[petalas]

Summary

Scoped implementation-preservation proof and measured engineering improvement: a per-certificate prefix trie reduces the complete PR5235 dirty-circuit replay median by 22.57%, while preserving every certificate predicate and equation. This contribution was produced by Nick Petalas. No new dirty-circuit theorem, supplier admission, selected-frontier change or kappa is claimed.

validate the complete output index and word
reuse each rooted prefix within this one check call
check every initial span, terminal and operator closure as before
release the trie when the call returns

Only research/cached-dirty-paths/ changes. The source compiler, field layer, independent checker, fixtures and complete caller retain zxv / PR5235 credit, including its explicit repeated-path performance handoff and full classical/echo/phase/tensor lineage. The source package remains unchanged. The copied checker retains its attribution; the exact-delta gate admits only the cache edit.

Evidence

• Before: five complete runs have median 5.680195 seconds, range 5.459807–6.071584.
• After: five alternating complete runs have median 4.398449 seconds, range 4.318587–4.558831. Zero failures; every scientific output field agrees after removing exactly two elapsed-time fields. The generated BENCHMARK.json binds the measured executables and thirteen inputs.
• All original coverage remains, including 210 echoes, 120 differential circuits, 180 literal counterexamples, 15 certificate and nine input rejections, and the 2^64-word fixture. These are retained predecessor checks, not newly claimed mathematical results.
• New controls pass 80 two-root cases over five fields and both shifted interpretations, enumerate exactly 1,680 avoided transition calls, verify per-call lifetime, and reject twelve malformed-certificate cases across the two implementations.
• Direct warning-strict normal/optimized verification passed in 9.86/9.92 seconds. Both registered commands, metadata/source pins, committed bytes/modes and full declared source-history checks pass. The official 22-file payload export and integrity check pass. Both direct modes pass from a read-only export with Git absent from PATH, preserving all bytes and modes. Actual exported source corruption and an incorrect cache-root mutation are rejected.

Reproduce from the repository root with CPython 3.12.15 and no third-party dependencies:

/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 --check-modes
/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

The scientific verifier prints PASS_CACHED_DIRTY_PATHS. Replace the absolute interpreter path with any CPython 3.12 executable. Timing samples include startup, source authentication, imports, the complete unchanged scientific caller and output. An untimed profile identifies repeated path evaluation as the changed work. Local timing is not a portable speed guarantee.

Limitations

The cache trades extra sparse-row storage for fewer transitions: O(S(U+R)) additional retained space for S states, U distinct nonempty rooted prefixes and R requested roots. Larger callers need a measured memory budget. No transitions are saved when every requested prefix is distinct. The implementation is opt-in; no shared code is changed.

No selected-supplier scientific replay, physical/native admission, rounded execution, compiler closure, stock/tape/precision or analytic-recovery proof was run. Lean, Docker, independent human and formal proof-kernel review are unclaimed. All five selected framework assumptions remain.

Open next questions

Can one larger source-bound independent-symbol adapter retain this benefit within a stated peak-memory budget? First measure its actual rooted-prefix count and sparse-row sizes, then time the complete producer/checker path. A compatible real adapter and measured memory budget remain blockers. This contribution stops at the first verified complete-caller improvement.

Related open work

The completion refresh inspected all sixteen open account PRs created since the advance CLAIM, including this PR. None of the fifteen other PRs studies this exact PR5235 checker or reports its rooted-prefix traversal quantities. No shared-instance numerical disagreement was found; no additional computations were run to check other contributions. Adjacent replay improvements use separate fixtures:

• PR6270 changes the rational-box solve/check implementation, rather than dirty-circuit path traversal.
• PR6272 clears denominators in rational-rank certificate products; its certificate equations and caller differ.
• PR6274 uses binary ranks for mapped-contact distances; its geometry and cache contract differ.
• PR6276 prepares rational gate coefficients in the pivot-440 pulse replay, a separate propagation caller.
• PR6281 uses Gaussian-integer products in the nonlinear support replay; it does not change this certificate checker.
• PR6282 uses intersection counters in the E7 classification replay, a separate binary codeword engine.
• PR6283 skips zero elimination updates in a coupled-recurrence certificate producer; its sparse CLI workload differs.

No numerical performance comparison with those PRs is asserted. PR5235 is merged and remains the credited predecessor. The refreshed exact-object search found no other open PR on this checker. These are bounded overlap checks, not a global novelty guarantee.

CI notes

Both hosted checks, plan and replay (research/cached-dirty-paths), passed at exact head 586f36c90586a02d2f866081469649e44cf94fbd in run 41068115208. The completed checks were read once; separate run metadata confirms the matching head, completed status and successful conclusion.

Every registered command also passed locally, together with the direct warning-strict normal/optimized replay, source-history/byte/mode checks, export integrity and read-only Git-free replay. Hosted replay certifies the registered finite checks and source bindings. It does not certify the local timing percentage, independent human review or a formal proof-kernel theorem. No local package verification obligation is left unrun.

Advance claim: #1166 (comment)

Merge Danger

Door: two-way. Blast radius: isolated. Removing this opt-in package restores the prior behavior; frozen inputs and selected-frontier files are unchanged.