Further coordinated frame cuts on #186: conditional κ = 6.62651985348746e-4

[huxint]

Change and mathematical scope

Continue #186's physical-frame search with coordinated intersections and joins, including line/hyperplane proposals. The complete checked result is κ = 331325992674373 / (5·10^17) = 0.000662651985348746, about 0.1158% above #186.

This changes 1,361 operation frames on #186's unchanged scalar word. All 2,310 aliases, read deadlines and 46 terminal actions remain fixed. Complex W=13,326, rank=878,196 and deficit=1,320 are unchanged; the paid complex saving rises to 0.000663091384170935. The parent's completed bank-bit supplier remains checked and sufficient.

Concurrent #193 reports a higher 0.0006647872 using a different source-assisted word; this is not a current-record claim. The contribution is a further fully replayed frame witness and open integer-capacity cut search on the #186 construction. Directed cut and #186's subspace method are credited, not claimed as new.

Stacked on #186 at 166a34d75e853e933855f0f7e940fe77c4bb6b8d. All inherited all-size compiler, bank/shared-core, weighted-bit, restored-row, prime, precision, recovery, balanced-layout and fixed-tape interfaces remain conditional. No unconditional theorem or practical runtime improvement is claimed.

Validation

python3 -B research/continued-frame-cuts-186/verify.py

The full offline authoring run passed in 143 s. It verifies the immutable parent/source archive and its entire complex/bit certificate, then independently checks the new complex geometry, every rational source/target/dirty column in both shear directions, all 46 terminal trajectories, exact moment/successor, the full paid bridge, all 47 strict inequalities and seven margins. Corruption controls reject omitted group stock, a bad child recount, a zero frame and the next kappa grid point. No search or third-party dependency is used by verification.

RESULTS.md is generated from the certificate and checked on reproduction. Optional search.py requires numpy and writes a separate candidate; its output still requires full terminal and assembly admission. The cut solver uses Python integer capacities; its min cuts were independently compared with exhaustive cuts on 70 small graphs, including capacities above 32 bits.

The new CI runs the read-only aggregate. Original package bytes are unchanged.

Credits

#186 / @Dugongue supplies the combined witness, subspace-cut direction, rematch and entrance-bank construction. @chafreaky supplies the shared-edge word and exact formal/terminal checks; @eumemic supplies PR168 v4 and its module/word/physical-layer lineage; @jamesyc supplies terminal accumulation and compensated birth reuse; @icekylinx and all predecessor contributors retain the full framework credit. Original manifests, notices and immutable source package remain intact.

Prepared by huxint with substantial OpenAI Codex assistance. Apache-2.0.

[Mister-Meeseeks]

Thank you @huxint. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: Further coordinated rational frame cuts on PR186.

Review and limits: Prior exact-head full stdlib finite replay. New frame geometry and paid profile are checked without changing the scalar word.

The complete original source, notices and relevant execution evidence are retained through the pinned source archive. The review distinguishes fresh local runs, source-bound historical Linux CI and prior exact-head review; it does not claim 100 fresh full mathematical audits. Closing this historical PR as reconciled. This preserves parallel and cumulative credit without replacing the selected frontier or promoting priced research targets to completed constructions.

Reviewed head: d3e6b83af33c3aad940e737776937706e25b0b19. Publication: 50d768818f579d4e165b4c257c6ee25bca300802.