Mister-Meeseeks · Oct 31, 2026 · Oct 30, 2026
diff --git a/research/cached-dirty-paths/BENCHMARK.json b/research/cached-dirty-paths/BENCHMARK.json
@@ -0,0 +1,73 @@
+{
+  "executable_sha256": {
+    "SOURCES.json": "c8ac64e892500c3423d1d5733b19e1d793d977704f476f1d10281c5e43ba5951",
+    "benchmark.py": "a123eaf27a7dec4edda569e832985760dfc3927e6ebfe5996ee83a2eef565fd8",
+    "check_certificate.py": "ee53974866ba979b9e2ff13bcb44ba63f770351b9f24e5eccb18aaf44d66bfd9",
+    "replay.py": "af6feb7d42c909f5057c64f9173de30753a253f50f5215bc24145253c7f88a86"
+  },
+  "failures": 0,
+  "input_sha256": {
+    "research/cyclic-dirty-commutator-audit/echo.py": "63d44c48801f51720a7cc994d6b5e2e857d1aa4fae4c6b83c0cca032b3d9e13b",
+    "research/universal-dirty-certificates/README.md": "fb8d94a58b6c0448aa893e65f263b9d71639b1aa79cd10f054d0dc740a570dca",
+    "research/universal-dirty-certificates/SOURCES.json": "5d2c0b2a8921b8dc0f724fa11f93cdfeb764e57cfdfb7fa236ec958d72306899",
+    "research/universal-dirty-certificates/check_certificate.py": "09cba2605c62f8af0dc48cf60b4eab9f8711cba820e22698d0447833c1a16c37",
+    "research/universal-dirty-certificates/examples/binary-echo3.certificate.json": "cd088d9d5c0a8378361341c99e25ae5654a6be0b20398c9757a76804df2ab66a",
+    "research/universal-dirty-certificates/examples/binary-echo3.json": "a5199c1dc6236e346891c641b9402d8065c5bd29087c560e76fcdf2299cdfcf9",
+    "research/universal-dirty-certificates/examples/dirty-echo3.certificate.json": "21444c604e17d0cbd707ffbecde10edb4bdff0bdc5a3ffb71819be04c3ac58c5",
+    "research/universal-dirty-certificates/examples/dirty-echo3.json": "862281041cd5616a8785b526d0cee57a50aa7457a8cb64a0abff1133d6d60798",
+    "research/universal-dirty-certificates/examples/wrong-order.certificate.json": "54850450cc231e4db2a1c4637fc3f7a49dfb694d9c64cfeb8faa8df91d529a79",
+    "research/universal-dirty-certificates/examples/wrong-order.json": "137def9876c1195456a312b8c232d656ff063cc5caae645be6afc3d06709742c",
+    "research/universal-dirty-certificates/fields.py": "0829ad6ed3775ba6e3d11cf04cfb3513ac763549b730aaed74958b1238e660d7",
+    "research/universal-dirty-certificates/linear_words.py": "fe825cf7c886de61bb5ec5a02171c5a392a7bddc185280726f4c359b3f289584",
+    "research/universal-dirty-certificates/verify.py": "2759a2e7514453012ed0e4ffc7017375dea973925672dc16f127d91790dcb6e5"
+  },
+  "load_average_at_end": [
+    5.4560546875,
+    4.09814453125,
+    2.72216796875
+  ],
+  "logical_cpus": 18,
+  "median_seconds": {
+    "baseline": 5.680195042,
+    "cached": 4.398449334
+  },
+  "platform": "macOS-27.0.1-arm64-arm-64bit",
+  "python": "3.12.15 (main, Oct 14 2026, 00:55:37) [Clang 23.1.3 ]",
+  "reduction_percent": 22.56517071196725,
+  "samples_seconds": {
+    "baseline": [
+      5.680195042,
+      5.481301333,
+      6.071584333,
+      5.704761833,
+      5.459807334
+    ],
+    "cached": [
+      4.318586542,
+      4.34075425,
+      4.426208458,
+      4.558830625,
+      4.398449334
+    ]
+  },
+  "schema": "complete-dirty-path-benchmark/v1",
+  "scientific_output": {
+    "certificate_rejections": 15,
+    "committed_examples": 3,
+    "differential_cases": 120,
+    "echo_identities": 210,
+    "exponential_support": {
+      "basis_rows": 65,
+      "distinct_words": 18446744073709551616,
+      "states": 130
+    },
+    "finite_field_operations": 596,
+    "gaussian_field_controls": 51,
+    "input_rejections": 9,
+    "literal_counterexamples": 180,
+    "max_echo_basis_rows": 38,
+    "max_echo_states": 284,
+    "tensor_of_sum_rejections": 1
+  },
+  "successful_complete_replays": 10
+}
diff --git a/research/cached-dirty-paths/README.md b/research/cached-dirty-paths/README.md
@@ -0,0 +1,157 @@
+# Shared-prefix replay for complete dirty-circuit certificates
+
+This contribution was produced by Nick Petalas. Apache-2.0.
+
+Claim type: exact implementation-preservation argument and measured performance
+improvement. The complete PR5235 scientific caller runs with a prefix cache
+local to each certificate check. No new dirty-circuit theorem, supplier,
+selected-frontier update or kappa is claimed. Independent human and formal
+proof-kernel review are unclaimed.
+
+## Result and evidence
+
+The implementation replaces repeated rooted path traversal with a trie. Every
+requested output role owns a separate root. All certificate predicates and every
+initial,
+terminal and operator-closure equation remain in place. The source producer,
+field arithmetic, fixtures and complete scientific caller are unchanged.
+
+Five alternating runs per side give a **22.57% reduction** in complete replay
+wall time, with zero failures and identical scientific output.
+
+| Complete replay | Median seconds | Range seconds |
+| --- | ---: | ---: |
+| baseline | 5.680195 | 5.459807 to 6.071584 |
+| cached | 4.398449 | 4.318587 to 4.558831 |
+
+The timed path includes interpreter startup, authentication of thirteen source
+files, imports, the complete scientific replay and its output. Only the two
+explicit elapsed-time fields are removed for scientific output comparison.
+Every replay retains 210 echo identities, 120 differential circuits,
+180 literal counterexamples, 15 certificate rejections, 9 input rejections,
+596 finite-field operations, 51 Gaussian controls, three committed examples
+and the 130-state, 65-basis-row exponential-support fixture with 2^64 words.
+These are predecessor coverage counts, preserved here, not new mathematical results.
+
+An untimed profile found rooted path evaluation used 5.906 of 20.534 instrumented
+seconds. Those times identify the changed work and are excluded from performance
+samples. Producer elimination and full closure checks remain paid. The machine
+has 18 logical CPUs and other research processes may run concurrently. Alternating
+the sides limits drift. These are local measurements, not a portable speed ratio.
+
+## Why the checker accepts the same certificates
+
+For ordinary JSON inputs, fix one call, its reconstructed roots and exact
+transition function. Define
+R(i,empty)=root_i and R(i,wa)=step(R(i,w),a). The old function evaluates this
+recursion by a finite loop on each requested word.
+
+The new trie starts with root_i. When a child labelled a is absent, it stores
+step(R(i,w),a). Induction on prefix length proves that every stored row equals
+the old R(i,w). An existing child therefore returns exactly the old result.
+Roots remain keyed by output role, and the trie belongs to one check call.
+No reuse crosses problems, fields, shifted interpretations or certificates.
+
+Stored row dictionaries remain unchanged. The retained transition, terminal
+and linear-combination functions build new dictionaries, and scalar operations
+do not mutate operands. Every request still checks its output index and every
+symbol before consulting the cache. A valid cached prefix cannot bypass path
+validation. The rest of the checker is byte-for-byte unchanged. `verify.py`
+reverses the declared cache-only edit and requires exact equality with the
+authenticated predecessor source.
+
+Let P be the sum of requested path lengths, U the number of distinct nonempty
+rooted prefixes and R the number of requested roots. The old path evaluator
+applies P transitions; the cache applies U. Full closure evaluation is unchanged.
+For S dependency states, each sparse row has at most S entries, so extra retained
+space is O(S(U+R)). This is a memory tradeoff, not a constant-memory claim.
+
+New controls use two roots with shared symbol sequences over Q, Q(i), F2, F3
+and F5, degrees one through eight, and both shifted interpretations. They compare
+verdicts and check the exact P-U transition saving. Repeated calls test cache
+lifetime. Both implementations reject malformed shared-prefix paths, Boolean or
+out-of-range roles, missing initial/closure coverage and wrong source digests.
+The complete old and new scientific outputs must agree as well.
+
+## Reproduce
+
+From the repository root, using standard-library CPython 3.12:
+
+```sh
+/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/cached-dirty-paths
+/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/cached-dirty-paths/verify.py
+/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -O -B research/cached-dirty-paths/verify.py
+/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/cached-dirty-paths --check-source-history
+```
+
+Expected result: `PASS_CACHED_DIRTY_PATHS`. Registered checks run both complete
+variants and all new controls. Normal execution writes nothing. Any CPython 3.12
+executable can replace the absolute interpreter path.
+
+For a fresh ten-run measurement, choose a new path outside the checkout:
+
+```sh
+/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/cached-dirty-paths/benchmark.py --receipt /absolute/new/external/benchmark.json
+```
+
+`BENCHMARK.json` is the retained generated measurement artifact. Replay checks
+its executable/input hashes, success count, exact scientific output and derived
+medians. A fresh measurement need not reproduce the local wall times. It must
+preserve the scientific output. Every live source file is pinned by SHA256 and
+Git blob in SOURCES.json and declared in VERIFY.json.
+
+## Scope and implementation constraints
+
+Only this opt-in package changes. The retained PR5235 package stays immutable.
+`replay.py --baseline` uses its checker; the default uses the cached copy. The
+wrapper authenticates every source file before loading it. The copied checker
+keeps its original attribution. No general adoption is made here.
+
+New cache code has no recursion, eviction or global result cache. Traversal is
+bounded by word length. The new fixtures have at most sixteen unary calls;
+the retained complete caller bounds the shipped replay. The benchmark has ten
+child processes with 90-second deadlines and captures bounded complete reports.
+
+Power-of-ten deviations: Python dictionaries and exact arithmetic allocate during
+execution. The cache bound above and fixed replay domains constrain live memory;
+no fixed-allocation compliance is claimed. The retained independently transcribed
+`reconstruct` function is 86 lines and remains byte-identical. Splitting it would
+exceed this cache-only change and its exact-delta gate. New functions are below
+60 lines. The fixed-module loader is needed to run the unchanged caller and
+authenticates its source inventory first. Warning-strict normal and optimized
+Python, exact-delta and behavioral checks provide the available diagnostics.
+A future larger adapter must price its cache memory explicitly.
+
+No selected supplier replay, native/physical admission, rounded execution,
+compiler closure, storage/stock/tape pricing, analytic recovery, Lean, Docker or
+independent human review is supplied. The five selected framework assumptions
+remain. Faster replay does not improve the selected multiplication bound.
+
+## Open next questions
+
+Can a larger source-bound independent-symbol program retain the benefit within
+a stated peak-memory budget? Start by measuring its rooted-prefix count and
+sparse-row sizes, then compare the complete producer/checker path. A compatible
+real adapter and measured memory budget are blockers. The present cache avoids
+no transitions when every requested prefix is distinct.
+
+## Credit and overlap
+
+zxv / [PR5235](https://github.com/CrocSwap/integer-mult-bounds/pull/5235) supplies
+the compiler, independent checker, scalar layer, proof, fixtures and explicit
+repeated-path performance handoff. Classical weighted-automata equivalence and
+noncommutative identity testing retain their Kiefer and Raz-Shpilka credit.
+The echo scheduler retains androolloyd, Chafik Boukhalfa / PR628 and Ali Romman /
+PR621 credit. Cinna Davis / PR4100 and PR4088, ToikY, Sagar Thakrar, roger-sato,
+Charles Bethin and Ross Richardson retain the dirty-phase, tensor and register
+attribution in the predecessor README. No predecessor mathematics is claimed
+or audited as this contribution.
+
+The cache, preservation argument and measurements were produced by Nick Petalas.
+The target was reserved in the [advance CLAIM](https://github.com/CrocSwap/integer-mult-bounds/discussions/1166#discussioncomment-19294845).
+Live PRs, active Discussions, local reservations, recent account work, main README
+text and merged object/formula searches were checked. The cached search covered
+333 open PRs and 6,046 Discussion records but omitted 8,623 sparse main notes.
+Separate Git searches covered relevant main README text. Arbitrary diffs,
+unpublished work and later publications remain outside that coverage.
+These searches do not establish global novelty.
diff --git a/research/cached-dirty-paths/SOURCES.json b/research/cached-dirty-paths/SOURCES.json
@@ -0,0 +1,96 @@
+{
+  "schema_version": 1,
+  "base_commit": "2485805a6d47f36ea83ddde6327d453ac82d44dc",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "d59b5035e7b4cbaa9d688a1d32dd0d6eb79c466a",
+      "sha256": "9b8d0eea95b3bf0dfcb7938a732a6439b87a2685dec2a5ab9e525b3b34debbfa"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "3404fbdd5e7529a0674eef26114b5071e4586cec",
+      "sha256": "ead6cdc9d0af6d58e8a49744d8ec8c7c15e13d2ba93c276c434bcf9b51b93a81"
+    },
+    {
+      "path": "research/cyclic-dirty-commutator-audit/echo.py",
+      "usage": "input",
+      "sha256": "63d44c48801f51720a7cc994d6b5e2e857d1aa4fae4c6b83c0cca032b3d9e13b",
+      "git_blob": "76a31171368eb945815cc00dce931c6c7a88e836"
+    },
+    {
+      "path": "research/universal-dirty-certificates/README.md",
+      "usage": "input",
+      "sha256": "fb8d94a58b6c0448aa893e65f263b9d71639b1aa79cd10f054d0dc740a570dca",
+      "git_blob": "be4e5981e57bdd2aa8d2ba8c36479594cf38b5d2"
+    },
+    {
+      "path": "research/universal-dirty-certificates/SOURCES.json",
+      "usage": "input",
+      "sha256": "5d2c0b2a8921b8dc0f724fa11f93cdfeb764e57cfdfb7fa236ec958d72306899",
+      "git_blob": "78109486a46ebc0f6552d8de4cc09afa5a783535"
+    },
+    {
+      "path": "research/universal-dirty-certificates/check_certificate.py",
+      "usage": "input",
+      "sha256": "09cba2605c62f8af0dc48cf60b4eab9f8711cba820e22698d0447833c1a16c37",
+      "git_blob": "cdb1d3fe14ba929cbe343d181cd08ff56f7f42e9"
+    },
+    {
+      "path": "research/universal-dirty-certificates/examples/binary-echo3.certificate.json",
+      "usage": "input",
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+      "git_blob": "34996f4e4234ad769010ba88b108b8141b835e75"
+    },
+    {
+      "path": "research/universal-dirty-certificates/examples/binary-echo3.json",
+      "usage": "input",
+      "sha256": "a5199c1dc6236e346891c641b9402d8065c5bd29087c560e76fcdf2299cdfcf9",
+      "git_blob": "8bb08f646562569d4c48168f9f4459cb57e8a120"
+    },
+    {
+      "path": "research/universal-dirty-certificates/examples/dirty-echo3.certificate.json",
+      "usage": "input",
+      "sha256": "21444c604e17d0cbd707ffbecde10edb4bdff0bdc5a3ffb71819be04c3ac58c5",
+      "git_blob": "f19706f07112e6d6b0b8a5301a6b1284274d5cea"
+    },
+    {
+      "path": "research/universal-dirty-certificates/examples/dirty-echo3.json",
+      "usage": "input",
+      "sha256": "862281041cd5616a8785b526d0cee57a50aa7457a8cb64a0abff1133d6d60798",
+      "git_blob": "13c38bf647c050243f5691d5a61be75ea3e4a4d9"
+    },
+    {
+      "path": "research/universal-dirty-certificates/examples/wrong-order.certificate.json",
+      "usage": "input",
+      "sha256": "54850450cc231e4db2a1c4637fc3f7a49dfb694d9c64cfeb8faa8df91d529a79",
+      "git_blob": "20e3102d5a6e68b6fa19345080d0eeb957977c23"
+    },
+    {
+      "path": "research/universal-dirty-certificates/examples/wrong-order.json",
+      "usage": "input",
+      "sha256": "137def9876c1195456a312b8c232d656ff063cc5caae645be6afc3d06709742c",
+      "git_blob": "85482942f052694a3a6d15d364d18823b51e1b00"
+    },
+    {
+      "path": "research/universal-dirty-certificates/fields.py",
+      "usage": "input",
+      "sha256": "0829ad6ed3775ba6e3d11cf04cfb3513ac763549b730aaed74958b1238e660d7",
+      "git_blob": "f1b6dc83e26bd9fd9ec67ded3fedb330ef89598d"
+    },
+    {
+      "path": "research/universal-dirty-certificates/linear_words.py",
+      "usage": "input",
+      "sha256": "fe825cf7c886de61bb5ec5a02171c5a392a7bddc185280726f4c359b3f289584",
+      "git_blob": "4a877e1ab9a87a0f01eb13e28ddf309c2060bd5e"
+    },
+    {
+      "path": "research/universal-dirty-certificates/verify.py",
+      "usage": "input",
+      "sha256": "2759a2e7514453012ed0e4ffc7017375dea973925672dc16f127d91790dcb6e5",
+      "git_blob": "abccca3c9e9005343e254a78dc3482693eabd993"
+    }
+  ]
+}
diff --git a/research/cached-dirty-paths/TASK.json b/research/cached-dirty-paths/TASK.json
@@ -0,0 +1,61 @@
+{
+  "schema_version": 1,
+  "task_id": "replay-runtime",
+  "priority_revision": 8,
+  "base_commit": "2485805a6d47f36ea83ddde6327d453ac82d44dc",
+  "original_card": {
+    "id": "replay-runtime",
+    "question": "Can one measured replay bottleneck be sped up without dropping coverage?",
+    "starting_points": [
+      "scripts/run_isolated_tests.py",
+      "scripts/verify_replay_coverage.py",
+      "certificates/selected-result.json"
+    ],
+    "methods": [
+      "Profile one isolated replay and optimize the measured bottleneck.",
+      "Design source-bound reuse with explicit dependency invalidation and negative controls."
+    ],
+    "acceptance_gate": "Report before/after wall time on the same fixture, retained checks and invalidation behavior.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_selected_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Resolve the current selected review, separate complex/ordinary BIT/admitted BIT/outer budgets, and compare the card against live handoffs before starting. Historical ceilings require exact source/model equivalence.",
+      "scope": "Source-binding orientation only; not a scientific replay or all-size proof. Materialize selected inputs if this checkout is sparse."
+    },
+    "first_experiment": "Measure one unchanged fixture, preserve check coverage, and test one optimization with invalidation controls.",
+    "bottleneck_link": "Faster trustworthy replays increase review throughput and let mechanism candidates be checked sooner.",
+    "allowed_variations": [
+      "Profile one stage or design one source-bound cache boundary."
+    ],
+    "scope_change_triggers": [
+      "Skipping coverage or comparing different fixtures to claim speedup."
+    ],
+    "overlap_terms": [
+      "replay runtime",
+      "cache invalidation",
+      "isolated tests"
+    ]
+  },
+  "scope_status": "refined",
+  "actual_scope": "Cache rooted path prefixes within each complete PR5235 certificate check, preserving every predicate and equation; measure the complete unchanged scientific caller.",
+  "scope_change_reason": "The replay-runtime card is narrowed to the explicit repeated-path traversal handoff of PR5235.",
+  "bottleneck_link": "Quicker exact complete-endpoint checking helps test recursive-interface candidates while preserving all dirty returns. This is verifier engineering, not a supplier or kappa improvement.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop at the first source-bound complete-caller timing improvement with exact output parity, five alternating runs per side and all rejection controls; otherwise release the failed method.",
+  "outcome": "completed",
+  "evidence": "README.md; BENCHMARK.json; verify.py; replay.py; source-bound cache-only delta; normal and optimized registered replay.",
+  "author": "Nick Petalas",
+  "ai_assistance": "Independent human and formal proof-kernel review are unclaimed.",
+  "open_questions": [
+    {
+      "question": "Can a larger source-bound independent-symbol adapter retain a benefit within a measured peak-memory budget?",
+      "why_it_matters": "The trie trades extra sparse-row retention for fewer repeated transitions; large callers need a complete cost comparison.",
+      "first_step": "Measure distinct rooted prefixes, sparse row sizes and complete producer/checker time on one compatible actual adapter.",
+      "blocked_by": "A source-bound real adapter and measured memory budget are absent."
+    }
+  ]
+}