[petalas]

Summary

A fixed bitset cache implements SHIN09-git's PR6046 shared-tail predicate with identical complete caller behavior. Across all thirty retained alternating fresh-process pairs, median paired wall time is 10.96% lower, with 28 paired wins and zero errors. This answers the source's explicitly open cached-Hamming-envelope implementation question. Claim type: scoped proof of implementation equivalence, exact finite conformance and a local performance measurement. No new kappa.

unchanged complete DFS and cheap checks
    cached reachable sets and XOR translations
    identical shared-tail decisions and complete word tuples

The new implementation, equivalence argument and measurements were produced by Nick Petalas. Credit SHIN09-git for the predicate, theorem, original comparison caller and open question; Ali Romman, Mihir Srivastava, Ross Richardson, Nicholas Stone, unpaidmoon, James Reed and the retained word-census lineage keep their source attribution. Classical bitsets and Hamming geometry are not claimed as new. Only research/cached-hamming-tail/ is added.

Evidence

• Baseline and candidate each enter 7,350 nodes, prune 4,381 and return the same 828 closed/universal words. Both full tuple hashes agree.
• All 21,640 canonical simple prefixes agree on future vertices, full support masks and rejection decisions. All 13,312 cache translations agree with literal set translation. Six controls cover cache over-permission, visited-mask and XOR omission, unsupported mode, adapter restoration after failure and actual source corruption.
• All sixty full-process observations are retained. Baseline median/range: 63.815 ms / 62.508–72.149 ms. Candidate: 56.849 ms / 55.466–167.177 ms. Cache setup, startup, source authentication, traversal and output are included. The slow outlier is retained. An initial nine-pair run was inconclusive; one additional predeclared twenty-one-pair run used unchanged timed bytes, and the result uses all thirty pairs. The combined exact descriptive rank-sum probability is about 1.90e-7. Other host work was uncontrolled; this is not a portable speed guarantee.
• Warning-strict normal and optimized direct checks, all three registered commands, metadata, committed bytes, modes and full declared source history pass locally at fd5bbae8e275713d25bca205a7137a6e5f192eaf. Each registered command takes under one second locally.
• Official export integrity and all three direct checks pass from a read-only Git-free export with empty PATH. All seventeen exported files retain their bytes and modes.

Reproduce from the repository root with CPython 3.12.15 and the standard library:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/cached-hamming-tail/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -O -W error -B research/cached-hamming-tail/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/cached-hamming-tail/timing_check.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/cached-hamming-tail
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/cached-hamming-tail --check-source-history --check-modes

An installed CPython 3.12 can replace the recorded interpreter path. timing_check.py validates the retained measurements and their source bytes; CI does not rerun performance measurements. To collect new timings, run benchmark.py --pairs 9 --output /absolute/external/new-file.json with the same interpreter and flags. The proof, raw observations, untimed profile, exact dependencies and limits are in the package.

Limitations

This fixes dimension five, length twelve and PR6046's complete no-cap shared-tail caller. It supplies an exact implementation of the predecessor predicate, not a new pruning theorem or a predecessor audit. The cache has a fixed extra memory cost. No larger census, maintained-engine integration/default change, selected cold replay, Lean, Docker, native/dirty-restoration construction, supplier admission or complete multiplication theorem was run or established. The selected frontier and five framework assumptions remain unchanged. Independent human and formal proof-kernel review are unclaimed.

Canonical main was refreshed at 2485805a6d47f36ea83ddde6327d453ac82d44dc before selection and submission. Live claims and open/merged work were checked again before committing. The overlap helper had incomplete sparse-note coverage and a timed-out broad Discussion refresh; separate live GraphQL reads covered current handoffs and active threads. Absence of a match is not a novelty certificate. Advance claim.

Open next questions

Does this cache improve one named maintained-engine caller after full setup and the other predicates are paid? Select an exact small caller and a separate resource budget, then compare complete enabled/disabled outputs and runtime. These results do not justify a larger census or default change. No follow-up is reserved.

Related open work

• research: independently audit L22 union prune on tiny domain #3899 independently studies a different union-support predicate at four labels and length eight; the present contribution changes only PR6046's shared-tail implementation and does not audit its theorem.
• Research: seven-source weight-at-most-four connector boundary (L<=18 excluded, 216-call floor) (no new kappa) #4079's title concerns a seven-source sparse-mask connector boundary; this package makes no seven-source or new-exclusion claim, and its template body supplies no further result to compare.
• Research: high-arity connector toggle cost floor #2249 studies charged higher-arity six-source connector calls; the present fixed singleton-prefix caller does not change that alphabet or its prices.
• Six-source one-TRIO path misses full paired coverage at 14 calls #2134 studies six-source words with one TRIO call; this cache changes no source alphabet and computes no comparable six-source maximum.
• Prove exact heterogeneous three-source clean-row tariffs (no κ) #6254 gives fifteen minimal call profiles for three-source paid clean-row tariffs. This five-label shared-tail implementation changes search execution under a different connector contract and computes no comparable three-source price or profile optimum.

The completion refresh inspected this account's open PRs created since the advance CLAIM. PR6254 is the adjacent connector contribution listed above; the other newer account PRs study different objects or quantities. No new same-instance numerical comparison was needed, and no disagreement was identified in the inspected descriptions. No extra computations checked another contribution.

CI notes

Both hosted checks, plan and replay (research/cached-hamming-tail), passed at head fd5bbae8e275713d25bca205a7137a6e5f192eaf in run 41049147311. The completed checks were read once, and the run's successful conclusion and exact head were confirmed. All local registered checks also passed. Hosted replay certifies the registered finite checks and source bindings; it does not certify the local performance percentage or provide independent human or formal proof-kernel review.

Merge Danger

Door: two-way. Blast Radius: package. The change adds an isolated research package with explicit inputs and leaves maintained engines and selected sources unchanged.