Conditional κ = 0.001654192296855146: joint three- and four-call owners on PR656

[jeremydiviney]

This improves pinned #656 from κ = 0.001654108529511355 to κ = 0.001654192296855146, a 0.0050642% gain, by reassigning whole-helper owners across three and four calls together. The conservative witness is 0.001654192293959223.

The contribution is research/layered-joint-owners/: a standalone delta against #656, with frozen owners, reproducible search, solver-free owner audits, exact arithmetic, proof, source pins, and archived replay evidence. No existing repository files change. All 27 inherited Python files and every construction input remain byte-identical when staged; only the parent PLAN owner/profile bookkeeping, OWNERS, and frozen SPEC change.

What changes

• Generalizes jaymosley07's Conditional κ = 0.001652704716932828: joint-call owners beyond PR649 #653 two-call integer nomination model to several calls. From Conditional κ = 0.001654108529511355: joint two-call owner map on the PR655 gauge44-layered word #656, 180 three-call groups accepted eight strict improvements; 120 four-call groups accepted four more. A bounded five-call follow-up accepted none; no neighborhood or global optimality is claimed.
• The final idle distribution is {1:1, 3:1, 28:1, 32:2, 48:2398}. Its integer stop-loss certificate strictly majorizes Conditional κ = 0.001654108529511355: joint two-call owner map on the PR655 gauge44-layered word #656 at the same total rank. Both solver-free auditors check all 35,424 roles, literal footprints and profile accounting; the independent auditor re-derives controller windows and actual 73-column charts from fresh baseline evidence.
• Adds a fixed-provider relaxed packing ceiling: with these exact local costs and capacities, every owner map has κ below 0.001654249113130438 (exact fraction and certified root bracket supplied). This follows by relaxing to 2,400 dimension-48 idle remainders. Feasibility of that ideal packing is not asserted. The ceiling does not constrain different circuits or integer multiplication generally.

Validation

On Linux, CPython 3.12.3, low CPU/I/O priority:

• Complete default replay from fresh outputs, no reused local/global artifacts: PASS, 199.427 seconds across 11 driver stages.
• Rebuilt the retained scalar word and all layers; 30 pivot-swap and 59 layer-end mutations rejected; native ledgers, wrappers, exact phases and independent scalar audit passed.
• Strict baseline Conditional κ = 0.001654108529511355: joint two-call owner map on the PR655 gauge44-layered word #656 replay and independent owner audit passed; nine additional owner mutations rejected.
• New global controller, finite invoice, two exact moment engines and outer assembly passed, including 15 controller, 69 admission and 12 bit-supplier controls.
• Independent profile price and exact relaxed-ceiling check passed; final packaged incremental replay also passed.
• git diff --check passed. Earlier make verify on the identical unchanged main base 17ce0c79 passed all 18 groups, including gen4-bank-verify, and 84 isolated test modules. That earlier run is explicitly distinguished from this addition's fresh replay; its receipt/log are retained.

README.md has immutable fetch pins and the single replay command. VALIDATION.json and evidence/ contain source identities, 24 selected artifacts and all 43 fresh replay logs. Verification needs only the Python standard library; NumPy/SciPy are optional discovery dependencies. Historical #645 evidence retained inside #656 is not treated as current owner/local evidence.

Scope and credit

This is a conditional finite witness under the retained compiler, common-label/mutable-source, whole-call hosting, precision/tape, exact-recovery, analytic-transfer and bit H1–H5 interfaces. #589's bit circuit is cited unchanged and its full profile/surcharge freshly priced; it is not rebuilt here. No unconditional multiplication theorem or complete Lean proof is claimed.

Prepared by Jeremy Diviney with substantial OpenAI Codex assistance. Credits retained: Jay Mosley / jaymosley07 (#653) for the two-call model, auditors and staging pattern; jeremykothe2 (#655/#656, Claude Code) for the layered provider and seed map; icekylinx (#645, GPT-6 Astra/Codex) for Gauge44; the #601/#604/#617/#627/#635/#637 end-construction lineage including DreamingOfClouds, jeremydiviney and CarrierBypass; vectorsss / Chi Zhao (#638) for earlier packing work; and DreamingOfClouds (#589) with its eumemic/Claude lineage for the bit supplier. Pinned source notices and Apache-2.0 licensing remain in force.

[Mister-Meeseeks]

Thank you @jeremydiviney. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: Joint three- and four-call owner improvement.

Review and limits: Strict integer stop-loss comparison and literal maps support the gain. Failed five-call exploration is bounded evidence, not optimality.

The complete original source, notices and relevant execution evidence are retained through the pinned source archive. The review distinguishes fresh local runs, source-bound historical Linux CI and prior exact-head review; it does not claim 100 fresh full mathematical audits. Closing this historical PR as reconciled. This preserves parallel and cumulative credit without replacing the selected frontier or promoting priced research targets to completed constructions.

Reviewed head: a1f15d0c78e1ca44d3414d184e57637b36c6822d. Publication: b3c9e5c269fcfb25dfb4eda4ebc419c052d4c93d.