[petalas]

Summary

Finite exact circuit certificate and scoped substitution proof, produced by Nick Petalas. A new chart-127 circuit for selected PR6030 saves 119 events and 2,510 units of the retained scalar allowance.

- local events 2970; scalar allowance 25988
+ local events 2851; scalar allowance 23478
- complete word: 22803 events; scalar allowance 189428
+ complete word: 22684 events; scalar allowance 186918

The interval is [17461,20431), disjoint from CubeJerry's first-prefix construction in #6116. Every permutation and scale is charged. Full arbitrary-entry matrix equality, existing storage and the ordered non-scalar events are preserved. This is a local circuit result, with no new kappa, supplier admission or selected-frontier update.

Package and scoped proof. Credit CubeJerry #6116 for the whole-block synthesis approach and second-block question, DreamingOfClouds #6030/#5907, Ali Romman's retained word/checker lineage, Matarener #5975, Mason Hale #5811 and all retained P104/native/compiler contributors. Classical row sharing and elimination are credited as such.

The advance claim initially named [17461,22795) as one chart-127 suffix. The scope update records the intervening chart-245 ADD and the narrower delivered block. That boundary is preserved. The first improving candidate was frozen; no other blocks or pivot orders were searched.

Evidence

• A separate integer-row engine checks all 297,025 coefficients of the 545-by-545 local matrices, including role 758, which the new circuit leaves untouched. Both exact local intermediate row-l1 maxima are 67.
• The source-authenticated complete-word interpreter checks the new circuit's full 799-row endpoint, chronological frames, 770 public inputs, 29 owned fields, 31 owned lifetimes and peak 13 owned fields. The recursive paid and productive target profiles are unchanged.
• Eleven negative controls, the hand-computed two-role positive fixture and inverse-block equality pass.
• Both warning-strict registered commands passed locally on CPython 3.12.15/macOS arm64, in 0.99 and 1.02 seconds, below their individual 180-second caps. These are timeout measurements, not performance comparisons.
• Package metadata/replay, exact committed-byte/full-source-history preflight and official nine-file export integrity pass. Normal and optimized Git-free replays with empty PATH and files marked read-only pass; all ten exported files, including the export manifest, retain identical hashes.

Reproduce from the repository root:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/p104-chart127-suffix/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -O -B research/p104-chart127-suffix/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/p104-chart127-suffix
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/p104-chart127-suffix --check-source-history

An equivalent CPython 3.12 installation can replace the local path; only its standard library is needed. Expected direct output is PASS_P104_CHART127_SUFFIX events=2970->2851 allowance=25988->23478 matrix=545x545 full_word=22684 controls=11. Add --receipt /absolute/external/path/result.json or --emit-word /absolute/external/path/WORD.json to generate hash-bound evidence or the complete candidate outside the checkout. Default checks write nothing.

Scientific base: canonical main 721c03822c421b7f7fcbb2598993b947c4d88419, priority revision 8. Both live inputs are pinned main-tree files. Pending #6116 is cited context; no pending executable or unmerged Git-history dependency is required. No predecessor scientific replay was run as an audit deliverable.

Limitations

The signed recursive moment is unchanged. Complete native, physical-caller, compiler, rounded precision, stock, tape and outer cold replays were not run. No optimality or measured runtime gain is claimed. All five framework assumptions remain. Independent human and formal proof-kernel review are unclaimed. No combined circuit containing #6116's prefix is claimed or tested.

Open next questions

• Combine the disjoint replacements here and in Resynthesize P104 scalar prefix: 3,577 fewer events (No new κ) #6116 in one source-bound word, then complete native/caller/precision integration. Pending independent review and that full replay remain blockers.
• Specify a changed paid/helper trajectory that uses the smaller ordinary allowance, with arbitrary-dirty restoration and a complete signed invoice. No such construction is supplied here.

Related open work

• Resynthesize P104 scalar prefix: 3,577 fewer events (No new κ) #6116 constructs a cheaper first scalar prefix and poses the disjoint-block question answered here; this circuit changes a different matrix and does not assume its pending code.

• Bind the merged gate-table zero_state to the selected PR6030 primary replay: 2.4x normal, 1.5x -O, identical RESULT.json (no new κ) #6112 speeds selected PR6030 native replay; this contribution changes an ordinary scalar circuit and makes no replay-runtime comparison.

• Audit #6030's deferred layer and current BIT stock #6115 studies the selected deferred-layer and BIT-stock transfer; those costs and theorem obligations are unchanged here.

• Bind PR6030's remaining 30 strict and 4 functional outer checks to written sources; stopped-recursion theorem's 1−c term has no row (no new κ) #6110 binds selected outer predicates to written sources; no outer predicate changes here.

• Bind PR6030 uniform compiler and nine outer rows to written theorems; j=47005 is first passing grid point (no new κ) #6109 binds the selected compiler and outer ledger; this local circuit does not discharge that compiler contract.

• P104 leak corrections: third-engine check of #6067/#6069 on PR6030, and a scalar-level witness on PR5907 (no new κ) #6108 studies carrier corrections and a distinct PR5907 scalar witness; this replacement preserves the PR6030 endpoint and paid/helper paths.

• P104: exclude two non-carrier ADDs across helper572’s chart seam (no new kappa) #6088 studies two non-carrier corrections at helper572's earlier chart seam; the present interval starts later and changes no helper capture.

• Exclude helper469 rung removal by invertible receiver endpoint recoding #6084 studies receiver recoding for helper469's frame593 rung; this circuit removes no rung and changes no transport.

• P104: certify fixed-word carrier and endpoint exclusions (no new κ) #6069 studies fixed-word carrier and endpoint exclusions; this circuit preserves every whole-block endpoint and recursive interface.

• Exclude combination-carrier correction programs on the selected P104 word (no new κ) #6067 studies combination-carrier corrections on the selected word; this circuit changes only a same-chart scalar realization.

• No inserted carrier correction legalizes a PR5718-shape leak class on the PR6030 P104 word (no new κ) #6045 studies inserted carrier corrections; no such insertion or changed helper target occurs here.

• Corroborating audit of PR6030: fresh full dense replay, itinerary delta, invoice and crossing (no new κ) #6043 audits the original PR6030 word; this package constructs a distinct scalar substitute and does not repeat that audit.

• Prove source gauges cannot help before the third use (no new κ) #6130 proves a restored source-gauge threshold in ADD-once bipartite shears under a scalar-allowance tariff. This contribution instead changes the full arithmetic circuit of one PR6030 matrix; its 2,510-unit saving is not an optimum for that restricted gauge model.

The completion refresh inspected all twelve other open account PRs created since the CLAIM: #6123, #6124, #6125, #6126, #6127, #6128, #6129, #6130, #6131, #6132, #6134 and #6135. They concern centre kernels, samplers, leaf laws, Gaussian bounds, Walsh error, source gauges, ADDRESS characters, random queries and verifier serialization. The adjacent scalar-allowance result #6130 is distinguished above. None reports a competing value for this chart-127 interval or its replacement circuit. No additional mathematical computation was run to compare them.

No competing numerical quantity from these PRs was recomputed for comparison. Live claims/open bodies, exact main-tree terms and merged PR searches were refreshed before commit; sparse local and arbitrary historical-diff coverage remains incomplete.

CI notes

Uncertified by CI at contribution commit 804d25e8a868354134b6e3dc635356a3a0dbf064. In run 40694190103, plan failed in Onboarding helper tests and replay was skipped. The package replay did not run in CI. This hosted run certified none of the package's scientific checks. All registered commands and publication/export checks passed locally, as reported above.

The failure is inherited from main 721c03822c421b7f7fcbb2598993b947c4d88419, the PR6030 kappa-admission commit pushed with [skip ci]. The selected record changed without matching the documentation format/navigation expected by these two tests:

• test_research_current_status.CurrentStatusTests.test_current_section_matches_selected_record expects the exact marker **0.003125804** in docs/research/current-status.md. The document instead bolds the longer expression 0.003125804 = 781451/250000000, so that substring is absent.
• test_research_current_status.CurrentCiNavigationTests.test_current_ci_section_matches_selected_record expects make frontier6030-verify in the CI navigation document. The test source reads docs/ci-verification.md, which still describes PR5599 and make frontier5599-verify. This is the actual checked path; there is no docs/ci.md at the pinned base.

The failed-job log reports 678 tests, two failures and 23 skips. PR #6120's run 40691776027 has the same two failure names and expected-marker failures, confirmed from its log. Incidental negative-fixture diagnostics are not additional test failures. This package changes neither failing document nor the selected record and did not cause either failure.

A maintainer re-run is required after main is fixed. The checks were read once at completion. No branch push, main-documentation change or CI re-run was performed for this blocker. Local passing evidence remains separate from the missing hosted certification.

Merge danger

Door: two-way. Blast radius: package. Seven files are added in one scoped directory. Shared code, predecessor packages, frozen evidence and the selected frontier are unchanged.