[petalas]

Summary

The complete PR1212 P112 primary replay takes 32.78% less median wall time locally, from 14.881683875 s to 10.003980833 s. The complete P120 command improves by 26.16%. The claim type is a scoped implementation-equivalence proof with exact finite conformance and local performance evidence. No new decoder theorem or kappa is claimed.

 RUP propagation, same clauses and queue
- call value(l), take abs(l), multiply by its sign
+ read the signed-literal table directly

The adapter, equivalence argument, conformance checks and measurements were produced by Nick Petalas. Credit Brett Halligan / burntout76's PR1212, exact head 57099cb5684f38877f31d149d598801671a633db, for the original verifier, mathematical results, proof data and controls. Its DreamingOfClouds, themilkman216, GamingPuzzled, Mihir Srivastava and woklerx decoder lineage is retained. Classical signed arrays and RUP are existing methods; P108/P110 successors and PR4360 already offer distinct watched-literal checkers.

Evidence

Before, the complete P112 profile makes 205,432,164 calls to the value helper. After, the exact same propagation trace uses direct indexed values. The ternary table adds at most 32,256 list-slot bytes on the measured 64-bit interpreter.

Five alternating fresh-process runs per side and unit have zero errors, identical complete stdout and certificate objects, and disjoint timing ranges. P112 ranges are 14.2584 to 15.3644 s before and 9.5808 to 10.3723 s after; P120 ranges are 6.6521 to 7.0884 s before and 4.7748 to 5.0615 s after. BENCHMARK.json is generated and source-hash bound. All 61/41 retained check lines, all eight proof files across the pair, geometry, rational calculations and existing rejection controls remain covered.

Local checks passed on CPython 3.12.15, macOS 27.0.1 arm64:

• All 12,030 finite signed-literal reads, 9,282 actual original/transformed parser/decision/count cases and 11 admission controls.
• All four registered warning-strict normal/optimized and complete P112/P120 equivalence commands. Separate measured times are 0.100 s, 0.114 s, 24.500 s and 11.582 s.
• The complete package runner, committed-byte/source-history preflight, official 19-file export integrity with all nine declared inputs, and read-only Git-free exported optimized controls plus complete P112 equivalence replay.

Exact reproduction from the repository root, with an existing external scratch directory:

export TMPDIR=/absolute/path/to/existing/scratch
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/rank8-rup-signed-values
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/rank8-rup-signed-values/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -B research/rank8-rup-signed-values/adapter.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -B research/rank8-rup-signed-values/adapter.py --live P120
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/rank8-rup-signed-values/benchmark.py --output-dir "$TMPDIR/new-benchmark"
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/rank8-rup-signed-values --check-source-history

Expected PASS_RANK8_RUP_SIGNED_VALUES and PASS_REGISTERED_RESEARCH_PACKAGE; the adapter preserves PASS_COMPLEX_RANK8_DECODER_RIGIDITY. Another CPython 3.12 path may replace the absolute local interpreter. The benchmark output directory must be new.

Limitations

These are local timing measurements, not host-independent guarantees or scientific supplier admission. The representation argument proves behavior equivalence under the predecessor's legal input contract; its decoder mathematics is cited, not claimed as independently audited. Shared/default code, frozen evidence and the selected frontier are unchanged. Default adoption, complete Linux workflow timing, selected cold replay, physical/native/compiler/precision/analytic admission, Lean and Docker remain unrun. All five selected framework assumptions remain. Independent human and formal proof-kernel review are unclaimed.

Open next questions

Should an explicit successor adopt the signed table by default? First preserve its source binding and measure the complete workflow on Linux. This opt-in package does not supply default adoption or a wider workflow bill.

Related open work

• PR3040 extends rank-eight E8 rigidity to arbitrary deletions of at most eight lines. It changes the mathematical domain; this contribution changes only PR1212's fixed replay representation.

• PR2832 studies general masked decoder costs and named conjectures. This contribution provides no new decoder floor and does not settle its open mathematical questions.

• PR6579 determines a root-low E8 reader-basis tariff. It concerns a different correction space and does not change this RUP replay or compute the timing quantity reported here.

• PR6599 improves PR3806's chirp-residue replay. Its input, states, checks and timing workload differ from this fixed PR1212 RUP replay; no performance numbers are compared.

• PR6589 improves PR5624's alternating-plane spectral replay. It changes a different kernel on a different fixture and does not compute this RUP timing quantity.

Completion refresh inspected all thirteen account open PRs created since the advance CLAIM at 2026-11-03T11:07:01Z, including this PR. None of the other twelve studies this fixed PR1212 RUP workload or reports its timing quantity. No additional mathematical computations checked those contributions, and no same-instance numerical disagreement was identified.

The live source/rigidity/RUP searches, current handoffs, new submissions and local reservations were checked before commit. Sparse notes, arbitrary diffs and unpublished work remain coverage limits. The advance claim is #1166 (comment).

CI notes

Both hosted checks passed at exact head d562956726caa39ff588c6595ba16cae7391c07a in run 41626177567: plan in 4m35s and replay (research/rank8-rup-signed-values) in 5m10s. The completed check list was read once with gh pr checks; separate run metadata confirms completed success and the matching head.

All four registered local commands, complete package replay, exact committed-byte/source-history checks and standalone export checks also passed. Hosted replay certifies execution of the registered checks and source validation in its environment. It does not certify the local speedup percentage, independent mathematical acceptance of the predecessor, or discharge of the five selected framework assumptions. No CI failure remains. Independent human and formal proof-kernel review are unclaimed.

Merge danger

Door: two-way.

Blast radius: isolated.

Ten new package files. The adapter is opt-in, authenticates its nine live inputs and refuses source changes. No shared verifier, predecessor credit or selected-frontier file is edited.