[petalas]

Summary

The complete retained PR2069 replay takes 39.62% less median wall time locally, from 8.703675 s to 5.255297 s. Claim type: scoped implementation-preservation proof, exact finite conformance and local performance evidence. This contribution was produced by Nick Petalas. No new mathematical endpoint or kappa is claimed.

 authenticate the original search, checker and saved result
- scan coefficient bits at every right monomial multiplication
+ prepare twelve immutable 4096-entry permutation rows once
+ use the exact table entry at each original call
 execute the unchanged complete original main function

Only research/dic3-shift-table-replay/ is added. Cinna Davis / 1337isnot1337's PR2069 retains the mathematical result, search and controls. Credit David Govea / PR720, eumemic / PR288 and the retained register-model lineage. Finite lookup tables and bit-permutation recurrences are classical. The new contribution is the bounded optional adapter, preservation argument and complete-command measurements. Nick Petalas's older PR5205 is a different mathematical layer and is neither extended nor replayed here.

Evidence

• Before: five fresh-process complete-command samples, median 8.703675 s, range 8.585230 to 9.105424 s. After: median 5.255297 s, range 5.058666 to 5.884180 s. The five pairs alternate baseline/candidate; every candidate beats every baseline. All ten outputs are byte-identical, with zero failures and empty stderr. CPython 3.12.15, macOS arm64, 18 CPUs; shared-host load was uncontrolled. MEASUREMENTS.json retains all raw samples, commands, environment and source hashes.
• The complete authenticated driver runs the same original main in both modes. Timing includes startup, authentication, source execution, preparation, both searches, raw-word controls, saved-result comparison and output capture. Each fresh process starts with an empty original ring-product cache. No completed-search cache or reduced domain is used.
• A separate profile finds 58,798,872 shift calls and 64,868,328 old bit-scan iterations. The old shift accounts for 9.857 of 21.962 profiled seconds. The candidate profile leaves tuple construction and the join loops dominant; both profiles are retained in PROFILE.json and excluded from reported wall times.
• All 49,152 coefficients agree with the unchanged function and a separate normal-form reference. All 589,824 action compositions and nine rejection/distinction controls pass. Each input source is authenticated before execution. The unchanged full replay retains its 56 operations, 2409/94727 state inventories, 1482/1230 endpoint domains and both original coverage digests.
• Warning-strict normal and optimized direct commands pass in 5.34 s and 5.45 s, under their 120-second limits. Both registered commands pass. Source compilation, function-size inspection and whitespace checks pass. Committed-byte, executable-mode and declared-source-history preflight passes at head 5c014d52e16bf71ca1cb0394c23e25a3a4dae66e. Official export integrity and read-only Git-free normal/optimized replay pass with unchanged exported bytes and modes.

From the repository root, standard library only:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/dic3-shift-table-replay/replay.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/dic3-shift-table-replay/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -O -B research/dic3-shift-table-replay/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/dic3-shift-table-replay
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/dic3-shift-table-replay --check-source-history --check-modes

Any CPython 3.12 path may replace the displayed interpreter. Expected markers are PASS_DIC3_BOUNDED_DIAGONAL_SEARCH, PASS_DIC3_SHIFT_TABLE_REPLAY, PASS_REGISTERED_RESEARCH_PACKAGE and PASS_RESEARCH_COMMIT_BYTES. The verifier generates a receipt bound to all package files. No scientific receipt is handwritten. README.md gives the complete five-pair timing command with a fresh external output path.

Limitations and unrun obligations

This is a source-bound optional implementation for the original finite Dic3 command. It is not a new audit or independent scientific acceptance of the predecessor. The internal mask domain, exact source pins and stable-checkout assumption are essential. Default adoption and historical-source migration are not implemented. Local timing is not a portable speed guarantee; registered CI replays correctness without imposing a runtime-improvement threshold.

Native/physical realization, ownership/restoration, compiler, stock, precision/tape and outer admission remain outside scope. Selected scientific cold replay, Lean and Docker were not run. Independent human and formal proof-kernel review are unclaimed. No selected-frontier file or frozen predecessor is changed.

Open next questions

Should a future default replay adopt the prepared table? First specify the default-entry migration while preserving historical source pins and the complete original command. No additional search layer or optimization is reserved.

Related open work

No open PR studying this exact Dic3 replay or its coefficient-permutation implementation appeared in the refreshed live object search and open-PR list. Merged PR2069 supplies the original command; merged PR5205 studies a separate six-call layer and supplies no timing comparison here. Sparse cached notes, arbitrary historical diffs and unpublished work remain coverage limits. No additional computation was run to compare another contributor's mathematical result.

The completion refresh inspected all eight account open PRs created since the CLAIM, including this PR. The seven others, #6676, #6677, #6678, #6679, #6681, #6682 and #6683, study distinct objects or commands. None studies this Dic3 replay or reports a conflicting common-instance value. PR6681 optimizes Gaussian Newton membership and PR6683 reduces mirror-window classification work; neither supplies a timing comparison for the command measured here. No additional computations checked another contribution.

Advance CLAIM. Canonical main was refreshed unchanged at 7c49fe32c55de02c2c873655c804b16e4c3fef0a, priority revision 8, selected PR6030. Live claims, account contributions, local reservations and distinctive main/merged searches were checked before claiming and committing.

CI notes

Both hosted checks passed at head 5c014d52e16bf71ca1cb0394c23e25a3a4dae66e in run 41693611027: plan and replay (research/dic3-shift-table-replay). The completed checks were read once; run metadata confirms completed success and the matching head. Hosted replay certifies execution of the registered normal and optimized conformance commands, not a portable runtime improvement, independent scientific acceptance or physical supplier admission. All required local checks and publication preflights also passed. No failed or waived check remains.

Merge Danger

Door: two-way. Blast radius: research. Nine new files in one optional package. Shared code, immutable inputs and the selected frontier are unchanged.