Research: four helper placements improve selected T16 kappa

[lydakis]

Four whole-helper placements improve the currently selected PR1094 T16 packing from conditional κ = 0.001672660197076918 to 0.001672664045494084 (+0.000230077643548%). The local R480 supplier, widths, 144-call order, physical stock and bit supplier are unchanged.

A two-move vacancy path exposes an eight-slot suffix; two width-four helpers from distinct calls fill it. The complete profile changes by H7 - 2 H3 - H1 < 0 for every Hr = r^p, 0 < p < 1. Only four of 69,120 owner rows change. MOVES.json gives every before/after row, and build.py reconstructs the data and bindings without an optimizer.

Validation:

• The unchanged strict T16 verifier passes all 11 stages, including fresh controller emission, audit and finite invoice; 69 admission, 12 bit, 15 controller and six independent owner rejection controls pass.
• Both exact moment engines and 47 strict outer inequalities per native/conservative assembly pass. The complete published wrapper also passes locally on CPython 3.14.8; registered Python 3.12 CI is declared.
• All 278 external inputs are pinned and declared for CI invalidation. Frozen predecessors are unchanged. Native local ancestry is source-bound reuse, not a new cold rebuild. Package metadata and diff checks pass.

This is an improvement to the selected PR1094 benchmark, not the best known packing of that supplier. PR1407 already reports κ = 0.001672680818492982 for the same unchanged supplier; this PR provides a compact four-row alternative. The two patches overlap at owner rows2010 and34306 and affected bins, so they cannot be composed as written. PR1154, PR1992 and PR2044 also report higher values for changed suppliers or transfer assumptions. All inherited all-size/compiler, realization, hosting, precision/tape, recovery, analytic and bit H1-H5 assumptions remain; no unconditional theorem or global packing optimum is claimed. The selected certificate is not edited.

philippeVV's independent review, with disclosed Claude assistance, reports full CPython3.12 strict/registered replay and metadata-check passes, plus a separate seed67 owner audit with eleven rejection controls and no blocking finding. The package now explicitly states that offsets reserve static disjoint prefix slices; their order need not match the unchanged call chronology.

Reproduce from a complete checkout:

python3 -I -B research/complex-t16-vacancy-chain/verify.py --work /absolute/fresh/output
python3 scripts/research_package.py --package research/complex-t16-vacancy-chain --check-only

Prepared for George Lydakis with substantial OpenAI Codex assistance and coordination with Ody. Predecessor attribution and exact source lineage are retained in the package. Fresh overlap search covered 347 open PRs and 723 discussion records with complete pagination; this is not a novelty certificate.

[philippeVV]

Independent replay of head 62761d91 on CPython 3.12.

Replay. verify.py passes all 11 strict stages and prints PASS_GAUGE44_T16_STRICT_GLOBAL_REPLAY 0.001672664045494084 and PASS_FOUR_HELPER_VACANCY_CHAIN. The registered package command passes too, as does --check-only in a clean worktree.

Independent checks. None of these import the PR's code.

• Josie Elliston's seed67 owner auditor (R1–R7, with X1 rebuilt from the event stream, and X2) accepts both the selected map and the PR map. All 11 mutation controls reject.
• Exactly 4 of 69,120 rows change: 2010, 4474, 34306 and 46308. Call, time, helper and width are unchanged in each, and each new placement sits strictly inside its owner window. No helper is reused within a call.
• Idle goes from {1:2276,3:377,7:7,48:4866} to {1:2275,3:375,7:8,48:4866}. Rank mass (1,041,408) and deficit (5,120) are unchanged. Prefix (397, charged at 512) and physical stock (14,826) are unchanged, so nothing is double-counted.
• The Independent verification: code-disjoint pricing of all 16 pending kappa claims; every one has deficit W - 64N (no new kappa) #1069 pricing sweep passes every flag.
• Re-pricing with the pinned multicold engines gives native κ = 0.001672664045494084 and conservative κ = 0.001672664042642178. That is +2.30e-6 relative over PR1094, below the PR1240 local-word ceiling.

Two non-blocking notes.

1. Please cite Conditional T16 κ gain through neutral whole-helper hosting paths #1407. It claims a higher κ (0.001672680818492982) on the same PR1094 supplier and changes rows 2010 and 34306 and bins (0,0,102), (11,8,103) and (13,15,14). The two PRs therefore do not compose as written, and maintainers will need to choose between them or merge them.
2. This is the first packing whose offsets inside a bin are not in time order (3 of 27,390 bins). Every checker treats slices as a static disjoint prefix, so this is admitted, but a sentence in PROOF.md saying so would help reviewers.

(Review prepared with substantial Claude (Anthropic) assistance; the checker script is available on request.)

[lydakis]

CI note for head 40771210: run 38629312138 fails in the skip-clones producer and certificate tests with Pinned inherited source changed: scripts/exclusion_circuit.py.

The script and research/skip-clones/SOURCE.json are byte-identical in the run's base 0fdd7d82 and tested merge 587ab8f7. The manifest expects b253f9d7…; the current script hashes to f9fbcd6e…. This mismatch is inherited from the base.

The two upstream support-mask rewrites passed 6,940 focused comparisons against the historical predicates: 1,735 forward and 5,205 reverse. These checks do not replace the full clone replay.

A one-hash refresh is insufficient because the certificate also binds the SOURCE.json digest. If maintainers choose to adopt the current dependency, the proposed repair is to retain the old/new provenance, update only the reviewed dependency pin, regenerate the certificate through the unchanged witness, run make skip-clones-verify, and audit downstream pins. Preserving the historical dependency/replay is the alternative policy choice. Full replay and downstream validation for this repair remain pending; no pins, guards or PR code have been changed.