Conditional κ = 0.001675608585476885: X54 slot on #1148's joint-entrance k8 word with exact T37 owners (independent; equals #1196)

[GamingPuzzled]

This is 335121717095377 / (2·10^17). It is +3.9910e-8 over #1169 (0.001675568675201533, T37 owners on the same joint word without X54), +5.40e-9 over #1183 (0.001675603180601302) and +4.76e-8 over #1148's T16 value (0.001675560947524449). The complex side binds. The PR589 bit supplier is unchanged.

Concurrent identical result. chafreaky's #1196 reports the same composition and the same κ, 0.001675608585476885. This package was built independently: its own flow, owner map and package. It is submitted as an independent construction and check, not a new record. At submission, #1193 (0.001675672695827067), #1192 and #1195 are higher.

Composition

1. Local word. Thomas DiFiore's joint-entrance k8 word (Conditional κ = 0.001675560947524449: joint k8 entrances, rank-seven ends, and T16 hosting #1148, research/k8-joint-entrances, head 3ba07f19) receives 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).
   • The recipe is Rohan Arun's Conditional κ = 0.001675161536733127: X54 slot on #1148's three-demotion k8 word with its T16 owners #1178 RECIPE-X54-dem.json, unchanged in edits and frames: 5 B deletes, 5 inserts, holder 335 restored at FULL and holder 367 restored early. Only the base/result pins and the report profile change.
   • The word is built with NewBArch's unchanged build_tri.py. Its content is ac95ff95….
   • Profile {1:2364,2:498,3:412,4:130,5:82,8:8} → {1:2364,2:498,3:414,4:126,5:84,8:8}.
   • The slot is width-neutral. The widths stay {4:44,5:44,7:38,8:114,9:240}.
2. Owners. The package uses Ali Romman's Conditional κ = 0.001674097969905390: an attaining T37 construction and fixed R480 owner optimum #1129 T37 machinery (r480-owner-optimum): order, groups, constructor, admission code and independent audit, retargeted as in Conditional κ = 0.001674137810105185: X54 slot on the seven-slot k8 word with the exact T37 owner optimum #1157.
   • Conditional κ = 0.001674097969905390: an attaining T37 construction and fixed R480 owner optimum #1129's integer flow does not fit this inventory. Its nine-pattern basis is infeasible here because there are 12 more width-5 helpers per call.
   • A new integer pattern flow over 15 of the 20 tight patterns attains the all-replica optimum for this inventory. It was found with an LP and a support-restricted MILP during discovery; verification runs no solver.
   • That optimum is {1:834,48:11374}. It is the same normalized idle as Conditional κ = 0.001675560947524449: joint k8 entrances, rank-seven ends, and T16 hosting #1148's own ALL-T-BOUND.json, from Independent exact certificate of PR741 owner-profile optimality #795's signed prices and the Conditional κ = 0.001661957774647029: T21 whole-owner packing and fixed-family bound #890/Conditional κ = 0.001661960547713947: T37 whole-owner packing and all-T bound #942/Conditional κ = 0.001674097969905390: an attaining T37 construction and fixed R480 owner optimum #1129 argument.
   • The unchanged construct.py expands the flow into 159,840 literal roles in 333 calls.

Complete profile: {1:788046,2:165834,3:137862,4:41958,5:27972,8:2664,48:11374}. Live stock is 33,152 and the deficit is 11,840. The root lies in (0.001678420962050942454559, …560).

Verification (no network or solver):

python3 -B research/k8-joint-x54-t37/check.py --work /new/dir
# PASS_K8_JOINT_X54_T37_ALL_REPLICA_OPTIMUM_AND_ATTAINING_CONSTRUCTION 0.001675608585476885
CPLUS_INCLUDE_PATH=/path/to/boost python3 -B research/k8-joint-x54-t37/construction/word/build_local.py --out /new/dir2
# PASS_K8_JOINT_X54_LOCALS

check.py covers:

• the all-replica certificate: 1,163 patterns, two exact engines and all 47 outer inequalities;
• 18 certificate controls;
• the literal owner reconstruction;
• the strict replay: bind, lift, emit, controller audit with 15 mutations, the full invoice (prefix 775 < 1024, row 17,495 < 20,161), assembly, 69 admission and 12 bit controls, and the independent owner audit with 2,016 disjoint pending-axis checks.

build_local.py rebuilds the native locals from the repository and checks every pinned identity:

• Conditional κ = 0.001675560947524449: joint k8 entrances, rank-seven ends, and T16 hosting #1148's build_word.py;
• the X54 build;
• NewBArch's controls: the recipe passes and all 8 mutants are rejected;
• the independent audit_local;
• PR635's native chain with 2,904 phase edges.

Both commands passed from a fresh git archive of the commit (macOS arm64, Python 3.11). Receipts are in evidence/.

Package: only research/k8-joint-x54-t37/ is added. The branch is #1148's head with #1129's branch merged, because the T37 admission code and its pinned dependencies live there. Please merge after, or together with, #1148 and #1129. The README lists every file changed relative to #1129/#1157. construct.py, verify.py and code/ are byte-identical to #1129.

Credits

• Thomas DiFiore (tomdif) for Conditional κ = 0.001675560947524449: joint k8 entrances, rank-seven ends, and T16 hosting #1148: the joint-entrance word, its local ancestry and the all-replica bound for this inventory. seslly/shipstuff for Conditional κ = 0.001672780159952542: reverse one entrance promotion to fill T16 gaps #1111's entrance-demotion lead.
• 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 Conditional κ = 0.001675161536733127: X54 slot on #1148's three-demotion k8 word with its T16 owners #1178's X54 recipe rebase and Conditional κ = 0.001674137810105185: X54 slot on the seven-slot k8 word with the exact T37 owner optimum #1157's T37 retargeting layout. Conditional κ = 0.001675568675201533: joint entrances with T37 owner packing #1169 is concurrent T37 work on the same word without X54; it is not imported.
• Ali Romman (aliromman) for Conditional κ = 0.001674097969905390: an attaining T37 construction and fixed R480 owner optimum #1129's T37 owner theorem, flow, matching constructor and audits.
• Chafik Boukhalfa (chafreaky) for the Independent exact certificate of PR741 owner-profile optimality #795 signed prices and the T37 constructions 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 for Conditional κ = 0.001661960547713947: T37 whole-owner packing and all-T bound #942's parent lift and all-replica argument.
• NewBArch for the triangle-hybrid builder and controls.
• Hao Yan for the T16/source-event 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. The packing optimum is scoped to this fixed word, inventory, bin family and outer recipe. This is not an unconditional theorem.

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

🤖 Generated with Claude Code

🤖 Generated with Claude Code