Reduce complete A2+E6 primary replay time by 27.86% (no κ)

research/a2-e6-cached-contractions/PROOF.md

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+# Exact contraction reuse in the PR2061 primary replay
+
+This scoped implementation-equivalence proof was produced by Nick Petalas.
+New work is Apache-2.0. Independent human and formal proof-kernel review are
+unclaimed. Adam Gall's COPY69 theorem is a cited predecessor result, not a
+new mathematical claim of this package.
+
+## Contract and equality
+
+The pinned primary verifier checks each requested ordered pair by computing
+
+```text
+sum_k rows[i][k] * (sum_s Q(E.LINES[j][s]) * frame.F[k][s]) / 4
+    == 2 * E.G[i][j].
+```
+
+Its actual domain has 112 live indices, nine normals and eight coordinates.
+All contractions use exact rational arithmetic. During an identity invocation
+the indices, normals, roots and Gram matrix are fixed. No callback or mutation
+occurs inside a contraction.
+
+Define `C[j,k]` to be the parenthesized sum divided by four. Its inputs do not
+depend on i. The adapter computes each C once, then uses
+`sum_k rows[i][k] * C[j,k]` in the same i,j,k order. Each coefficient is exactly
+the original coefficient, including rational conversion and division. Therefore
+each entry comparison has exactly the same value. The first failing ordered
+pair is unchanged, and success still requires every requested ordered pair.
+Eagerly computing later coefficients adds no exceptional behavior on this
+fixed finite rational domain.
+
+The cache is local to one call. It is discarded before the next invocation,
+so changing normals, input rows, roots or Gram data cannot reuse stale values.
+The adapter authenticates all nine live files before importing predecessor
+code. The predecessor retains its own source checks as well.
+
+## Exact work reduction
+
+The original `run()` invokes the identity routine twice. Its positive witness
+compares 12,544 entries. Its existing deliberately changed coefficient fails
+on comparison 4,817. Both invocations and both outcomes remain present.
+
+For V visited pairs, the original executes 9V eight-coordinate contractions.
+For each invocation the adapter executes 9*112=1,008 contractions. Hence
+
+```text
+original: 9*(12544+4817) = 156249 contractions
+cached:   2*9*112       =   2016 contractions
+removed:                  154233 contractions
+removed rational products: 8*154233 = 1233864
+```
+
+These are counts of explicit `Q(a) * b` operations in the inner contraction.
+No claim counts the saved additions, conversions or divisions as further
+multiplications. The outer nine-term entry sums are unchanged. The verifier
+enumerates the visited pairs and checks these exact counts.
+
+## Complete workload and measurement
+
+Both benchmark modes invoke the unchanged complete `run()`. It still performs
+the geometry checks, every character-compatibility and triple-compatibility
+check, support and rank calculations, attaining identity, all existing
+rejection controls and both rational interval budget screens. Both compare
+the entire freshly computed result with the pinned `RESULT.json` and print
+the same complete-primary success line. Only `exact_identity` is replaced.
+
+The complete primary CLI is the measurement boundary. Import, all source hash
+checks, construction, scientific execution, certificate comparison and output
+are inside the subprocess timer. It is not a whole four-command registered
+workflow measurement. The independent checker and six-test driver remain
+unchanged and are not claimed to be faster.
+
+Five alternating original/cached fresh processes each passed, with identical
+stdout and no stderr. Median elapsed time was 2.354848833 seconds original
+and 1.698670834 seconds cached, a 27.8649733% reduction. Original range was
+2.331363334 to 2.602431125 seconds; cached range was 1.675971083 to 1.886004875.
+The ten integer nanosecond samples are reproduced in README.md.
+These are local macOS measurements, not a portable timing guarantee.
+
+A separate, untimed cProfile run attributed 2.769 of 4.770 profiled run-seconds
+to the two original identity invocations. The measured saving is below that
+profile share. Other exact rational work, especially the unchanged interval
+budget calculation, limits the complete-CLI gain. Profiling overhead is not
+included in the reported timings.
+
+## Scope and stopping point
+
+The proof applies to this fixed source-bound rational routine, not arbitrary
+side-effecting or mutable input objects. The new finite controls compare the
+original and cached routines on rational inputs, every single-entry mutation
+of five bounded domains, changed normals and changed Gram data. Separate
+source controls reject corruption of each live file and one missing file.
+
+The first verified improvement ended optimization. This package does not
+re-establish the predecessor's optimum, change its decoder, lower a native
+invoice or prove a multiplication bound. Complete supplier, physical, stock,
+precision/tape, compiler and outer obligations retain their prior status.

research/a2-e6-cached-contractions/README.md

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+# Cached contractions in the complete A2+E6 primary replay
+
+The opt-in PR2061 adapter removes 154,233 repeated exact contractions and
+1,233,864 rational multiplications. The complete primary CLI's local median
+time falls by 27.86%, preserving its complete result and all original checks.
+This is a scoped implementation-equivalence proof, exact operation-count
+certificate and local performance result. It is not a new decoder theorem,
+supplier admission or kappa. The contribution was produced by Nick Petalas.
+
+`replay.py` authenticates nine live source files, imports the unchanged primary
+verifier and replaces only `exact_identity`. The new implementation computes
+the fixed 112-by-9 root-normal contraction table once per call. It retains
+every ordered entry comparison, the original early rejection and the complete
+`RESULT.json` comparison. The cache never survives an invocation.
+[PROOF.md](PROOF.md) proves exact equality and gives the counting argument.
+No frozen predecessor file or selected record changes.
+
+## Measurements
+
+CPython 3.12.15, macOS 27.0.1 arm64, 18 logical CPUs, standard library only.
+Five alternating original/cached fresh-process pairs passed with no errors,
+identical stdout and empty stderr. The timer encloses the entire CLI, including
+imports, source authentication and both rational budget screens.
+
+| Mode | Median seconds | Minimum | Maximum |
+| --- | ---: | ---: | ---: |
+| Original | 2.354848833 | 2.331363334 | 2.602431125 |
+| Cached | 1.698670834 | 1.675971083 | 1.886004875 |
+
+The integer nanosecond samples, in alternating pair order, are:
+
+```text
+original   cached
+2332376792 1886004875
+2602431125 1675971083
+2354848833 1841411000
+2331363334 1698670834
+2503531083 1684102000
+```
+
+The one-minute load average rose from 3.00 to 4.41 during the run. Other work
+could not be controlled; the sides were interleaved on the same machine.
+A separate profile places about 58% of the original `run()` time in the two
+identity invocations. The unchanged interval budget calculation is a remaining
+limiter. Profiler runs are excluded from the timing sample. The measured gain
+is below the original identity share; no isolated helper timing is substituted
+for the complete CLI. This is not a whole four-command workflow speedup or a
+guarantee on another machine.
+
+## Reproduce
+
+From the repository root with CPython 3.12 and its standard library:
+
+```sh
+/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/a2-e6-cached-contractions/verify.py
+/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -O -W error -B research/a2-e6-cached-contractions/verify.py
+/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/a2-e6-cached-contractions
+/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/a2-e6-cached-contractions --check-source-history
+/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/a2-e6-cached-contractions/benchmark.py
+```
+
+Any CPython 3.12 path may replace the local absolute path. Put `TMPDIR` and
+redirected receipts in an external scratch directory if retaining outputs.
+The benchmark defaults to five alternating pairs and accepts at most nine.
+It checks every exit status and exact stdout; a failed run aborts the report.
+Registered verification runs normal and optimized Python and writes a generated
+stdout receipt bound to every package-file hash. No receipt is handwritten.
+Expected markers are `PASS_A2_E6_CACHED_CONTRACTIONS`,
+`PASS_REGISTERED_RESEARCH_PACKAGE` and `PASS_RESEARCH_COMMIT_BYTES`.
+
+The verifier retains the complete primary science, including 12,544 positive
+identity comparisons and the coefficient mutation's rejection at comparison
+4,817. It adds 37 rational control cases and ten real source-admission controls.
+Each of the nine live dependencies is independently corrupted and rejected;
+one missing input is rejected. The package exports with all declared inputs
+and can replay without Git or network access. No source receipt is rewritten.
+
+## Scope and implementation constraints
+
+The first successful contraction change ended optimization. `independent.py`
+and `test_verify.py` from PR2061 are unchanged, unoptimized and outside the timed
+primary CLI. Their mathematical results are not this contribution. No selected
+cold replay, Lean, Docker, native supplier or complete multiplication theorem
+was run or proved. The selected conditional kappa 0.003125804 and its five
+framework assumptions remain unchanged. Independent human and formal
+proof-kernel review are unclaimed.
+
+The adapter has at most 120 indices, nine normals and eight coordinates from
+the authenticated source. Its cache has at most 1,080 rational entries, 1,008
+on the actual fixture. New functions fit within 60 lines, use no recursion and
+enforce bounded domains. Source-control copies are temporary and removed on
+every exit. Each subprocess has a 60-second timeout; the benchmark has at most
+18 subprocesses. CPython allocation and fixed-target dynamic module imports are
+documented Power of Ten deviations. The legacy imported `run()` exceeds the
+function-size target; it remains frozen to preserve the exact workload.
+Warning-strict normal and optimized runs provide recurring diagnostics.
+
+## Open next questions
+
+Should this adapter be adopted by PR2061's registered workflow? Start with an
+explicit successor source binding and the complete four-command Linux replay.
+Default adoption and a whole-workflow measurement are still missing. They
+cannot be inferred from the primary CLI measurement. [TASK.json](TASK.json)
+records the same first step and blocker. No further optimization is reserved.
+
+## Credit and overlap
+
+Adam Gall's [PR2061](https://github.com/CrocSwap/integer-mult-bounds/pull/2061),
+head `eed23989eddf7ec0b2c24d9e3794d0fca53f11ab`, supplies the complete scientific
+workload, COPY69 result and rejection controls. Credit joaqcoo / PR1224 for the
+normal family and geometry implementation; Philipp / mightyOil / PR1248,
+commdata2338 / PR1304 and Hanson Sun / bbMisk / PR1612 for the deficiency method;
+DreamingOfClouds, GamingPuzzled, themilkman216, woklerx, Sagar Thakrar and Douglas
+Colkitt for the decoder, coverage and ceiling lineage retained in PR2061.
+Their files and notices are unchanged. The new contribution is the contraction
+adapter, equality proof, operation reduction and complete-CLI measurements.
+Exact source pins are in [SOURCES.json](SOURCES.json). New work is Apache-2.0.
+
+Base canonical main `7c49fe32c55de02c2c873655c804b16e4c3fef0a`, priority revision 8.
+[Advance claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/1166#discussioncomment-19371337).
+Live open PRs, recent account PRs, handoffs and all-main README searches were
+checked for this particular replay. The overlap helper had complete remote
+pagination and incomplete sparse local-note coverage, supplemented by Git main
+searches. These searches are bounded evidence, not proof of global novelty.
+No related open PR studying this exact A2+E6 primary replay was found.

research/a2-e6-cached-contractions/SOURCES.json

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+{
+  "schema_version": 1,
+  "base_commit": "7c49fe32c55de02c2c873655c804b16e4c3fef0a",
+  "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/a2-e6-nine-normal-floor/RESULT.json",
+      "usage": "input",
+      "git_blob": "c87f58ee3d4394ee8a1d2bb4a1ad85cc184747b9",
+      "sha256": "d6712b33ad02b9c894b3e8253f75103297ad725c196e63b02af7fab2df62f0ca"
+    },
+    {
+      "path": "research/a2-e6-nine-normal-floor/SOURCES.json",
+      "usage": "input",
+      "git_blob": "749c5e467b8cec6bfaf80657e41975c364c6ecb8",
+      "sha256": "47d3b549df431f199617ecc70be4a597ecd7d05443494c2517b1be3c12db59da"
+    },
+    {
+      "path": "research/a2-e6-nine-normal-floor/verify.py",
+      "usage": "input",
+      "git_blob": "46113056d907077ad60c5542d4b8452a70dd36f3",
+      "sha256": "93f9d9293dbee222f926d9da003742959f6b55ff337abe3d7a8acd85f2a2f345"
+    },
+    {
+      "path": "research/a8-one-pair-frame-floor/README.md",
+      "usage": "input",
+      "git_blob": "8f3748696ab69b1ba57a400e0e2070bf09b817d8",
+      "sha256": "bd0fa2ec318eb5b8ac21c69b5be3dbcabdb7a9e51d8cecdbc79e46bfe56ef94c"
+    },
+    {
+      "path": "research/complex-local-word-ceiling/RESULT.json",
+      "usage": "input",
+      "git_blob": "77f55043a679dd722330f1e2499863e36376d9f9",
+      "sha256": "d91d6c46509875abf1f61de67c2609656d3dc685451299f83caa6f922493692d"
+    },
+    {
+      "path": "research/complex-local-word-ceiling/ceiling.py",
+      "usage": "input",
+      "git_blob": "6c0f54527d879396f689523bfde19928a9b6157c",
+      "sha256": "86a1432870b3b21d8454106ec9162fddc0471472d9214c590a1420f2426cedfc"
+    },
+    {
+      "path": "research/nine-term-decoder-normal-form-seed42/PROOF.md",
+      "usage": "input",
+      "git_blob": "e510fd180a286445fd6fc484057001bfc60f8c9c",
+      "sha256": "0503e07f1764708e9e72c01be88d3dad1b213e73eb3c23397a603032791fd23a"
+    },
+    {
+      "path": "research/nine-term-decoder-normal-form-seed42/e8lab.py",
+      "usage": "input",
+      "git_blob": "6aef95fc972f56e600b7c9699238e3a1ce7f7413",
+      "sha256": "772349edc9dff45fa3cac89fdbbe8bf1bab734e9776a245fcac8e8bd60d94634"
+    },
+    {
+      "path": "research/nine-term-decoder-normal-form-seed42/verify.py",
+      "usage": "input",
+      "git_blob": "994e429042f292084546c8d1efe287dfb5930fd9",
+      "sha256": "248763cf5ff85f073766aa8a85187a1d314fcf3a716b2586ca8fc1197d4c6c4e"
+    },
+    {
+      "path": "research/a2-e6-nine-normal-floor/README.md",
+      "usage": "provenance",
+      "git_blob": "188643388662d639b4d1e798ac70bdfdadd37a22",
+      "sha256": "be549abbe2b617e2868ab086b1602f711a11a2064174d41a9cd30a6cf2945827"
+    }
+  ]
+}

research/a2-e6-cached-contractions/TASK.json

@@ -0,0 +1,75 @@
+{
+  "schema_version": 1,
+  "task_id": "replay-runtime",
+  "priority_revision": 8,
+  "base_commit": "7c49fe32c55de02c2c873655c804b16e4c3fef0a",
+  "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": "Source-bound exact implementation equivalence, operation reduction and complete primary CLI timing for PR2061.",
+  "scope_change_reason": "Choose the complete PR2061 primary scientific CLI as one bounded replay; cache only its fixed exact contractions.",
+  "bottleneck_link": "Reduce repeated exact arithmetic in a complete retained geometry/decoder replay without losing its scientific checks.",
+  "budget_minutes": 60,
+  "stop_rule": "Ship the first verified complete-CLI improvement; no second optimization.",
+  "outcome": "completed",
+  "evidence": "PROOF.md, replay.py and verify.py; benchmark.py generates exact per-run timings outside the checkout.",
+  "author": "Nick Petalas",
+  "ai_assistance": "Independent human and formal proof-kernel review are unclaimed.",
+  "open_questions": [
+    {
+      "question": "Should the opt-in adapter be adopted by PR2061's registered workflow?",
+      "why_it_matters": "The measured primary-CLI saving does not change the predecessor's default replay.",
+      "first_step": "Arrange an explicit successor source binding and run its full four-command registered workflow on Linux.",
+      "blocked_by": "Production adoption and a whole-workflow measurement are outside this isolated contribution."
+    }
+  ],
+  "source_pr": 2061,
+  "source_author": "adamgall",
+  "source_head": "eed23989eddf7ec0b2c24d9e3794d0fca53f11ab",
+  "claim_url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1166#discussioncomment-19371337",
+  "environment": {
+    "python": "CPython 3.12.15",
+    "platform": "macOS 27.0.1 arm64",
+    "dependencies": "standard library"
+  },
+  "limitations": [
+    "Complete primary CLI only; independent.py and test_verify.py are unchanged and not optimized.",
+    "No new decoder optimum, supplier admission, kappa or multiplication theorem.",
+    "All five selected framework assumptions remain; selected scientific replay, Lean and Docker were not run."
+  ]
+}