[petalas]

Summary

Reduce the complete pinned PR1443 D8 replay's local median wall time by 27.09%, from 30.78 ms to 22.44 ms. All fifteen alternating fresh-process pairs improve, with identical scientific stdout and zero failures. The absolute saving is about 8.34 ms per invocation on this host.

Claim type: scoped implementation-equivalence proof, exact finite conformance and local performance evidence. The eight-call mathematical minimum remains woklerx's result. The new adapter, proof and checks were produced by Nick Petalas. No new mathematical minimum, kappa or selected-frontier change.

original source checks and complete radius-four search
  replace step(state, generator) with packed two-column arithmetic
  retain original balls, witnesses, independent products and certificate

The opt-in package authenticates every live source input and replaces only the transition function in the fixed original program. Original source files and notices remain unchanged. Credit woklerx / PR1443 and its retained Ali Romman, eumemic / PR288 and Gareth Davidson / PR1333 lineage. Advance CLAIM.

Evidence

• Before: four allocated coefficient cells and nested Python row/column loops on every transition. After: two byte-table lookups and a packed scatter, with the same complete scientific calculation. Separate profiles identify the transition as the main replay cost.
• Exact conformance passes 1,572,864 column comparisons, all 67,800 outgoing transitions from the 5,650-state ball union, both complete first-witness maps, full certificate equality and eleven controls. The written argument covers every 32-bit state; the finite checks do not enumerate that entire state domain.
• Normal and optimized direct conformance pass. All three registered commands pass locally, taking 0.023 s, 1.56 s and 1.58 s. Metadata/pins, thirteen-file committed-byte/mode/source-history preflight, official export integrity and source compilation/function bounds pass.
• All three direct commands also pass in a read-only Git-free export with empty PATH. All fourteen exported files remain unchanged, and normal/optimized receipts agree.
• BENCHMARK.json retains all fifteen timing pairs, environment, flags, exact source hashes and output hash. Original range 29.79 to 32.13 ms; packed range 21.61 to 23.19 ms. Startup, table creation, source checks, scientific checks and certificate comparison are inside each fresh-process timing. The shared macOS arm64 host uses CPython 3.12.15. This local percentage is not a hosted performance claim.

Reproduce from the repository root with the exact local interpreter or another CPython 3.12 installation:

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

Expected markers are PASS_DIHEDRAL_COMMUTATOR, PASS_DIHEDRAL_PACKED_REPLAY, PASS_REGISTERED_RESEARCH_PACKAGE and PASS_RESEARCH_COMMIT_BYTES. Optional timing reproduction uses the same interpreter with research/dihedral-packed-replay/benchmark.py --pairs 15 --out /path/to/new/benchmark.json. The output must not exist.

Canonical main was refreshed before commitment and remained 7c49fe32c55de02c2c873655c804b16e4c3fef0a, priority revision 8, selected PR6030. Live claims, local reservations, open/recent-account PRs, distinctive main-tree searches and merged D8/UT3 runtime searches were checked. The offline helper searched a complete 438-open-PR snapshot and 6,420 Discussion records, with sparse-local and unavailable PR-file-map limits. No matching adapter was found within that coverage; unpublished work and arbitrary historical diffs remain outside it.

Limitations

The gain concerns one short historical replay and is small in absolute time. Shared-host scheduling and filesystem-cache effects remain possible. The transition-equivalence argument is written mathematics, outside a proof kernel. The predecessor theorem is cited context and is not this contribution's review deliverable.

Native implementation, physical caller, complete supplier/outer invoice, compiler closure, tape/precision and analytic obligations remain unprovided. The five selected framework assumptions remain. No selected scientific cold replay, Lean or Docker run was performed. Independent human and formal proof-kernel review are unclaimed.

Open next questions

Can a complete column-transition table repay initialization and memory costs on a genuinely larger complete replay? First pin that fixture and measure all construction/storage/full-process costs alongside exact conformance. No larger fixture, table implementation or follow-on gain is supplied or reserved here.

Related open work

• No open PR found studying this exact D8 replay or its transition runtime. PR1443 is the retained predecessor. Its larger-register question has known successors, and this package does not target that mathematical question.
• PR6479 optimizes the current P104 native replay, a different source and workload; no runtime number for that workload is computed here.
• PR6486 optimizes the complete dirty-phase replay, a different source and workload; no runtime number for that workload is computed here.

The completion refresh inspected twelve account open PRs created since the advance CLAIM, including this PR. None of the eleven others studies this exact D8 fixture or its transition runtime. The adjacent dirty-phase replay is listed above and uses a different source and timing workload. No additional scientific computations were run to compare another contribution.

CI notes

Both hosted checks passed at exact head 65627ec93ffb78390bb845516f6deccf87993c76 in run 41556103283: plan in 4m17s and replay (research/dihedral-packed-replay) in 1m46s. The completed checks were read once; run metadata confirms completed success and the matching head.

All three registered commands, direct conformance, committed-byte/mode/source-history and read-only Git-free export checks also passed locally. No required check was left solely to CI. Hosted replay exercises exact conformance, source binding and the complete retained scientific calculation. It does not remeasure the local 27.09% timing reduction or independently accept the written proof. Independent human and formal proof-kernel review remain unclaimed.

Merge Danger

Door: two-way. Blast radius: isolated. Nine new files in one opt-in package; no shared code, predecessor files or selected record change.