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22 changes: 22 additions & 0 deletions .claude/blackboard.md
Original file line number Diff line number Diff line change
Expand Up @@ -784,3 +784,25 @@ default is x86-64-v3 (avx2) so ndarray_simd activates on avx512 builds only.
digest's null space, the formal "which detours leave no comma";
PROBE-SIG-CHECKSUM on the Pillar-11 harnesses). Neither adds stored
tile fields.

---

## 2026-07-16 (4) — h268-probe-wave-v1 RESULTS (adjudicated)

- **PROBE-WH-MAG → NEUTRAL; bare-tile leg CLOSED NOT-TRANSFERRING.**
B/A 0.929/1.317/1.869 — WHT₁₆ spreads outlier energy tile-wide,
inflating the per-cell quantization floor; the row-level win needs the
passthrough escape + centroid residual the probe deliberately omits.
Shipped row codec untouched. PROBE-WH-MAG-2 named, deferred.
- **PROBE-SIG-CHECKSUM → PASS** with the depth-2 bound: parallel-chord
interior displacement is EXACTLY signature-invisible — null space
exceeds tree-like equivalence; mitigate via depth 3 or paired digest.
- **PROBE-WALK-SPECTRUM → KILL** of §10(g)'s "decorrelated by
construction" (walk lattice |R| 0.875 vs PRNG 0.0205 = 42.7×;
C(13)=−15 sidelobe, coprimality ≠ decorrelation); "known period-17
structure" half CONFIRMED (R(17m)=1−8m/N). D-QUANTGATE unaffected.
- Doc updates: §10(g) corrected, §10 forward-synthesis RESULT lines,
§5 results sub-table. Canonical verdicts: lance-graph
E-H268-PROBE-WAVE-1-RESULTS + plan h268-probe-wave-v1.md Results.
Probes: bgz-tensor probe_wh_mag / jc sig_checksum / helix
walk_spectrum (all suites green).
66 changes: 57 additions & 9 deletions .claude/knowledge/pr-x12-h268-morton-wgpu-synergies.md
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Expand Up @@ -115,6 +115,15 @@ any float-path GPU bit-exactness claim.
| Plan E bench | bits/Gaussian on Mip-NeRF 360 | ≤4 bits | R-10 re-derived; web-streaming claim withdrawn |
| a2ui N2 | wgpu `webgl` feature + texture upload, wasm32-tested | render parity headless vs browser | GPU raster tier deferred; CPU raster only |

**Run this wave — h268-probe-wave-v1 (2026-07-16, reviewer-adjudicated;
probes live in lance-graph `bgz-tensor`/`jc`/`helix`):**

| Probe | Verdict | Numbers | Consequence |
|---|---|---|---|
| PROBE-WH-MAG | NEUTRAL / bare-tile leg NOT-TRANSFERRING | B/A 0.929 / 1.317 / 1.869 (grad+spike / heavy-tail / noise) | §10 [H] leg: WH-on-bare-tiles does not transfer; shipped row codec (lance-graph E-PALETTE-RESIDUAL-LADDER-1) untouched; PROBE-WH-MAG-2 deferred |
| PROBE-SIG-CHECKSUM | PASS (depth-2 blind-spot bound) | replay 0.0; tree-like 0.0<1e-9; non-tree 11.31>0.05 | §10 [S] leg confirmed; digest ≠ catch-all — parallel-chord displacement is signature-invisible at depth 2 |
| PROBE-WALK-SPECTRUM | KILL of §10(g) "decorrelated" half | period-17 \|R\| 0.998/0.996/0.994; lattice max 0.875 vs PRNG 0.0205 = 42.7× | §10(g) corrected: known structure ≠ low correlation; D-QUANTGATE / bijectivity unaffected |

## 7. Comma closure — the replayable irrational (constants correction folded in)

The Pythagorean comma is the residue of a stack of pure fifths that never
Expand Down Expand Up @@ -351,15 +360,30 @@ bytes actually stored are magnitudes. Same object, two consumers.
(the integer-only GPU caveat) unless a deterministic-backend probe is
added. Within that scope, counterfactual replay stores **zero**
exploration state.
- **(g) Anti-confabulation = anti-moiré in concept space [H, probe-gated]**
— a coprime probe schedule is decorrelated from the palette lattice by
construction, and a *known* period-17 dependence structure is plausibly
friendlier to `I-NOISE-FLOOR-JIRAK`'s weak-dependence analysis than an
*unknown* PRNG correlation structure. The "friendlier" half is an
**unverified inference**: the period-17 permutation self-test proves
bijectivity, NOT decorrelation. Promotion to FINDING requires a measured
dependence probe — the walk's correlation spectrum against the palette
lattice vs a PRNG baseline, judged under Jirak weak-dependence rates.
- **(g) Anti-confabulation — the "decorrelated by construction" half
KILLED 2026-07-16 (PROBE-WALK-SPECTRUM); the "known structure" half
CONFIRMED.** The coprime walk's period-permutation self-test proves
bijectivity and gives a KNOWN, replayable, closed-form dependence
structure (period-17 harmonics measured |R| = 0.998/0.996/0.994,
matching R(17m)=1−8m/N) — real value for auditability and conformance.
But it is **NOT decorrelated from the palette lattice**: the parity of
a full-period-17 permutation is an exact period-17 ±1 waveform, so its
autocorrelation at lag τ is governed by C(τ mod 17) at EVERY lag, and
the lattice periods land on large sidelobes — measured walk |R| max
0.875 at τ=64 (64 mod 17 = 13, C(13)=C(4)=−15, −15/17 ≈ −0.882) vs a
PRNG baseline's 0.0205, i.e. 42.7× (≫ the 3× kill bar).
`gcd(17,τ)=1` guarantees a full-period permutation, NOT low
autocorrelation. So the "anti-moiré in concept space / friendlier to
`I-NOISE-FLOOR-JIRAK`" inference is **struck** — strong periodic
autocorrelation is if anything worse for weak-dependence rates than a
PRNG's ≈−1/N floor. Genuine decorrelation, if ever needed, requires a
DESIGNED low-autocorrelation sign sequence (Legendre/quadratic-residue
Paley over a prime p≫17, or a maximal-length LFSR m-sequence), NOT the
coprime walk. **Unaffected:** the walk's bijectivity/quantization role
and OGAR D-QUANTGATE stay canon — the coprime walk QUANTIZES by
construction (bijective closure + WGSL-portable integer stride), which
this probe does not challenge; only the anti-moiré / lattice-
decorrelation consequence dies.
- **(h) Exact phase-side unbinding** — sign is recomputable per address
with no cleanup codebook needed; a cleanup codebook is only needed for
magnitudes. The two-algebra rule (sign = XOR, magnitude = `vsa_bundle`,
Expand Down Expand Up @@ -402,6 +426,20 @@ fourth-mode/anchor discussion (§8):
**PROBE-WH-MAG:** reconstruction error of WHT₁₆+i4/i2 vs direct i4/i2
on real tile magnitudes (bgz-tensor's row-level win does not
automatically transfer to 16-cell tiles).
**RESULT (2026-07-16, PROBE-WH-MAG, plan h268-probe-wave-v1):**
NEUTRAL — bare-tile leg NOT-TRANSFERRING. B/A = 0.929 (gradient+spike)
/ 1.317 (heavy-tailed) / 1.869 (uniform-noise) over 256 tiles/class at
dim 16: misses the <0.9 PASS bar everywhere, regresses past 1.1 on two
classes. WHT₁₆ spreads a tile's outlier energy across all 16 cells,
inflating the per-cell quantization floor where the direct cascade
quantized 13-14 near-zero cells for free; WH helps only where energy
is pre-spread (the 0.929 smooth-gradient class) or where an outlier
escapes to a passthrough tier first. The bare-tile probe has neither
the passthrough escape nor the centroid residual the shipped row codec
(lance-graph E-PALETTE-RESIDUAL-LADDER-1) pairs WH with — so the
row-level win does not transfer to per-tile granularity, and the
shipped row codec is untouched. Follow-up PROBE-WH-MAG-2 (WH + escape
tier + centroid residual) deferred to a per-tile-codec consumer.
- **[S] Signature as the replayable-trajectory checksum.** The x264
contrast in §7 asked for a replayable, checksummable stream; the
Hambly–Lyons signature is the canonical path digest with a uniqueness
Expand All @@ -414,6 +452,16 @@ fourth-mode/anchor discussion (§8):
the Pillar-11 harness) of a temporal-stream trajectory as its digest —
verify replay-identity, tree-like edits invisible (correctly), non-tree
perturbations caught.
**RESULT (2026-07-16, PROBE-SIG-CHECKSUM, plan h268-probe-wave-v1):**
PASS, with a depth-2 blind-spot bound. Replay bit-exact; tree-like
mid-path A→B→A excursion invisible (0.0 < 1e-9); non-tree interior
displacement caught (11.31 > 0.05). Bound (exact identity): at DEPTH=2
an interior displacement PARALLEL to the neighbor chord
`path[i+1]−path[i−1]` is signature-invisible (the level-2 signed-area
term vanishes; level-1 is endpoint-invariant), so the digest's null
space strictly EXCEEDS tree-like equivalence — the depth-2 digest does
not catch ALL non-tree edits. Mitigable by depth 3 or a paired
independently-projected digest.
Both stay conditional on the same ledger above; neither adds a stored
field to the tile (the WH rotation is derivable, the signature is a
derived digest).
Expand Down
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