Conditional κ = 0.001675608585476885: X54 slot on #1148's joint-entrance k8 word with #1169's exact T37 owners

[rohanarun]

Result

Conditional κ = 0.001675608585476885 (exact 335121717095377/200000000000000000).

• Over Conditional κ = 0.001675568675201533: joint entrances with T37 owner packing #1169 (0.001675568675201533): +3.9910275352e-8, i.e. 0.0023819%.
• Over Conditional κ = 0.001675560947524449: joint k8 entrances, rank-seven ends, and T16 hosting #1148 (0.001675560947524449): +4.76e-8.
• Conservative endpoint: 0.001675608582632503.

Construction

The base is #1169: #1148's joint entrance groups 603/611/635 with an exact T37 owner flow. This PR adds one ingredient to it: jeremykothe2's width-neutral eighth triangle-hybrid slot X54/E589 (holders 335, 367) from #1130.

• Recipe. The edits and frames are identical to RECIPE-X54-ends7.json, rebased onto k8-joint-entrances/FULL-WORD.json.gz (content 1f666402…). The joint-entrance recipe changes only frames, and none of its 39 changed B frames lies on an X54 position.
• Local profile. It goes from {1:2364,2:498,3:412,4:130,5:82,8:8} to {1:2364,2:498,3:414,4:126,5:84,8:8}, a change of {3:+2, 4:−4, 5:+2}. The width inventory {4:44,5:44,7:38,8:114,9:240} is unchanged.
• Reused from Conditional κ = 0.001675568675201533: joint entrances with T37 owner packing #1169 unchanged:
  • the 159,840 whole-helper roles in 333 calls;
  • the owner map and pattern flow;
  • the windows and parent geometry;
  • idle {1:834,48:11374}.
• Provider identity. This is the only new identity. It is rebound name-by-name (15 identities) to a fresh native replay of the new word, and the SPEC is re-frozen through the unchanged discovery/freeze path.
• Ceiling. Conditional κ = 0.001675560947524449: joint k8 entrances, rank-seven ends, and T16 hosting #1148's all-T signed-dual bound, pinned to the X54 plan, gives a grid ceiling of exactly 0.001675608585476885. The construction attains the fixed-family ceiling for this local word and inventory.

The global profile is {1:788046,2:165834,3:137862,4:41958,5:27972,8:2664,48:11374}, with live stock 33,152 and deficit 11,840.

Validation (passed)

• Local audit. The independent exact local audit of the X54 word passes on all 704 columns in both orientations (PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES).
• Local controls.
  • Conditional κ = 0.001675560947524449: joint k8 entrances, rank-seven ends, and T16 hosting #1148's 27 entrance controls.
  • NewBArch's slot controls: C0, the recipe, and four mutants, run globally and for X=54. All 10 outcomes are as pinned.
• Native replay. A fresh five-stage native replay of the new word.
• Strict T37 admission with the retained Conditional κ = 0.001674097969905390: an attaining T37 construction and fixed R480 owner optimum #1129 engines:
  • bind, emit, audit, invoice and assembly;
  • 69 admission and 12 bit controls;
  • the independent owner checker with 7 controls;
  • all 47 outer inequalities;
  • result: PASS_STRICT_T37_THREE_DEMOTIONS 0.001675608585476885.
• Fixed-family upper bound. PASS_ALL_T_K8_JOINT_X54_SIGNED_DUAL_UPPER_RELAXATION 0.001675608585476885.

Receipts are in research/joint-x54-t37/evidence/. The package verify.py chains all of the above from the pinned sibling #1169 layout. Along the way it rebuilds the owner table and plan, rebinds the provider from the fresh native replay, and checks that every reproduced artifact matches.

python -B research/joint-x54-t37/verify.py --work /absolute/new/output-directory

This needs Python 3.11+, a C++ compiler and Boost headers. It uses no network and no solver.

The branch sits on #1169's head 13d02293. It reuses these files from that package, pinned in SOURCE-PINS.json:

• upstream-layout.tar.gz
• construct.py
• PATTERN-FLOW.json
• OWNERS.json.gz
• GLOBAL-TEMPLATE.json.gz

Scope

This is a conditional finite construction. These obligations remain:

• all-size compiler;
• common-label and mutable-source realization;
• whole-call hosting;
• precision and tape;
• exact recovery;
• analytic transfer;
• the PR559 recurrence correction;
• PR589 bit H1–H5.

No unconditional theorem, full formalization or global packing optimality is claimed.

Credit

• Conditional κ = 0.001673006105142741: eighth triangle slot X54, rank-seven helper ends and T16 owner packing on the eight-slot k8 word #1130 (jeremykothe2): the X54 recipe.
• NewBArch: the triangle-hybrid builder and controls, vendored byte-for-byte.
• Conditional κ = 0.001675560947524449: joint k8 entrances, rank-seven ends, and T16 hosting #1148 (Thomas DiFiore/Codex) and its local ancestry.
• Conditional κ = 0.001675568675201533: joint entrances with T37 owner packing #1169: the T37 owner flow and packaging.
• Conditional κ = 0.001674097969905390: an attaining T37 construction and fixed R480 owner optimum #1129 (Ali Romman/Codex): integer flow, matching and T37 audit.
• Conditional κ = 0.001674097969905390: seven-slot k8 with T37 whole-owner packing #1131: wave order.
• Conditional κ = 0.001661960547713947: T37 whole-owner packing and all-T bound #942, Independent exact certificate of PR741 owner-profile optimality #795 and Conditional κ = 0.001661957774647029: T21 whole-owner packing and fixed-family bound #890: the dual all-T bound.
• Bit c = 0.001733427039589844: two A-section transports on #555's punctured R439 word (+0.0216%, κ unchanged) #589: the unchanged bit supplier.

New composition by Rohan Arun with AI assistance (Claude). Apache-2.0; all original notices are retained.

🤖 Generated with Claude Code

https://claude.ai/code/session_01TGoMCHAqctZe4wTb4Qr7VV

[Mister-Meeseeks]

100-PR batch review at aac9ce7d83e02989eed76e08815cfd2399214e90.

This remains open after scoped triage. Next review step: Supplier-family review pending: bind native local replay, physical owners and complete admission; reconcile overlapping historical package versions.

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.