[jeremykothe2]

Summary

Conditional κ = 0.001659319032684569 (conservative 0.001659319029797309). This is +6.04×10⁻⁷ over PR671 (0.001658714981837397). The complex side binds; PR589's bit supplier gives 0.0017334.

Construction, on PR659's no-triangle layered word (sha a9de804f):

1. p6n: six dim-8 cold ends in three pairs, [512,513] at U66_34_16, [311,510] at U72_40 and [522,327] at U66_34_18, each with one dim-6 partner split. Δ{1:+6, 2:+12, 3:−12}, width −6. This is the p123 lane re-chosen so that no end needs a second split on the no-triangle word.
2. Three entrance promotions (as in PR664) on top, using a minimal deterministic recipe that raises only each group's entry gates (36 gate frames). Δ{1:+24, 2:−24, 3:−12, 4:+12}, width −12.

Width 3782 per call. The owner map is at this word's exact packing ceiling (idle 2391 × rank-48). It was found by an exact pattern-flow search in the style of PR660, which releases every defect window class across all calls in one HiGHS solve; it equals the packing relaxation's optimal bound.

Construction drivers: construction/layers_p6n/reproduce_p6n.py (rebuilds p6n 34b683fa from PR659's word, with 95 per-end controls) and a generalised construction/promo/reproduce_promo.py --base p6n (rebuilds a38bb414, with 10 promotion controls). All verifier code is byte-identical to PR659/PR664's reviewed set.

Independent reviews: both SOUND. One reviewer covered the p6n layer and driver: exact replay with 0 bad rows, (N) 21/21, payload 55/72 bits, 95/95 controls plus 165 extra mutants, and a clean clone that reproduces this κ. A second covered the promotions and the committed tree: byte-identical rebuild, 10/10 controls plus its own mutants rejected by both audits, the full 8-step clean rebuild, and its own strict run reproducing this κ.

Verification

From a fresh clone of commit 18649d6, with no reused artifacts (Windows, CPython 3.11.11):

• verify_manifest.py: PASS, 116 files
• reproduce.py, reproduce_notri.py, reproduce_np.py: PR659's word rebuilt
• reproduce_p6n.py: p6n rebuilt; PASS layer-end-controls 95
• reproduce_promo.py --base p6n --k p6n-k3: PASS promo-controls, PASS layer-end-controls, PASS phases
• audit_local.py: PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES
• verify_global.py: PASS invoice, assembly, admission-controls and bit-supplier-controls; PASS_GAUGE44_NATIVE_EXACT_GLOBAL_ASSEMBLY 0.001659319032684569

The rebuilt locals equal the strict locals except two seconds timing fields. Exact commands are in research/gauge44-promo-p6/README.md.

Scope

Conditional on PR645's premises and on PR589's bit-supplier assumptions. No unconditional theorem or Lean certification is claimed.

Credits

• icekylinx (PR645): gauge44 construction, package and verifier.
• chafreaky (PR660): the exact pattern-flow packing approach; jeremydiviney (PR658), jaymosley07 (PR653) and vectorsss (PR638): owner-search methods.
• PR589 lineage (bit supplier); the PR601/604/617/622/627/635 lineage and every upstream contributor credited in PR645.

Prepared with Claude Code (Anthropic).

[Mister-Meeseeks]

The 20-PR pilot triaged 18649d6b37a6865894e0c0775ba4b558e3168877 and is leaving this PR open for focused follow-up.

Remaining maintainer review: Authenticate/replay six new cold ends and minimal promotion recipe; then changed owner/phase/global admission. Reuse unchanged #659/#664 code only with complete source-bound artifact coverage.

This is a bounded-review disposition, not a rejection or a request to repeat unrelated full-suite checks. Pilot record. Your contribution and original attribution remain in the queue ledger.