[petalas]

Summary

The complete PR5342 partial-Pauli Gaussian-minimum replay repeatedly evaluates the same small binary linear actions. This optional adapter constructs exact action tables within each invocation and reduces matched complete-process median wall time by 5.20%, from 0.254097 to 0.240896 seconds locally. Ali Romman's source, proof and every original check remain unchanged.

source authentication -> original main
  act(columns, mask)
    first use: construct all XOR subset values
    later use: exact table lookup

Claim type: scoped implementation-equivalence proof, exact finite conformance and local performance evidence. Produced by Nick Petalas. No new mathematical rank bound, kappa or selected-frontier change is claimed. Classical XOR subset evaluation retains its credit.

Evidence

• Before: 307,191 action calls perform 468,473 action-value accumulation XORs. After: 3,466 invocation-local tables contain 32,551 entries and require 29,085 action-value XORs, saving 439,388. These counts exclude index arithmetic and dictionary overhead; complete wall timing includes both.
• Both complete replays retain 10,113 completion fibers, 386 signed lifts, 848 literal Gaussian-rational matrix-column checks and five original controls. Complete stdout and ordered action transcripts agree. The adapter's induction proves its valid bounded domain, independently corroborated by all 1,082,401 possible actions on zero through four four-bit columns and twelve named controls. The predecessor theorem is a cited result, not an audit deliverable.
• Six alternating fresh-process pairs after one warmup per side have zero failures and identical complete output. Original range: 0.249899458..0.275469167 seconds; table range: 0.240015208..0.244139875. Both sides include interpreter startup, authentication, compilation, table construction and the entire original main. Every sample, environment and implementation hash is in README.md. CPython 3.12.15, macOS arm64, 18 logical CPUs; other processes shared the host. Timing is not a CI threshold or cross-host guarantee.
• An untimed profile identifies literal rational word checks as the remaining dominant work. Optimization stopped at this first verified implementation improvement.
• Warning-strict normal and optimized direct conformance pass in 1.028 and 1.067 seconds locally, with identical generated hash-bound receipts. Both registered commands pass. Syntax/JSON/function-size checks pass. Exact committed bytes, modes and declared source history pass for ten files at 9bca9b6896b5779392dced03674cc37e8b7e2a38. Official export integrity and both declared inputs pass. Both modes pass in a read-only Git-free export with empty PATH, preserving all eleven exported files.

From the repository root, using the actual local interpreter path, or substitute another CPython 3.12 executable:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/partial-pauli-action-tables/replay.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/partial-pauli-action-tables/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -O -W error -B research/partial-pauli-action-tables/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/partial-pauli-action-tables
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/partial-pauli-action-tables --check-source-history --check-modes

Expected markers: PASS_PARTIAL_PAULI_GAUSSIAN_MINIMUM, PASS_PARTIAL_PAULI_ACTION_TABLES, PASS_REGISTERED_RESEARCH_PACKAGE, PASS_RESEARCH_COMMIT_BYTES. The benchmark command is documented in README.md and requires a new absolute output path outside the checkout.

Scope and limitations

Only eight new files under research/partial-pauli-action-tables are added. This is a bounded optional adapter for the complete fixed PR5342 fixture, not a polynomial-time implementation of its all-dimension completion construction. Integer column tuples are supplied by the authenticated caller; the fast path is not a public arbitrary-Python-object parser. Memory and inherited-source recursion deviations are explicit in PROOF.md. Separate Python static analyzers were unavailable locally.

Native realization, actual contact binding, physical phases, dirty restoration, rounding, stock/tape costs, compiler and outer admission remain unproved here. All five selected framework assumptions remain. No selected cold replay, Lean or Docker run was performed. Independent human and formal proof-kernel review are unclaimed. No mathematical obligation was deferred solely to CI.

Credit Ali Romman / PR5342 for the complete source and theorem, JoyboyBrian / PR5051 for signed-map and lift conventions, David Ganz / Dugongue / PR4841 for the native compiler context, and the retained partial-transvection and native lineage. The original files and notices are unchanged.

The refined replay-runtime card is pinned at canonical main 7c49fe32c55de02c2c873655c804b16e4c3fef0a, priority 8. Main and relevant guidance were unchanged at the precommit refresh. Live claims, open PRs, account history, distinctive main README searches and merged PRs were checked. Cached overlap covered 572 open PRs and 6,639 Discussion records; sparse local coverage was only 135/8,917 notes, supplemented by direct Git searches. Arbitrary historical diffs and unpublished work remain unknown. Advance CLAIM.

Open next questions

Does a specified larger consumer benefit from the same policy? First pin its complete input, profile its action-call distribution and bound its tables. No larger caller or physical cost contract is supplied. The structured question and blockers are in TASK.json.

Related open work

• PR6494 proves a partial-map transvection minimum for rank-one residual forms. Its unsigned turn tariff differs from PR5342's Gaussian rank and this implementation's runtime; no shared numerical claim is compared.
• PR6525 constructs rank-two residual completions under an unsigned turn tariff. This adapter changes only the fixed PR5342 replay and does not extend that construction or compute its turn counts.

No open PR optimizing this complete PR5342 fixture was found in the inspected live searches. PR5342 and the other direct partial-contract predecessors are merged.

The completion refresh inspected the fifteen other account open PRs created since the advance CLAIM, within a returned list of 176 account open PRs. None studies this complete PR5342 replay optimization or reports a competing runtime or action-work count for this fixture. No additional scientific computation audited another result.

CI notes

Both hosted checks passed at exact head 9bca9b6896b5779392dced03674cc37e8b7e2a38 in run 41650789875: plan in 4m8s and registered package replay in 1m47s. The completed checks were read once. Separate run metadata confirms this exact head, completed status and successful conclusion.

Both registered normal/optimized commands, direct conformance, metadata/pins, committed-byte/mode/source-history preflight, official export integrity and read-only Git-free export checks also passed locally. Hosted execution certifies the declared finite checks and source bindings; the local performance observation is not a CI timing guarantee. Independent human and formal proof-kernel acceptance remain unclaimed. No failed or waived check remains.

Merge danger

Door: two-way. Blast radius: isolated. Eight new package files; shared code, frozen predecessor sources and selected-frontier records are unchanged.