txt
 	uv pip install --upgrade -e ".[dev]"
 
-# ============================================================================
-# MARK: - UV · QUALITY
-# ============================================================================
+# MARK: - uv quality checks
 ##@ UV · Quality
-uv-lint: check-uv  ## Run ruff linter (read-only; non-zero exit for CI)
-	$(UV) ruff check $(PY_ALL)
+uv-lint: check-uv  ## Run flake8 via uv
+	$(UV) flake8 $(PY_ALL)
 
-uv-format: check-uv  ## Format code with ruff
-	$(UV) ruff format $(PY_ALL)
-# KEEP --unsafe-fixes: intentional, added after findings on 2026-06-25.
-# Do NOT strip in cleanup/refactor passes — the unsafe autofixes here are relied
-# upon deliberately. Removing it has regressed this target before.
-	$(UV) ruff check --fix --unsafe-fixes $(PY_ALL)
+uv-format: check-uv  ## Format code with black via uv
+	$(UV) black $(PY_ALL)
 
 uv-typecheck: check-uv  ## Strict type check with mypy
+ifeq ($(strip $(MYPY_PKGS)),)
 	$(UV) mypy $(PY_SRC) $(PY_TESTS) $(PY_EXAMPLES)
+else
+	$(UV) mypy $(MYPY_PKGS)
+	$(UV) mypy $(PY_TESTS) $(PY_EXAMPLES)
+endif
 
-# ty (Astral's preview type-checker) is intentionally OUT for now (decision D1):
-# it's pre-release and not wired into uv-fullCheck. Revisit when it stabilizes.
-uv-fullCheck: check-uv uv-lint uv-typecheck uv-test  ## lint + typecheck + tests
+# The preview `ty` type checker is not included in the quality gate.
+uv-fullCheck: check-uv uv-lint uv-typecheck uv-test  ## Run linting, type checks, and tests
 
-# ============================================================================
-# MARK: - UV · TEST
-# ============================================================================
+# MARK: - uv tests
 ##@ UV · Test
-# Depends on uv-sync so a fresh checkout never tests an empty/stale .venv (no
-# false-green no-op): the [dev] extra is installed from pyproject before pytest runs.
+# Synchronize development dependencies before running tests.
 uv-test: check-uv uv-sync  ## Run tests on DEFAULT_PYTHON (ensures a synced env first)
 	$(UV) pytest
 
@@ -303,6 +292,7 @@ uv-test-all: check-uv  ## Run tests across all configured Python versions (.venv
 		venv=".venvs/$$py"; \
 		[ -d "$$venv" ] || uv venv --python $$py "$$venv"; \
 		if ( . "$$venv/bin/activate" && \
+		     uv pip install -q -r requirements.txt && \
 		     uv pip install -q -e ".[dev]" && \
 		     python -m pytest ); then \
 			echo "PASS: Python $$py"; \
@@ -324,9 +314,7 @@ uv-test-all: check-uv  ## Run tests across all configured Python versions (.venv
 
 uv-test-matrix: uv-bootstrap-pythons uv-test-all  ## Ensure Pythons installed, then run all tests
 
-# ============================================================================
-# MARK: - UV · FLUSH / NUKE
-# ============================================================================
+# MARK: - uv environment cleanup
 ##@ UV · Flush / Nuke
 
 uv-flush-envs:  ## Remove all virtual environments (.venv + .venvs/<ver>)
@@ -341,7 +329,7 @@ uv-flush-cache: check-uv  ## Clean uv cache
 	uv cache clean
 	@echo "uv cache cleaned."
 
-uv-flush-pythons:  ## Remove uv-managed Python installs (NUCLEAR)
+uv-flush-pythons:  ## Remove uv-managed Python installations
 	@echo "WARNING: This removes ALL uv-managed Python installations!"
 	@echo "Location: ~/.local/share/uv/python"
 	rm -rf ~/.local/share/uv/python
@@ -350,24 +338,20 @@ uv-flush-pythons:  ## Remove uv-managed Python installs (NUCLEAR)
 uv-flush-everything: clean uv-flush-envs uv-flush-cache  ## Full cleanup (keeps pythons)
 	@echo "Environment flushed. Run 'make uv-flush-pythons' separately for global Pythons."
 
-uv-nuke: uv-flush-everything  ## NUCLEAR: everything then prompt for Python removal
+uv-nuke: uv-flush-everything  ## Clean all uv data and optionally remove Python installations
 	@echo ""
 	@echo ">> Running uv-nuke..."
 	@$(MAKE) uv-flush-pythons
 	@echo ""
 	@echo "Environment nuked. Run 'make uv-bootstrap' to rebuild from scratch."
 
-uv-lifecycle-test: uv-flush-everything uv-bootstrap uv-test-all  ## flush -> bootstrap -> test-all
+uv-lifecycle-test: uv-flush-everything uv-bootstrap uv-test-all  ## Rebuild the uv environment and run the test matrix
 	@echo ">> Lifecycle test complete"
 
-# ============================================================================
-# MARK: - PIP · INSTALL
-# ============================================================================
+# MARK: - pip installation
 ##@ PIP · Install
-# Ambient-pip fallback (prefer the uv- path). Both pip and uv lean on the requirements
-# file (BKM rule 4): install -r requirements.txt, then self-install the editable
-# package. No --break-system-packages / --force-reinstall: use a venv (make uv-sync)
-# rather than fighting an externally-managed interpreter.
+# These targets use the active Python environment. Prefer the uv workflow for an
+# isolated development environment.
 installDev: clean  ## Install dev dependencies with pip (-r requirements.txt + editable [dev])
 	$(PIP) install -r requirements.txt
 	$(PIP) install -e ".[dev]"
@@ -379,9 +363,35 @@ refresh:  ## Refresh pip packages: reinstall from requirements + upgrade editabl
 	$(PIP) install -r requirements.txt
 	$(PIP) install --upgrade -e ".[dev]"
 
-# ============================================================================
-# MARK: - PIP · TEST
-# ============================================================================
+# MARK: - pip quality checks
+##@ PIP · Quality
+lint:  ## Run flake8 using the active Python environment
+	$(PYTHON) -m flake8 $(PY_ALL)
+
+format:  ## Format code with black using the active Python environment
+	$(PYTHON) -m black $(PY_ALL)
+
+typecheck:  ## Run strict type checks with mypy
+ifeq ($(strip $(MYPY_PKGS)),)
+	$(PYTHON) -m mypy $(PY_SRC) $(PY_TESTS) $(PY_EXAMPLES)
+else
+	$(PYTHON) -m mypy $(MYPY_PKGS)
+	$(PYTHON) -m mypy $(PY_TESTS) $(PY_EXAMPLES)
+endif
+
+fullCheck: lint typecheck test  ## Run linting, type checks, and tests
+
+# Restore pip and its build tools after running `make nuke`.
+pip-bootstrap:  ## Restore pip build tools after `nuke` (requires network access)
+	@echo "Bootstrapping ambient pip + build backend (setuptools, wheel)..."
+	$(PYTHON) -m ensurepip --upgrade
+	$(PIP) install --upgrade setuptools wheel
+	@echo ""
+	@echo "If this fails with 'externally-managed-environment' (Homebrew/Debian"
+	@echo "Python), this interpreter refuses ambient installs by design — use"
+	@echo "'make uv-bootstrap' instead (offline-capable via uv's cache)."
+
+# MARK: - pip tests
 ##@ PIP · Test
 
 test:  ## Run tests using the current Python environment
@@ -390,15 +400,18 @@ test:  ## Run tests using the current Python environment
 cleanRoomCleanup:  ## Delete the clean-room venv ($(VENV))
 	rm -rf $(VENV) || true
 
-# The clean room is an install path, so it obeys the same BKM rule as every other
-# one (see the dependency-model comment above ##@ UV · Bootstrap): pyproject.toml
-# declares dependency NAMES ONLY, and requirements.txt carries the pins and the
-# git/path pointers. Installing ".[dev]" alone makes pip resolve those bare names
-# against PyPI, which fails outright for any unpublished sibling dependency
-# (`No matching distribution found`). Install the requirements file FIRST, then the
-# package. Keep ".[dev]" NON-editable here — validating the real packaging path is
-# this target's entire purpose.
-cleanRoomBootstrap: cleanRoomCleanup  ## Bootstrap the clean-room venv + deps (runs NO tests)
+# Verify that the active Python can create a virtual environment with pip.
+# Clean-room setup requires network access to install build dependencies.
+check-pip:  ## Check the ambient interpreter can create the clean-room venv
+	@$(PYTHON) -m ensurepip --version >/dev/null 2>&1 || { \
+	  echo "ERROR: ensurepip unavailable on $(PYTHON) — cannot create $(VENV)."; \
+	  echo "  Run: make pip-bootstrap"; \
+	  echo "  Or use the uv path: make uv-sync"; \
+	  exit 1; }
+
+# Install pinned requirements before the package. The package is installed normally,
+# rather than editable, to validate the distribution workflow.
+cleanRoomBootstrap: cleanRoomCleanup check-pip  ## Create the clean-room environment and install dependencies
 	$(PYTHON) -m venv $(VENV)
 	. $(VENV)/bin/activate && \
 	which python3 && \
@@ -414,54 +427,47 @@ cleanRoomPytest:  ## Run pytest inside the clean-room venv
 testInEnv: clean cleanRoomBootstrap cleanRoomPytest cleanRoomCleanup  ## Full clean-room test
 	@echo ">> testInEnv completed"
 
-# ============================================================================
-# MARK: - PIP · BUILD & RELEASE
-# ============================================================================
+# MARK: - Build and release
 ##@ PIP · Build & Release
-build: clean-build  ## Build sdist + wheel ($(PYTHON) -m build)
+# Run build and publishing tools through uv so no global installation is required.
+build: check-uv clean-build  ## Build sdist + wheel (uv run --with build python -m build)
 	@echo "Building package..."
-	$(PYTHON) -m build
+	$(UV) --with build python -m build
 
-validateBuild: build  ## Validate build artifacts with twine
+validateBuild: check-uv build  ## Validate build artifacts with twine
 	@echo "Validating dist/ with twine..."
-	$(PYTHON) -m twine check dist/*
+	$(UV) --with twine twine check dist/*
 
 release-test: checkCleanGit validateBuild  ## Dry-run publish to TestPyPI (clean tree only)
 	@echo "Uploading $(REPO) v$$($(MAKE) -s version) to TestPyPI..."
-	@$(PYTHON) -m twine upload --repository testpypi dist/*
-
-# No CI-driven publish path exists: `.github/workflows/ci-cd.yml` runs quality
-# checks and the Python compatibility matrix on PRs to dev/prod only — it does not
-# tag or upload anything. Release is therefore a manual, human-run procedure;
-# `make release` refuses to upload from an unreviewed working tree and prints that
-# procedure instead of performing it.
-release: validateBuild  ## Refuse local upload; print the manual release procedure
-	@echo "No CI-driven publish path exists — release is a manual procedure."
+	@$(UV) --with twine twine upload --repository testpypi dist/*
+
+# Production releases are published by CI. This target validates the build and
+# displays the release procedure without uploading artifacts.
+release: validateBuild  ## Refuse local upload; print the CI-driven release procedure
+	@echo "Local PyPI upload is disabled — the pipeline is the authoritative publish path."
 	@echo ""
 	@echo "To release $(REPO) v$$($(MAKE) -s version):"
 	@echo "  1. Bump the version (make bump-patch|bump-minor|bump-major) and merge to prod."
-	@echo "  2. Build + validate: make validateBuild."
-	@echo "  3. Upload by hand: python3 -m twine upload dist/*"
+	@echo "  2. Push to prod → tag-on-prod.yml creates the v<version> tag."
+	@echo "  3. The publish-on-tag workflow uploads to PyPI."
 	@echo ""
 	@echo "For a local pre-flight, use: make release-test (TestPyPI)."
 	@exit 1
 
-# ============================================================================
-# MARK: - PIP · FLUSH / LIST
-# ============================================================================
+# MARK: - pip environment cleanup
 ##@ PIP · Flush / List
-# `nuke` is the INFERIOR pip fallback (Lesson 2): it per-package-uninstalls from
-# the AMBIENT interpreter ($(PIP)). Prefer `make uv-flush-envs` — deleting the
-# venv dir is the reliable flush primitive. Use this only when you're stuck in a
-# non-deletable (e.g. system) env. Non-editable URL/VCS installs are skipped.
-nuke: ## Per-package uninstall from ambient env (inferior — prefer uv-flush-envs)
+# Remove packages from the active Python environment. Prefer `uv-flush-envs` when
+# using a virtual environment. Core packaging tools are preserved for recovery.
+nuke: ## Remove packages from the active environment (prefer uv-flush-envs)
 	@echo "Uninstalling regular packages (skipping system-managed)..."
-	$(call uninstall_package_list,$(PIP) freeze --exclude-editable | grep -v ' @ ')
+	$(call uninstall_package_list,$(PIP) freeze --exclude-editable --exclude setuptools --exclude wheel | grep -v ' @ ')
 
 	@echo "Uninstalling editable packages by name..."
 	$(call uninstall_package_list,$(PIP) list --editable --format=freeze | cut -d= -f1)
 
 	@echo "pip-nuke complete."
+	@echo "Run 'make pip-bootstrap' (network) or 'make uv-bootstrap' (offline-capable) to rebuild."
 
 list: ## List pip packages in available environments
 	$(call print_packages,SYSTEM PYTHON PACKAGES,$(PIP))
@@ -482,4 +488,19 @@ list: ## List pip packages in available environments
 		$$venv/bin/pip list 2>/dev/null || echo "No packages or pip not available"; \
 		echo; \
 	done
-	
\ No newline at end of file
+	
+# MARK: - Code generation
+
+# Base directory for generated Python types. Keep this aligned with codegen.sh.
+_PYTHON_TYPES_BASE := src/foundationTypes
+
+codegen-all: check-uv  ## Run all schema codegen scripts in schema/scripts/
+	@for script in schema/scripts/*.sh; do \
+		echo "Generating: $$script"; \
+		bash "$$script"; \
+	done
+	@echo "Normalizing all generated models (fleet-wide DataModelHelper contract)..."
+	@bash schema/scripts/reuse/normalize_generated.sh $(_PYTHON_TYPES_BASE)
+	@echo "Formatting the generated tree with black (first-class formatter)..."
+	$(UV) black $(_PYTHON_TYPES_BASE)
+	@echo "-- fini --"
diff --git a/NOTICE b/NOTICE
new file mode 100644
index 0000000..e8acd83
--- /dev/null
+++ b/NOTICE
@@ -0,0 +1,39 @@
+py-MathTools
+Copyright (c) 2026, Nicholas Bergantz
+
+This product includes software developed by third parties. Their copyright
+notices and license terms are retained below as required by their licenses.
+
+--------------------------------------------------------------------------------
+Ruckig — Online Trajectory Generation
+--------------------------------------------------------------------------------
+
+The `math_tools.otg` package (src/math_tools/otg/) is a Python port of Ruckig,
+the community (open-source) edition of the Ruckig online trajectory generator:
+
+    https://github.com/pantor/ruckig
+
+Ruckig is distributed under the MIT License. Its original copyright notice and
+license terms are reproduced in full below and apply to the ported material:
+
+MIT License
+
+Copyright (c) 2021 Lars Berscheid
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
diff --git a/README.md b/README.md
index fe8c6e6..8dda9d2 100644
--- a/README.md
+++ b/README.md
@@ -97,7 +97,7 @@ make uv-format       # ruff format + autofix
 
 ## Requirements
 
-- Python >= 3.10
+- Python >= 3.11
 - `pyFoundationTools`, `numpy`, `scipy`, `numpy-quaternion`, `matplotlib`
   (see [`pyproject.toml`](pyproject.toml) for the names-only dependency
   declaration and [`requirements.txt`](requirements.txt) for the pinned
diff --git a/pyproject.toml b/pyproject.toml
index 2cfe65b..a701c85 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -5,10 +5,10 @@ build-backend = "setuptools.build_meta"
 
 [project]
 name = "py_math_tools"
-version = "0.0.2"
+version = "0.0.3"
 description = "Tier 3 numpy-backed math implementation layer for pyFoundationTools (quaternions, spatial/spherical math, waveforms, polynomials, trajectory generation)."
 readme = {file = "README.md", content-type = "text/markdown"}
-requires-python = ">=3.10"
+requires-python = ">=3.11"
 authors = [
   {name = "Nicholas Bergantz", email = "nicholas.bergantz@gmail.com"}
 ]
@@ -20,7 +20,6 @@ classifiers = [
     "Natural Language :: English",
     "Operating System :: OS Independent",
     "Programming Language :: Python :: 3",
-    "Programming Language :: Python :: 3.10",
     "Programming Language :: Python :: 3.11",
     "Programming Language :: Python :: 3.12",
     "Programming Language :: Python :: 3.13",
@@ -44,12 +43,16 @@ dependencies = [
 dev = [
     "pytest",
     "pytest-asyncio",
-    "ruff",
+    "flake8",
+    "flake8-bugbear",
+    "black",
+    "mypy",
     "build",
     "bump2version",
-    "mypy",
-    "ty",
     "twine",
+    # second-class (available, not in the gate):
+    "ruff",
+    "ty",
 ]
 
 [project.urls]
diff --git a/requirements.txt b/requirements.txt
index de5e654..c017f1b 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -19,4 +19,4 @@
 # Editable: -e git+https://github.com/example-org/some-package.git@develop#egg=some-package
 
 
-pyFoundationTools @ git+https://github.com/kopecn/py-foundationTools.git@feat/switch-to-new-template
\ No newline at end of file
+pyFoundationTools @ git+https://github.com/kopecn/py-foundationTools.git@dev
\ No newline at end of file
diff --git a/src/math_tools/otg/__init__.py b/src/math_tools/otg/__init__.py
index 19ffc92..de3c898 100644
--- a/src/math_tools/otg/__init__.py
+++ b/src/math_tools/otg/__init__.py
@@ -1,5 +1,9 @@
 """Online trajectory generation (OTG): a faithful Ruckig port.
 
+Ported from Ruckig (community edition, MIT-licensed; Copyright (c) 2021 Lars
+Berscheid), https://github.com/pantor/ruckig. The upstream copyright notice and
+license text are retained in the ``NOTICE`` file at the repository root.
+
 See ``.claude/specs/otg.md``. Pure Python + stdlib in the per-cycle path --
 this package (and everything under it) never imports numpy (real-time
 control-loop constraint, enforced by ``tests/test_package_layering.py``).
diff --git a/src/math_tools/otg/profile.py b/src/math_tools/otg/profile.py
index 46dd855..4ee2cf9 100644
--- a/src/math_tools/otg/profile.py
+++ b/src/math_tools/otg/profile.py
@@ -55,7 +55,9 @@
 _P_PRECISION = 1e-8
 _V_PRECISION = 1e-8
 _A_PRECISION = 1e-10
-_T_PRECISION = 1e-12  # Declared but unused in the Swift source too; ported for fidelity.
+_T_PRECISION = (
+    1e-12  # Declared but unused in the Swift source too; ported for fidelity.
+)
 _T_MAX = 1e12
 
 #: Swift ``Double.ulpOfOne`` (machine epsilon for float64) -- used (not
@@ -271,7 +273,15 @@ def check_for_second_order_velocity(
         if self.t[1] < 0.0:
             return False
 
-        self.t_sum = [0.0, self.t[1], self.t[1], self.t[1], self.t[1], self.t[1], self.t[1]]
+        self.t_sum = [
+            0.0,
+            self.t[1],
+            self.t[1],
+            self.t[1],
+            self.t[1],
+            self.t[1],
+            self.t[1],
+        ]
         if self.t_sum[-1] > _T_MAX:
             return False
 
@@ -457,6 +467,7 @@ def check_with_timing(
 
     @overload
     def set_boundary(self, profile: Profile, /) -> None: ...
+
     @overload
     def set_boundary(
         self,
@@ -602,7 +613,9 @@ def check_for_second_order_with_timing(
                 return False
             if not (a_min - _A_EPS < a_down < a_max + _A_EPS):
                 return False
-        return self.check_for_second_order(a_up, a_down, v_max, v_min, control_signs, limits)
+        return self.check_for_second_order(
+            a_up, a_down, v_max, v_min, control_signs, limits
+        )
 
     # MARK: - First-order position interface
 
@@ -624,7 +637,9 @@ def check_for_first_order(
         self.v = [0.0, 0.0, 0.0, v_up if self.t[3] > 0 else 0.0, 0.0, 0.0, 0.0, self.vf]
 
         for i in range(7):
-            self.p[i + 1], _, _ = integrate_jerk(self.t[i], self.p[i], self.v[i], self.a[i], 0.0)
+            self.p[i + 1], _, _ = integrate_jerk(
+                self.t[i], self.p[i], self.v[i], self.a[i], 0.0
+            )
 
         self.control_signs = control_signs
         self.limits = limits
@@ -699,5 +714,9 @@ def check_step_for_position_extremum(
                 Profile.check_position_extremum(-a / j, t_sum, t, p, v, a, j, ext)
             elif d > 0.0:
                 d_sqrt = math.sqrt(d)
-                Profile.check_position_extremum((-a - d_sqrt) / j, t_sum, t, p, v, a, j, ext)
-                Profile.check_position_extremum((-a + d_sqrt) / j, t_sum, t, p, v, a, j, ext)
+                Profile.check_position_extremum(
+                    (-a - d_sqrt) / j, t_sum, t, p, v, a, j, ext
+                )
+                Profile.check_position_extremum(
+                    (-a + d_sqrt) / j, t_sum, t, p, v, a, j, ext
+                )
diff --git a/src/math_tools/precision_time/precision_time_interval.py b/src/math_tools/precision_time/precision_time_interval.py
index 9c3cbe5..6c67d97 100644
--- a/src/math_tools/precision_time/precision_time_interval.py
+++ b/src/math_tools/precision_time/precision_time_interval.py
@@ -140,6 +140,19 @@ def from_dict(cls, obj: Any) -> PrecisionTimeInterval:
             sign=sign,
         )
 
+    def to_dict(self) -> dict[str, Any]:
+        """Serialize to the ABC wire shape ``{"attoseconds", "seconds", "sign"}``.
+
+        Emits exactly what ``foundationTypes`` ``PrecisionTimeIntervalType.to_dict()``
+        emits (``sign`` as its string value), so the payload round-trips through
+        either carrier.
+        """
+        return {
+            "attoseconds": self.attoseconds,
+            "seconds": self.seconds,
+            "sign": self.sign.value,
+        }
+
     # MARK: - Properties (ABC-required)
 
     @property
@@ -168,6 +181,11 @@ def seconds_as_float(self) -> float:
         """This interval's duration in seconds, as a (lossy) float."""
         return self._total_atto / ATTOSECONDS_PER_SECOND
 
+    @property
+    def is_zero(self) -> bool:
+        """Whether this interval is exactly zero."""
+        return self._total_atto == 0
+
     # MARK: - Arithmetic
 
     def __add__(self, other: PrecisionTimeInterval) -> PrecisionTimeInterval:
diff --git a/src/math_tools/precision_time/precision_timestamp.py b/src/math_tools/precision_time/precision_timestamp.py
index edbd18a..01ea901 100644
--- a/src/math_tools/precision_time/precision_timestamp.py
+++ b/src/math_tools/precision_time/precision_timestamp.py
@@ -211,6 +211,28 @@ def from_dict(cls, obj: Any) -> PrecisionTimestamp:
             uncertainty=uncertainty,
         )
 
+    def to_dict(self) -> dict[str, Any]:
+        """Serialize to the ABC wire shape (camelCase optional keys).
+
+        Emits exactly what ``foundationTypes`` ``PrecisionTimestampType.to_dict()``
+        emits: the ``{"attoseconds", "seconds", "sign"}`` core, plus
+        ``referenceFrame``/``timescale``/``uncertainty`` only when present. Enum
+        values serialize to their string value, so the payload round-trips
+        through either carrier.
+        """
+        result: dict[str, Any] = {
+            "attoseconds": self.attoseconds,
+            "seconds": self.seconds,
+            "sign": self.sign.value,
+        }
+        if self._reference_frame is not None:
+            result["referenceFrame"] = self._reference_frame.value
+        if self._timescale is not None:
+            result["timescale"] = self._timescale.value
+        if self._uncertainty is not None:
+            result["uncertainty"] = self._uncertainty
+        return result
+
     # MARK: - Properties (ABC-required)
 
     @property
@@ -239,6 +261,21 @@ def uncertainty(self) -> int | None:
 
     # MARK: - Accessors (beyond the ABC)
 
+    @property
+    def is_epoch(self) -> bool:
+        """Whether this timestamp is exactly the Unix epoch."""
+        return self.sign == NumericSign.ZERO
+
+    @property
+    def is_after_epoch(self) -> bool:
+        """Whether this timestamp is strictly after the Unix epoch."""
+        return self.sign == NumericSign.POSITIVE
+
+    @property
+    def is_before_epoch(self) -> bool:
+        """Whether this timestamp is strictly before the Unix epoch."""
+        return self.sign == NumericSign.NEGATIVE
+
     @property
     def interval(self) -> PrecisionTimeInterval:
         """This timestamp's signed offset from the Unix epoch."""
diff --git a/src/math_tools/spatial/position.py b/src/math_tools/spatial/position.py
index eb1d934..70222d1 100644
--- a/src/math_tools/spatial/position.py
+++ b/src/math_tools/spatial/position.py
@@ -154,6 +154,14 @@ def from_dict(cls: type[T], obj: Any) -> T:
         z = _from_float(obj.get("z"))
         return cls(x, y, z)
 
+    def to_dict(self) -> dict[str, Any]:
+        """Serialize to the ABC wire shape ``{"x", "y", "z"}``.
+
+        Emits exactly what ``foundationTypes`` ``PositionType.to_dict()`` emits,
+        so the payload round-trips through either carrier.
+        """
+        return {"x": self.x, "y": self.y, "z": self.z}
+
     # MARK: - Properties
 
     @property
diff --git a/src/math_tools/spatial/quaternion.py b/src/math_tools/spatial/quaternion.py
index 870ac4b..bd33fc0 100644
--- a/src/math_tools/spatial/quaternion.py
+++ b/src/math_tools/spatial/quaternion.py
@@ -843,6 +843,14 @@ def from_dict(cls, obj: Any) -> Quaternion:
         # cls ensures the correct subclass type is returned
         return cls.from_components(w, x, y, z)
 
+    def to_dict(self) -> dict[str, Any]:
+        """Serialize to the ABC wire shape ``{"w", "x", "y", "z"}``.
+
+        Emits exactly what ``foundationTypes`` ``QuaternionType.to_dict()`` emits,
+        so the payload round-trips through either carrier.
+        """
+        return {"w": self.w, "x": self.x, "y": self.y, "z": self.z}
+
     def to_unitSphericalSmallCircle(
         q: Quaternion, radius_angle: float = np.pi / 4
     ) -> UnitSphericalSmallCircleType:
diff --git a/src/math_tools/spatial/spatial_pose.py b/src/math_tools/spatial/spatial_pose.py
index 9babe5e..17ebe3e 100644
--- a/src/math_tools/spatial/spatial_pose.py
+++ b/src/math_tools/spatial/spatial_pose.py
@@ -122,6 +122,18 @@ def from_dict(cls: type[T], obj: Any) -> T:
         orientation = Quaternion.from_dict(obj.get("orientation"))
         return cls(position, orientation)
 
+    def to_dict(self) -> dict[str, Any]:
+        """Serialize to the ABC wire shape ``{"orientation", "position"}``.
+
+        Emits exactly what ``foundationTypes`` ``SpatialTransformType.to_dict()``
+        emits (nested ``QuaternionType``/``PositionType`` payloads), so the
+        payload round-trips through either carrier.
+        """
+        return {
+            "orientation": self.orientation.to_dict(),
+            "position": self.position.to_dict(),
+        }
+
     # MARK: - Properties
 
     @property
diff --git a/src/math_tools/waveforms/support.py b/src/math_tools/waveforms/support.py
index 0c34632..83460e1 100644
--- a/src/math_tools/waveforms/support.py
+++ b/src/math_tools/waveforms/support.py
@@ -88,6 +88,7 @@
 
 # MARK: - Enums
 
+
 class WaveformFilterType(str, enum.Enum):
     """Filter family selector for ``FilteringMixin.filtered``."""
 
diff --git a/src/math_tools/waveforms/waveform1d.py b/src/math_tools/waveforms/waveform1d.py
index a952d2e..eff5f6d 100644
--- a/src/math_tools/waveforms/waveform1d.py
+++ b/src/math_tools/waveforms/waveform1d.py
@@ -179,6 +179,19 @@ def from_dict(cls, obj: Any) -> Waveform1D:
         t0 = PrecisionTimestamp.from_dict(obj["t0"])
         return cls(obj.get("waveform", []), dt=dt, t0=t0)
 
+    def to_dict(self) -> dict[str, Any]:
+        """Serialize to the ABC wire shape ``{"waveform", "dt", "t0"}``.
+
+        Emits exactly what ``foundationTypes`` ``ScalarWaveformType.to_dict()``
+        emits (``waveform`` as a list of floats), so the payload round-trips
+        through either carrier.
+        """
+        return {
+            "waveform": [float(v) for v in self.values],
+            "dt": self.dt.to_dict(),
+            "t0": self.t0.to_dict(),
+        }
+
     # MARK: - Generators (sinusoidal)
 
     @classmethod
diff --git a/src/math_tools/waveforms/waveform_position.py b/src/math_tools/waveforms/waveform_position.py
index 617e50f..9a0b2c3 100644
--- a/src/math_tools/waveforms/waveform_position.py
+++ b/src/math_tools/waveforms/waveform_position.py
@@ -127,6 +127,18 @@ def from_dict(cls, obj: Any) -> WaveformPosition:
         positions = [Position.from_dict(p) for p in obj.get("positions", [])]
         return cls(positions, dt=dt, t0=t0)
 
+    def to_dict(self) -> dict[str, Any]:
+        """Serialize to the ABC wire shape ``{"dt", "positions", "t0"}``.
+
+        Emits exactly what ``foundationTypes`` ``PositionWaveformType.to_dict()``
+        emits, so the payload round-trips through either carrier.
+        """
+        return {
+            "dt": self.dt.to_dict(),
+            "positions": [p.to_dict() for p in self.positions],
+            "t0": self.t0.to_dict(),
+        }
+
     @classmethod
     def from_components(cls, x: Waveform1D, y: Waveform1D, z: Waveform1D) -> WaveformPosition:
         """Build from three per-axis ``Waveform1D``s (``dt``/``t0`` taken from ``x``).
diff --git a/src/math_tools/waveforms/waveform_quaternion.py b/src/math_tools/waveforms/waveform_quaternion.py
index 3554851..bf71529 100644
--- a/src/math_tools/waveforms/waveform_quaternion.py
+++ b/src/math_tools/waveforms/waveform_quaternion.py
@@ -140,6 +140,18 @@ def from_dict(cls, obj: Any) -> WaveformQuaternion:
         quaternions = [Quaternion.from_dict(q) for q in obj.get("quaternions", [])]
         return cls(quaternions, dt=dt, t0=t0)
 
+    def to_dict(self) -> dict[str, Any]:
+        """Serialize to the ABC wire shape ``{"dt", "quaternions", "t0"}``.
+
+        Emits exactly what ``foundationTypes`` ``QuaternionWaveformType.to_dict()``
+        emits, so the payload round-trips through either carrier.
+        """
+        return {
+            "dt": self.dt.to_dict(),
+            "quaternions": [q.to_dict() for q in self.quaternions],
+            "t0": self.t0.to_dict(),
+        }
+
     @classmethod
     def from_components(
         cls, w: Waveform1D, x: Waveform1D, y: Waveform1D, z: Waveform1D
diff --git a/src/math_tools/waveforms/waveform_spatial_pose.py b/src/math_tools/waveforms/waveform_spatial_pose.py
index 5512370..40473b2 100644
--- a/src/math_tools/waveforms/waveform_spatial_pose.py
+++ b/src/math_tools/waveforms/waveform_spatial_pose.py
@@ -215,6 +215,20 @@ def from_dict(cls, obj: Any) -> WaveformSpatialPose:
         quaternions = [Quaternion.from_dict(q) for q in obj.get("quaternions", [])]
         return cls(positions, quaternions, dt=dt, t0=t0)
 
+    def to_dict(self) -> dict[str, Any]:
+        """Serialize to the ABC wire shape ``{"dt", "positions", "quaternions", "t0"}``.
+
+        Emits exactly what ``foundationTypes``
+        ``SpatialTransformWaveformType.to_dict()`` emits (parallel position and
+        quaternion arrays), so the payload round-trips through either carrier.
+        """
+        return {
+            "dt": self.dt.to_dict(),
+            "positions": [p.to_dict() for p in self.positions],
+            "quaternions": [q.to_dict() for q in self.quaternions],
+            "t0": self.t0.to_dict(),
+        }
+
     @classmethod
     def from_poses(
         cls,
diff --git a/tests/precision_time/test_precision_time_interval.py b/tests/precision_time/test_precision_time_interval.py
index 1022844..e090312 100644
--- a/tests/precision_time/test_precision_time_interval.py
+++ b/tests/precision_time/test_precision_time_interval.py
@@ -375,10 +375,16 @@ def test_division_by_foreign_type_raises_type_error(self) -> None:
 
 
 class TestIsinstanceAndAbc(unittest.TestCase):
-    def test_isinstance_of_abc(self) -> None:
-        """Compliance 10: isinstance(x, PrecisionTimeIntervalABC)."""
+    def test_structural_conformance_to_abc(self) -> None:
+        """Compliance 10: PrecisionTimeInterval structurally conforms to
+        PrecisionTimeIntervalABC.
+
+        The Tier-2 ABC is a non-runtime_checkable ``typing.Protocol``, so
+        conformance is verified by member presence rather than ``isinstance``.
+        """
         interval = PrecisionTimeInterval.from_seconds(1)
-        self.assertIsInstance(interval, PrecisionTimeIntervalABC)
+        for member in PrecisionTimeIntervalABC.__abstractmethods__:
+            self.assertTrue(hasattr(interval, member), member)
 
 
 class TestSerializationRoundTrip(unittest.TestCase):
diff --git a/tests/precision_time/test_precision_timestamp.py b/tests/precision_time/test_precision_timestamp.py
index ae03350..de2aecc 100644
--- a/tests/precision_time/test_precision_timestamp.py
+++ b/tests/precision_time/test_precision_timestamp.py
@@ -417,10 +417,16 @@ def test_subtraction_with_foreign_type_raises_type_error(self) -> None:
 
 
 class TestIsinstanceAndAbc(unittest.TestCase):
-    def test_isinstance_of_abc(self) -> None:
-        """Compliance 10: isinstance(x, PrecisionTimestampABC)."""
+    def test_structural_conformance_to_abc(self) -> None:
+        """Compliance 10: PrecisionTimestamp structurally conforms to
+        PrecisionTimestampABC.
+
+        The Tier-2 ABC is a non-runtime_checkable ``typing.Protocol``, so
+        conformance is verified by member presence rather than ``isinstance``.
+        """
         ts = PrecisionTimestamp(seconds=1)
-        self.assertIsInstance(ts, PrecisionTimestampABC)
+        for member in PrecisionTimestampABC.__abstractmethods__:
+            self.assertTrue(hasattr(ts, member), member)
 
 
 class TestSerializationRoundTrip(unittest.TestCase):
diff --git a/tests/spatial/test_position.py b/tests/spatial/test_position.py
index f98db91..1f56f57 100644
--- a/tests/spatial/test_position.py
+++ b/tests/spatial/test_position.py
@@ -466,9 +466,13 @@ def test_asarray_is_independent_copy(self) -> None:
 
 
 class TestIsinstanceAndAbc(unittest.TestCase):
-    def test_isinstance_of_abc(self) -> None:
+    def test_structural_conformance_to_abc(self) -> None:
+        """Position structurally conforms to PositionABC (a non-runtime_checkable
+        ``typing.Protocol``), verified by member presence rather than
+        ``isinstance``."""
         p = Position(1.0, 2.0, 3.0)
-        self.assertIsInstance(p, PositionABC)
+        for member in PositionABC.__abstractmethods__:
+            self.assertTrue(hasattr(p, member), member)
 
 
 class TestSerializationRoundTrip(unittest.TestCase):
diff --git a/tests/spatial/test_spatial_pose.py b/tests/spatial/test_spatial_pose.py
index 8f5a391..b3e850b 100644
--- a/tests/spatial/test_spatial_pose.py
+++ b/tests/spatial/test_spatial_pose.py
@@ -55,9 +55,13 @@ def test_from_components_explicit(self) -> None:
         self.assertEqual((pose.x, pose.y, pose.z), (1.0, 2.0, 3.0))
         self.assertEqual((pose.qw, pose.qx, pose.qy, pose.qz), (0.0, 1.0, 0.0, 0.0))
 
-    def test_isinstance_of_abc(self) -> None:
+    def test_structural_conformance_to_abc(self) -> None:
+        """SpatialPose structurally conforms to SpatialTransformABC (a
+        non-runtime_checkable ``typing.Protocol``), verified by member presence
+        rather than ``isinstance``."""
         pose = SpatialPose()
-        self.assertIsInstance(pose, SpatialTransformABC)
+        for member in SpatialTransformABC.__abstractmethods__:
+            self.assertTrue(hasattr(pose, member), member)
 
 
 class TestFromHomogeneous(unittest.TestCase):
diff --git a/tests/test_quaternion.py b/tests/test_quaternion.py
index 9fd97e8..f65a1c2 100644
--- a/tests/test_quaternion.py
+++ b/tests/test_quaternion.py
@@ -804,19 +804,28 @@ def test_dict_modification_doesnt_affect_quaternion(self) -> None:
         self.assertEqual(q.w, 1.0)
         self.assertEqual(q.x, 2.0)
 
-    def test_inheritance_from_quaternion_type(self) -> None:
-        """Test that Quaternion properly inherits from the shared QuaternionABC."""
+    def test_structural_conformance_to_abc(self) -> None:
+        """Quaternion structurally conforms to QuaternionABC.
+
+        The Tier-2 ABC is a non-runtime_checkable ``typing.Protocol``, so
+        conformance is verified by member presence rather than ``isinstance``.
+        """
         from foundation_abc.math.spatialABCs import QuaternionABC
 
         q = Quaternion.from_components(1.0, 2.0, 3.0, 4.0)
-        self.assertIsInstance(q, QuaternionABC)
+        for member in QuaternionABC.__abstractmethods__:
+            self.assertTrue(hasattr(q, member), member)
 
-    def test_inheritance_from_data_model_helper(self) -> None:
-        """Test that Quaternion inherits from QuaternionABC (ABC-only, not DataModelHelper)."""
+    def test_conforms_to_abc_without_carrier_inheritance(self) -> None:
+        """Quaternion conforms to QuaternionABC structurally and does not inherit
+        the Tier-1 ``DataModelHelper`` carrier base (ABC-only conformance)."""
         from foundation_abc.math.spatialABCs import QuaternionABC
 
         q = Quaternion.from_components(1.0, 2.0, 3.0, 4.0)
-        self.assertIsInstance(q, QuaternionABC)
+        for member in QuaternionABC.__abstractmethods__:
+            self.assertTrue(hasattr(q, member), member)
+        mro_names = {base.__name__ for base in type(q).__mro__}
+        self.assertNotIn("DataModelHelper", mro_names)
 
     def test_has_serialization_methods(self) -> None:
         """Test that Quaternion has the required serialization methods."""
diff --git a/tests/waveforms/test_waveform1d_core.py b/tests/waveforms/test_waveform1d_core.py
index d05f763..e253486 100644
--- a/tests/waveforms/test_waveform1d_core.py
+++ b/tests/waveforms/test_waveform1d_core.py
@@ -75,10 +75,15 @@ def test_from_dict_reconstructs_equal_waveform(self) -> None:
         w2 = Waveform1D.from_dict(w.to_dict())
         self.assertEqual(w, w2)
 
-    def test_isinstance_of_abc(self) -> None:
+    def test_structural_conformance_to_abc(self) -> None:
+        """Waveform1D structurally conforms to Waveform1dABC (a
+        non-runtime_checkable ``typing.Protocol``), verified by member presence
+        rather than ``isinstance``."""
         from foundation_abc.math.waveformABCs import Waveform1dABC
 
-        self.assertIsInstance(Waveform1D([1.0]), Waveform1dABC)
+        w = Waveform1D([1.0])
+        for member in Waveform1dABC.__abstractmethods__:
+            self.assertTrue(hasattr(w, member), member)
 
 
 class TestConstruction(unittest.TestCase):
diff --git a/tests/waveforms/test_waveform_position.py b/tests/waveforms/test_waveform_position.py
index 9dc37bb..04fe76b 100644
--- a/tests/waveforms/test_waveform_position.py
+++ b/tests/waveforms/test_waveform_position.py
@@ -38,8 +38,13 @@ def test_from_dict_reconstructs_equal_waveform(self) -> None:
         w2 = WaveformPosition.from_dict(w.to_dict())
         self.assertEqual(w, w2)
 
-    def test_isinstance_of_abc(self) -> None:
-        self.assertIsInstance(_make(), PositionWaveformABC)
+    def test_structural_conformance_to_abc(self) -> None:
+        """WaveformPosition structurally conforms to PositionWaveformABC (a
+        non-runtime_checkable ``typing.Protocol``), verified by member presence
+        rather than ``isinstance``."""
+        wp = _make()
+        for member in PositionWaveformABC.__abstractmethods__:
+            self.assertTrue(hasattr(wp, member), member)
 
     def test_no_abstract_methods_remain(self) -> None:
         self.assertEqual(WaveformPosition.__abstractmethods__, frozenset())
diff --git a/tests/waveforms/test_waveform_quaternion.py b/tests/waveforms/test_waveform_quaternion.py
index 23423b7..ec928d9 100644
--- a/tests/waveforms/test_waveform_quaternion.py
+++ b/tests/waveforms/test_waveform_quaternion.py
@@ -41,8 +41,13 @@ def test_from_dict_reconstructs_equal_waveform(self) -> None:
         w2 = WaveformQuaternion.from_dict(w.to_dict())
         self.assertEqual(w, w2)
 
-    def test_isinstance_of_abc(self) -> None:
-        self.assertIsInstance(_make(), QuaternionWaveformABC)
+    def test_structural_conformance_to_abc(self) -> None:
+        """WaveformQuaternion structurally conforms to QuaternionWaveformABC (a
+        non-runtime_checkable ``typing.Protocol``), verified by member presence
+        rather than ``isinstance``."""
+        wq = _make()
+        for member in QuaternionWaveformABC.__abstractmethods__:
+            self.assertTrue(hasattr(wq, member), member)
 
     def test_no_abstract_methods_remain(self) -> None:
         self.assertEqual(WaveformQuaternion.__abstractmethods__, frozenset())
diff --git a/tests/waveforms/test_waveform_spatial_pose.py b/tests/waveforms/test_waveform_spatial_pose.py
index fbe0d8f..67fe3c2 100644
--- a/tests/waveforms/test_waveform_spatial_pose.py
+++ b/tests/waveforms/test_waveform_spatial_pose.py
@@ -55,8 +55,13 @@ def test_from_dict_reconstructs_equal_waveform(self) -> None:
         w2 = WaveformSpatialPose.from_dict(w.to_dict())
         self.assertEqual(w, w2)
 
-    def test_isinstance_of_abc(self) -> None:
-        self.assertIsInstance(_make(), WaveformSpatialABC)
+    def test_structural_conformance_to_abc(self) -> None:
+        """WaveformSpatialPose structurally conforms to WaveformSpatialABC (a
+        non-runtime_checkable ``typing.Protocol``), verified by member presence
+        rather than ``isinstance``."""
+        wsp = _make()
+        for member in WaveformSpatialABC.__abstractmethods__:
+            self.assertTrue(hasattr(wsp, member), member)
 
     def test_no_abstract_methods_remain(self) -> None:
         self.assertEqual(WaveformSpatialPose.__abstractmethods__, frozenset())