Verified T16 packing gain with OR-Tools: conditional κ = 0.001673618490895016

[Gonzalo-Mier]

Change and mathematical scope

Adds a strict-replayed owner map for the unchanged selected PR1094 T16 word and suppliers. Exact conditional κ is 0.001673618490895016, an increase of 4.285169321e-9 (0.0002560428% relative) over the immediately preceding map. This is a packing improvement only; it changes no word, supplier, coverage law, template, outer guard, or mechanism. The finite CP-SAT search is not an optimum proof and does not establish a complete multiplication theorem.

The fixed-word ceiling from ceiling.ceiling() is a_hi = 0.001690054109089, hence κ < 0.001687202645325402…; this map realizes 99.194871% of that ceiling. The independent exact packing certificate gives Σ f ln(f) ≤ 908,139.013 and at most 4,887 empty capacity-48 bins; the candidate has 4,880. These packing bounds are not κ bounds.

Task and overlap

Task selected-packing, scope unchanged; base commit 463113d675af7410ac91d53a4fed51ec6494eb9a. The package pins all live source inputs and retains predecessor attribution. A live overlap refresh on 2026-10-17 21:23 UTC returned 350 open PRs and 321 discussion records; none matched this T16 multi-row owner-packing improvement. Discussion #1332 / closed PR #1343 exhaustively censused single whole-helper relocations and explicitly excluded multi-row repacking. Discussion #1265 / closed PR #1276 bounded within-group idle rank-48 repartitions, with a scoped κ ceiling of 0.001673151843213755 and no admitted gain; this candidate reaches 0.001673618490895016 through a broader owner-map repack. Discussion #1339 / PR #1387 priced an idle-axis optimum whose overlay failed actual stream composition. Open PR #1807 certifies selected owner-row bindings, while PR #3209 changes T16 audit parsing; neither changes the packing. These comparisons support the scoped distinction and do not claim global novelty.

Validation

• python3.12 scripts/research_package.py --package research/complex-t16-evacuation-increment --check-only
• python3.12 scripts/research_package.py --package research/complex-t16-evacuation-increment
• python3.12 scripts/check_research_commit.py --package research/complex-t16-evacuation-increment

The package replay reconstructs the 163-row delta, regenerates the owner data semantically, runs the unchanged 11-stage strict T16 replay (including recomputed 10,008 chart count and controls 69/12/6/15), the independent seed67 audit and 11 controls, pinned exact pricing of both suppliers, the PR1069 sweep, ceiling.ceiling(), and the exact-integer packing-ceiling check. All pass. The winning OR-Tools 9.11.4210 evacuation solve was FEASIBLE (objective 10,463,952; bound 10,540,812); later bounded neighborhoods did not improve exact κ.

Credit

The selected PR1094 supplier and predecessor packing, strict replay, seed67 auditor, pinned pricing engines, and ceiling proof retain their original authors and notices. This incremental map and package were prepared by OpenAI Codex at the user's direction with substantial AI assistance. No independent human review is claimed.

Open next questions

See the package's structured questions: use exact supplier marginal costs to guide adaptive CP-SAT neighbourhoods, and tighten or approach the remaining fixed-word κ ceiling. The smallest next step is to test a stable scaled marginal objective on bounded neighborhoods and exact-replay every accepted map.