[jeremykothe2]

Summary

Conditional κ = 0.001652528731617094 (conservative 0.001652528728737236). This is +1.43×10⁻⁶ over PR648 and +3.05×10⁻⁶ over PR645.

Two changes on PR645's gauge44 construction:

1. Bit supplier: PR589 instead of PR543. PR648 showed that with a well-packed owner map, the gauge44 complex side certifies more than PR543's bit supplier allows (0.0016538), so the bit side was binding. This package cites the merged PR589 tuned bit supplier (c = 0.001733427039589844, reproduced by main's own replay). Its EXPECTED.json is pinned by git blob e293ddc5, byte-identical to main's research/e8-bit-p111-tuned/tune/EXPECTED.json. The bit deficit is now derived from the bit word's parameters, 32·(888−567) = 10272, instead of PR543's hard-coded 9984, with an equality guard. With PR589 the complex side binds again.
2. Owner map: dissolve. Starting from gap-merge packing, a new "dissolve" move empties a bin by spreading its roles into defect gaps under the same window, capacity and one-per-time constraints. This leaves idle mostly in rank-48 bins.

Verifier changes (reviewed): code/assemble.py (load and derive the bit supplier), new code/bit_supplier_controls.py, and a new bit-supplier-controls stage in verify_global.py asserting 12 rejected controls, including a revert to the hard-coded 9984. Reverting the call site to 9984 makes the full chain fail at check_moment. The other 20 Python files are byte-identical to PR645. independent/price_profile.py is ported to PR589.

Review: an independent reviewer judged the composition SOUND (packaging fixes applied). It checked the pinned blob against main, recomputed the deficit, confirmed that no bit constant is left at PR543 values, and re-traced all 12 controls to their intended assertions. It also recomputed κ: 0.001651096360425895 under PR543 (bit binds; equal to PR648) and 0.001651929911890057 under PR589 for the previous map.

Scope: main's ledger records PR589 as supplier-only headroom; composing it into a complex assembly is new here and should be reviewed as such. The retained hosting/, evidence/ and RESULT.json files are PR645's historical, PR543-based evidence; the binding evidence is the SPEC and the fresh replay below.

Verification

Local result (Windows, CPython 3.11.11), from a fresh clone of commit 1b931ee with no reused artifacts: verify_manifest.py PASS (89 files); reproduce.py --until phases rebuilt the local supplier from PR635; verify_global.py on that fresh local passed invoice, assembly, admission-controls and bit-supplier-controls (12 rejected) and printed PASS_GAUGE44_NATIVE_EXACT_GLOBAL_ASSEMBLY 0.001652528731617094.

Reproduce from the repo root at this commit (Python 3.11+, assertions on):

git fetch https://github.com/CrocSwap/integer-mult-bounds.git a6895a69f8ad98ab45777b03e9e6f48888c39f6f
mkdir -p /tmp/gauge44-pr635 && git archive FETCH_HEAD research/complex-571-cold14-st2 | tar -x -C /tmp/gauge44-pr635
python -B research/gauge44-bit589/verify_manifest.py
python -B research/gauge44-bit589/construction/reproduce.py --main . --pr635 /tmp/gauge44-pr635 --out /tmp/gauge44-bit589-local --until phases
python -B research/gauge44-bit589/verify_global.py --main . --local /tmp/gauge44-bit589-local/local --work /tmp/gauge44-bit589-global

Conditional on PR645's premises (all-size compiler, common-label/mutable-source realization, normalized wrappers, whole-call hosting, precision/tape, exact-recovery, analytic transfer) and on PR589's bit-supplier assumptions in place of PR543's. No unconditional theorem or Lean certification is claimed.

Credits

• icekylinx (PR645): the gauge44 construction, package and verifier.
• eumemic and the PR589 authors: the tuned bit supplier. BitCap's earlier PR589 composition study supplied the derived-deficit checks and controls.
• vectorsss / Chi Zhao (PR638): relocate_two, generalised by our gap-merge; the dissolve move is new here.
• The PR635 lineage and every contributor credited in PR645.

Prepared with Claude Code (Anthropic).

[Mister-Meeseeks]

Thank you @jeremykothe2. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: Tuned PR589 bit supplier and dissolved Gauge44 owners.

Review and limits: Bit deficit is derived from the new supplier parameters with rejection controls. The bit circuit is cited rather than freshly reconstructed by this package.

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: 1b931ee055d738753778e1051300140c16ae219d. Publication: 64039f1bd3b6a523b96083fd858ad040a75e3030.