Conditional κ = 0.001675608585476885: joint entrances and X54 with T37 owners

[chafreaky]

Conditional κ = 0.001675608585476885 (1675608585476885/10^18), from composing #1148's joint-entrance supplier with #1130's X54 operation and #1169's exact T37 integer flow. This improves #1148's admitted 0.001675560947524449 and #1169's draft target 0.001675568675201533. The selected repository certificate remains unchanged.

Verification: full cold rebuilds from relocated, read-only source trees passed on macOS arm64 / Python 3.11.15 and Linux aarch64 / Python 3.14.8. Their complete MATH.json receipts are byte-identical: SHA-256 a9d279c9978f5264a608eda77192a4ff2836f16b816e0fbdbcdb615b13a3896e. Both use the exact submitted manifest and reconstruct the full ancestry, suppliers, owner map and strict admission. Approximate wall times were 27.0 and 28.3 minutes; these are verification durations, not a speedup claim. The external collection wrapper needed a rational-normalization fix after successful verification (1675608585476885/10^18 equals the emitted reduced fraction); recovered receipts retain the original wrapper errors and completed verifier/source bindings. No submitted source changed. The dedicated fork CI run also passed on Python 3.11 and 3.14 at the exact submitted head 7015903d1d01a2b50ff16f85184edc2686f69e37. Both hosted mathematical receipts match the complete cold receipt byte-for-byte. Upstream PR checks remain queued and are separate from this successful exact-head run.

The unchanged X54 operation changes the paid local profile by +2 H3 - 4 H4 + 2 H5, preserving every helper width. The final local profile is {1:2364,2:498,3:414,4:126,5:84,8:8}, with width inventory {4:44,5:44,7:38,8:114,9:240}. The 333-call T37 composition leaves idle profile {1:834,48:11374}. Its independent checker and controller invoice agree on the physical geometry, 775-bit prefix within a charged 1,024-bit reserve, and row coefficient 17,495 < 20,161.

The submitted integer entries come from Rohan Arun's #1169 at c79df8e3c61676445f8e1782814450199d8221e6. A checked normalization feeds our retained deterministic matching constructor; the owner map is freshly reconstructed for the final helper labels without an optimizer. The composition attains the exact outer-grid ceiling over all positive replica counts for this fixed local paid profile, helper inventory, source capacity stock and retained #589 bit endpoint. This ceiling does not bound mixed providers or other constructions.

Reproduce from a full checkout with Python 3.11+, a C++17 compiler and Boost:

python -m pip install -r research/e8-bit-p111-tuned/requirements.txt
CXX=g++ BOOST_INCLUDE=/usr/include python -B \
  research/complex-t37-joint-x54-owners/verify.py \
  --work /tmp/t37-joint-x54-fresh

Expected: PASS_FRESH_T37_JOINT_X54_CONSTRUCTION_AND_STRICT_ADMISSION 0.001675608585476885.

The driver rebuilds #589/#741/#799 ancestry, k8/seven-slot suppliers, the full #1148 eight-end/T16 and joint-entrance admissions, and the final X54 supplier before reconstructing owners and running strict T37 admission. It includes 32 endpoint, 27 joint-entrance, eight X54, eight flow, six independent owner, eight parent-lift, fifteen controller, 69 admission and twelve bit-supplier controls, alongside retained ancestral tests. All 1,387 retained dependency pins match main 1b59b624d21924f8e3537cdc1ac52d3be6eda2fe. Package manifest: aa7c2f90accfb214a8a32078c4236fe5a921d23cbc718b4cdf4d3ee2a9ba0b1e.

Only the new package and its workflow are added. The 897 vendored files preserve their original bytes, notices, Git-object identities and SHA-256 pins. Credits include Thomas DiFiore's #1148 construction; seslly/shipstuff's #1111 group-635 lead; Jeremy Kothe's #1130 X54 and #1005/#1018/#1022 supplier lineage; Rohan Arun's #1169 flow and #987 lineage; Ali Romman's #1129 flow/matching work; Alexander Schwartzman's #1030 endpoint mechanism; #1049's leaver-premise checker; Hao Yan's #858 controller; #870/#890 geometry/admission; Jon's #942 parent and all-replica argument; and the retained bit/complex ancestry. Full source boundaries are in NOTICE.md and SOURCE-PINS.json. Prepared for chafreaky with substantial OpenAI Codex assistance.

This remains a finite conditional construction. All-size/compiler, common-label and mutable-source realization, complete-call hosting, precision/tape, analytic transfer, the #559 recurrence correction and bit H1–H5 assumptions remain.

[Mister-Meeseeks]

100-PR batch review at 7015903d1d01a2b50ff16f85184edc2686f69e37.

This remains open after scoped triage. Next review step: Whole-head supplier review remains open for research/complex-t37-joint-x54-owners. 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.