Conditional κ = 0.001636569158555067: attain PR643 fixed-dispatch packing ceiling

[vectorsss]

Result

Conditional κ = 0.001636569158555067, improving PR643's 0.001636542223442109 by 0.000000026935112958. The conservative model gives 0.001636569155685695.

Thirty-six literal owner rows change. Idle gaps {12:1,32:1,48:2228} become {44:1,48:2228}. Both PR643 supplier words, widths, dispatch (71 JP8 / 1 JP8b), geometry and core admission code are unchanged. The included concavity proof establishes the fixed-dispatch packing ceiling: this map minimizes the idle moment for the fixed suppliers, complete helper roles and capacity limits. It does not bound different suppliers or geometry, nor identify the rounded decimal with the exact moment root.

Evidence

• PR643 pinned at bbfa9fe1d84d5572f4d144c2ee56a3eddc7a83f5; all source manifest pins checked. Its independent full fresh replay passed 58 stages without reuse, with all 46 artifact hashes and 58 stage-log hashes checked.
• The candidate's exact binding, owner admission and 23 mutation controls, finite invoice, both upstream moment engines and 114 assembly controls pass using those actual freshly rebuilt suppliers.
• A separate standard-library checker verifies both native profiles and widths, all 35,424 roles, physical families, windows, nonoverlapping intervals, global rank mass and strict rational moment inequality. Its five corruption controls pass under isolated optimized Python.
• The portable owner exporter reproduces all 36 changed rows and the canonical decompressed owner payload, and rejects four corruptions in normal and isolated optimized Python.
• The final candidate fresh replay passed 58/58 stages without reuse in 327.44 seconds, followed by all supplemental wrapper checks (independent native/owner/moment verification, five owner mutations, declarations, exact owner reproduction with four mutations, and six U4 mutations). All 46 artifact hashes and 58 stage-log hashes were checked. Full candidate/source replay archives and receipts are committed. The executed revision is 15595d482fd0f2fe6baf4d623e0f8e8a6b8047ef; only documentation and its manifest entry changed afterward. No GitHub CI or Linux execution is claimed.

Reproduce

PYTHON=python3 sh research/pr643-improvement-20261013/witness/verify.sh /tmp/pr643-improved-fresh

Python 3.10+, a C++ compiler, Boost headers and a new output directory are required. The package includes the six pinned source dependencies, independent checks, source review, fixed-dispatch proof and deterministic owner exporter. Research assets only; the selected main certificate is unchanged.

Credits and scope

PR643's twin supplier construction and its starting owner map are Jeremy Kothe's (jeremykothe2); prior contributor credits and licenses are preserved. The owner reassignment, independent checks and packaging were prepared by Chi Zhao with substantial OpenAI Codex assistance.

The inherited all-size/compiler, common-label/mutable-source realization, whole-call hosting, precision/tape/exact recovery, analytic-transfer and bit H1–H5 assumptions remain. This is finite conditional evidence, not an unconditional theorem or a complete Lean proof.