Conditional κ = 0.001675809683500501: source-holder fusions and X54 on #1193's mixed T37 construction (independent; equals #1218)

[GamingPuzzled]

This is 1675809683500501/10^18. It is +1.36988e-7 over #1193 (0.001675672695827067, the best fully admitted open value at submission). It is also +4.19206e-8 over #1201's draft nomination (0.00167576776285696, not yet admitted). The complex side binds, and the PR589 bit supplier is unchanged.

Concurrent identical result. Rohan Arun's #1218 reports the same κ, 0.001675809683500501, from the same composition. This package was built independently, with its own three-way word merge, literal recipes, 28 composition controls and fresh full cold replay. It is submitted as an independent construction and check, not a new record.

Composition. Jeremy Diviney's #1193 mixes two providers: 125 calls of #1148's joint-entrance word D3 and 208 calls of its group-627 variant D4. Both providers additionally receive two width-neutral local changes:

• Marius-Paul Dumitrean's Conditional κ = 0.001675658002271934: two source-holder fusions on #1148's joint-entrance k8 word #1195 two source-holder fusions at X=439 and X=444, with their refitted frames;
• Jeremy Kothe's Conditional κ = 0.001673006105142741: eighth triangle slot X54, rank-seven helper ends and T16 owner packing on the eight-slot k8 word #1130 X54/E589 slot, using the recipe Rohan Arun rebased in Conditional κ = 0.001675161536733127: X54 slot on #1148's three-demotion k8 word with its T16 owners #1178.

What stays and what changes

• No entrance, end, port or centre interface changes, so the helper widths stay the same. Conditional κ = 0.001675809683500501: mixed T37 allocation with X54 and fusions #1193's integer flow, its 159,840 literal owners, the call order and the dispatch are reused unchanged. Idle stays {1:2,48:11374}.
• Relative to Conditional κ = 0.001675560947524449: joint k8 entrances, rank-seven ends, and T16 hosting #1148's joint word, the fusion, X54 and group-627 edits touch disjoint ranges of A and B. Cleanup and early cleanup are merged semantically (discovery/compose.py). The verifier builds both words from frozen literal-diff recipes that check every removed element.
• Profiles:
  • D3' = {1:2358,2:504,3:410,4:130,5:82,8:8};
  • D4' = {1:2350,2:512,3:414,4:126,5:82,8:8};
  • complete: {1:783552,2:169496,3:137362,4:42458,5:27306,8:2664,48:11374}.

Verification (package research/mixed-fusions-x54-t37/, #1193's verifier plus two additions: it builds both words, and it runs the composition controls):

OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 python -B research/mixed-fusions-x54-t37/verify.py --work /new/dir
# PASS_MIXED_FUSIONS_X54_T37_COMPLETE_ADMISSION 0.001675809683500501

• Local, both new words: exact independent audit_local and the fresh PR635 native chain, including every phase edge.
• Controls: Conditional κ = 0.001675809683500501: mixed T37 allocation with X54 and fusions #1193's 11 entrance controls. There are also 28 new composition controls: each inserted fusion or X54 gate is dropped in turn from each word, and the exact audit rejects every mutant.
• Owners: frozen owner reconstruction, 8 flow controls, the independent owner audit and the parent check.
• Strict admission: controller audit with 23 mutations, full invoice (prefix 775 < 1024, row 17,495 < 20,161), 114 admission and 12 bit controls, both exact engines and all 47 outer inequalities.
• Ancestry: cold PR589/741/799 ancestry replay.
• The whole run passed from a fresh git archive of the commit (macOS arm64, Python 3.11). Receipts are in evidence/.

data/SPEC.json was re-frozen through the discovery → freeze protocol. Against #1193's SPEC, only the global profile, κ and the complex-root fields differ. data/PLAN.json.gz changes only in the provider identities and the profile.

Package and merge order: only research/mixed-fusions-x54-t37/ is added, on top of #1193's branch; #1193's own package is untouched. Please merge after, or together with, #1193.

Credits

• Jeremy Diviney (jeremydiviney) for Conditional κ = 0.001675809683500501: mixed T37 allocation with X54 and fusions #1193: the mixed dispatch, flow, owners and admission package.
• Marius-Paul Dumitrean (mdumitrean) for the Conditional κ = 0.001675658002271934: two source-holder fusions on #1148's joint-entrance k8 word #1195 fusions and the Tooling: exact frame solver and delivery-rewrite search for gauge44/k8 local words (no new κ) #1186 frame tools.
• Jeremy Kothe (jeremykothe2) for the X54 slot (Conditional κ = 0.001673006105142741: eighth triangle slot X54, rank-seven helper ends and T16 owner packing on the eight-slot k8 word #1130), the seven-slot k8 word (Conditional κ = 0.00167166528321877: seven triangle-hybrid slots (PR987 search) on the k8 leaver word #1018/Conditional κ = 0.001672651218919025: improved T16 owner packing on the seven-slot k8 word #1074) and the leaver chain.
• Rohan Arun (rohanarun) for the Conditional κ = 0.001675161536733127: X54 slot on #1148's three-demotion k8 word with its T16 owners #1178 X54 rebase, Conditional κ = 0.001662039077758742 — U10 (two new triangle-hybrid slots) on PR942's T37 owners #987, and concurrent Conditional κ = 0.001675568675201533: joint entrances with T37 owner packing #1169/Conditional kappa 0.001675670695307702: cross-call T37 entrance augmentation #1192/Conditional kappa 0.00167576776285696: mixed T37 source-holder fusions #1201. Conditional kappa 0.00167576776285696: mixed T37 source-holder fusions #1201's payload is not used.
• Thomas DiFiore (tomdif) for the Conditional κ = 0.001675560947524449: joint k8 entrances, rank-seven ends, and T16 hosting #1148 joint-entrance word and its ancestry, and seslly/shipstuff for Conditional κ = 0.001672780159952542: reverse one entrance promotion to fill T16 gaps #1111.
• Ali Romman (Conditional κ = 0.001674097969905390: an attaining T37 construction and fixed R480 owner optimum #1129), Chafik Boukhalfa (Independent exact certificate of PR741 owner-profile optimality #795/Conditional κ = 0.001674097969905390: seven-slot k8 with T37 whole-owner packing #1131/Conditional κ = 0.001674340686401949: rank-seven helper ends with T37 owner packing #1152), jon314159 (Conditional κ = 0.001661960547713947: T37 whole-owner packing and all-T bound #942), Hao Yan (Research: T16 owner concentration raises conditional κ to 0.001661642255531641 #858) and NewBArch for the T37 and triangle-hybrid machinery.
• Every upstream contributor in the retained notices.

All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape, exact recovery, analytic transfer, PR559 recurrence correction and bit H1–H5 obligations remain. No unconditional theorem and no optimality claim.

AI disclosure: prepared with Claude Opus 5.5 (Anthropic) via Claude Code, directed by Joel Pulikkan (GamingPuzzled).

🤖 Generated with Claude Code