Conditional κ = 0.001674097969905390: seven-slot k8 with T37 whole-owner packing

[chafreaky]

Conditional κ = 0.001674097969905390 (167409796990539/10^17). This improves the currently selected #1094 result 0.001672660197076918 and the submitted #1121 value 0.001672965558289236 at the comparison snapshot.

Ali Romman's concurrent #1129 reports the same κ and fixed-family ceiling. This submission contains our separately constructed owner flow and fresh cold supplier replay.

The PR combines Jeremy Kothe's unchanged #1022 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 {1:5622,48:11302}; 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-seven-slot-owners/verify.py \
  --work /tmp/t37-seven-slot-fresh

Expected: PASS_FRESH_T37_SEVEN_SLOT_CONSTRUCTION_AND_STRICT_ADMISSION 0.00167409796990539.

Full cold replays from relocated, read-only source trees passed on macOS arm64 / Python 3.11.15 (1,252.82 s) and Linux aarch64 / Python 3.14.8 (1,314.60 s). Their complete portable MATH.json receipts are byte-identical: SHA-256 cb333260fd34b74d62e2a22a8bcf07993259cd015da16221400947fb6cd2bf39. The cold-run package manifest was e3a9acdfe20b0210f30bdaf3e714acf4e8add3d7b63029af84ebe83d60abc69a. 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 6a83ab539c7224965209d5f1a59f3bd44bd84656173624cf97e9b688ded5f103. 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 and seven-slot 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 403 vendored files from #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 also include #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 fcdc42737b703323d8ed550a528141a482e68e96 passed on Python 3.11 and 3.14: run 38452685205. Both complete MATH.json artifacts are byte-identical (c515758df924819cb8edb3982f4c449a2ffa4d9e1418a9a5802c5edca96014cb) 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 fcdc42737b703323d8ed550a528141a482e68e96.

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