Conditional κ = 0.001674137810105185: X54 slot on the seven-slot k8 word with the exact T37 owner optimum

[rohanarun]

Conditional κ = 0.001674137810105185: X54 slot on the seven-slot k8 word with the exact T37 owner optimum

This is +3.98402×10⁻⁸ over the current best open result, #1129/#1131 (0.001674097969905390: the T37 owner optimum on the seven-slot k8 word). It is also above #1130 (0.001673006105142741). The complex side binds; the PR589 bit supplier is unchanged.

Change: a composition of two width-neutral pieces that have not yet been combined.

1. Local word. Jeremy Kothe's eighth triangle-hybrid slot X54/E589 (Conditional κ = 0.001673006105142741: eighth triangle slot X54, rank-seven helper ends and T16 owner packing on the eight-slot k8 word #1130) is applied to the seven-slot k8 word c2b29430… (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), instead of to the rank-seven-ends word.
   • construction/x54/RECIPE-X54-k8.json is Conditional κ = 0.001673006105142741: eighth triangle slot X54, rank-seven helper ends and T16 owner packing on the eight-slot k8 word #1130's RECIPE-X54-ends7.json with identical edits and frames: 5 deletes, 5 inserts, holder 335 restored at FULL and holder 367 restored early. Only the base and result pins and the profile change.
   • NewBArch's unchanged build_tri.py gives word content 512452c0….
   • Local profile {3:+2, 4:−4, 5:+2} → {1:2412, 2:418, 3:434, 4:138, 5:84, 8:8}.
   • Widths {4:56, 5:32, 7:30, 8:122, 9:240} (R=480) and the local prefixes (52/68) are unchanged.
   • Checks: the independent audit_local PASSES, the unchanged run_controls.py gives 10/10, and PR635's native chain (native, ledgers, replay, wrappers and all 2,896 phase edges) passes.
2. Owners. Ali Romman's exact T37 owner optimum (Conditional κ = 0.001674097969905390: an attaining T37 construction and fixed R480 owner optimum #1129; same map as Conditional κ = 0.001674097969905390: seven-slot k8 with T37 whole-owner packing #1131) is used unchanged: owners, order, pattern flow, 159,840 roles, idle {1:5622, 48:11302}.
   • The all-replica signed-dual bound, rerun with the eight-slot profile, has grid ceiling 0.001674137810105185, and the construction attains it.

Verification: python3 -B research/k8-x54-t37/check.py --work /tmp/k8-x54-check passes:

• the all-replica certificate and its 18 controls;
• literal owner reconstruction;
• the strict replay: bind8, lift, bind, emit, controller audit with 15 mutations, the full finite invoice (prefix 775 < 1024, row 17,495 < 20,161), assembly with all 47 outer inequalities, 69 admission and 12 bit controls, and the independent owner check.

Final line: PASS_K8_X54_ALL_REPLICA_OPTIMUM_AND_ATTAINING_CONSTRUCTION 0.001674137810105185 (Linux, Python 3.13). Receipts are in evidence/k8-x54/ and evidence/x54/.

Package: research/k8-x54-t37/ (built on #1129's branch; its research/r480-owner-optimum is untouched). It is #1129's package with:

• the eight-slot locals in inputs/local;
• provider identities rebound in vendor/pr1074/T8/PLAN.json, plus the T8 SPEC pins re-recorded by the unchanged bind code;
• the certificate root and κ, and two control values;
• the κ constant;
• data/PLAN.json and data/SPEC.json re-frozen by its own discovery replay.

Owners, order, flow, construct.py, lift.py, verify.py, independent_owner.py and code/ are byte-identical to #1129. The README lists every change. Please merge after (or together with) #1129.

Credits:

• Ali Romman (Conditional κ = 0.001674097969905390: an attaining T37 construction and fixed R480 owner optimum #1129) and Chafik Boukhalfa (Conditional κ = 0.001674097969905390: seven-slot k8 with T37 whole-owner packing #1131, PR795 prices): the owner optimum and its machinery.
• Jeremy Kothe: 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 (Conditional κ = 0.001671387264390146: all eight mutable-leaver all-K cells, U8 hybrids and frame re-optimisation on PR799's word #1005).
• NewBArch: the triangle-hybrid move and the unchanged builder and controls.
• Rohan Arun's Conditional κ = 0.001662039077758742 — U10 (two new triangle-hybrid slots) on PR942's T37 owners #987 slot search.
• Hao Yan's T16 machinery.
• Every upstream contributor in the retained notices.

🤖 Generated with Claude Code

https://claude.ai/code/session_01TGoMCHAqctZe4wTb4Qr7VV

[Mister-Meeseeks]

100-PR batch review at c5647aecc8ff44e49776860bb75520bfe3e88f1e.

This remains open after scoped triage. Next review step: Whole-head supplier review remains open for research/k8-x54-t37, research/r480-owner-optimum. Bind its exact native providers, physical owner allocation and admission evidence, then reconcile changed predecessor blobs before merge. Path overlap with a replayed descendant does not establish complete coverage; see SUPPLIER-FAMILIES.json.

This is a specific continuation point, not a rejection or a request to redo already recorded checks. Completed local evidence is retained separately from outstanding whole-head obligations.

Batch review, attribution and evidence. Thank you for the contribution.