Conditional κ = 0.001674340686401949: rank-seven helper ends with T37 owner packing

[chafreaky]

Conditional κ = 0.001674340686401949 (1674340686401949/10^18). This improves the currently selected #1094 result 0.001672660197076918 and the submitted #1121 value 0.001672965558289236 at the comparison snapshot. It improves our #1131 construction and the concurrent #1129 construction, both at 0.001674097969905390.

The PR combines Jeremy Kothe's unchanged #1107 rank-seven-end seven-slot k8 supplier with a new 333-call order and an exact integer-flow construction of 159,840 whole-helper owners. The constructor expands the frozen flow through deterministic bipartite matching, without an owner optimizer. The idle profile is {1:5424,48:11320}; the independent owner checker and emitted-controller invoice agree. The charged prefix reserve is 1,024 bits (actual 775), and the row coefficient is 17,495 < 20,161.

Both exact moment engines and all 47 outer inequalities certify the result. The construction also attains the outer-grid ceiling over all positive replica counts for this fixed local paid profile, helper inventory, source capacity stock and retained #589 bit endpoint. Changing those ingredients can still improve κ.

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-ends7-owners/verify.py \
  --work /tmp/t37-seven-slot-fresh

Expected: PASS_FRESH_T37_ENDS7_CONSTRUCTION_AND_STRICT_ADMISSION 0.001674340686401949.

Full cold replays from relocated, read-only source trees passed on macOS arm64 / Python 3.11.15 (1,348.51 s) and Linux aarch64 / Python 3.14.8 (1,427.82 s). Their complete portable MATH.json receipts are byte-identical: SHA-256 c3560609345647398bfe387e40e894c84c181d2812500d3bb3d9c234c186c404. The cold-run package manifest was 18cc9639fd8f9b4e2838557286739161c530999b27b5f55e425f5516b18f4fd3. The final dependency inventory pins the four ancestry scripts used by the verifier and omits unrelated repository administration scripts; all executable and mathematical data bytes are unchanged. The final manifest is 9f34dd578dc12c91f2a684e7d2f980ae064419b1835d6c266be28f34a02ce7e6. All 1,387 retained dependency pins match submission main ce7ad1b6ab09452c3478723a2e96ed5ff212dc08. These are verification durations, not a speedup claim.

The driver freshly rebuilds the retained #589/#741/#799 ancestry, the k8, seven-slot and rank-seven-end suppliers, the owner map and strict controller admission. It includes eight flow controls, six independent owner controls, eight parent-lift controls, fifteen controller controls, 69 admission controls and twelve bit-supplier controls, alongside the unchanged ancestral and supplier checks. The new CI matrix repeats the full rebuild on Python 3.11 and 3.14. Hosted CI remains separate from the local validation described above.

Only the new package and its workflow are added. The 600 vendored files from #1107, #1022 and #635 preserve their original bytes and notices, with Git-object and SHA-256 provenance; retained dependencies and all new package files are pinned. Credits include Alexander Schwartzman's #1030 helper-end mechanism, the #1049 leaver-premise checker, #1005/#1018 and their earlier sources, Hao Yan's #858 controller, the #870/#890 independent geometry and admission work, Jon's #942 parent lift and all-replica argument, and the retained bit/complex ancestry. Prepared for chafreaky with OpenAI Codex assistance.

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

Hosted CI for final head d376209304f05551f975b0ddf6eaa84edc4ae31a passed on Python 3.11 and 3.14: run 38452727193. Both complete MATH.json artifacts are byte-identical (7335e7796d3d2997066be9fa88d7fb09214fda6d29dcbb0751f113be3793a24d) and match the cold receipt with only the final package-manifest digest substituted. Upstream queued checks remain separate.

[Mister-Meeseeks]

100-PR batch review at d376209304f05551f975b0ddf6eaa84edc4ae31a.

This remains open after scoped triage. Next review step: Whole-head supplier review remains open for research/complex-t37-ends7-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.