κ = 7.7809154371141892133459e-4: transfer compatible PR340 frame components

[eumemic]

κ = 7.7809154371141892133459e-4

Exact value: 77809154371141892133459/100000000000000000000000000.

Frame assignments from Rohan Arun’s #340 at frozen head 695e703731491f81aa22d51b2def850afd7519c0 are transported to the six-direct/four-cache construction using original physical roles, signed scalar tuples, old-frame bases and unique occurrence checks. Incompatible assignments are omitted; the combined assignment is admitted again on the actual word. The exact original selector Git blob f635f0b0304fab807e5a5449f863c663d4c88cb0, NOTICE and license are preserved alongside explicitly labeled historical text copies.

Six of the ten blocked terminal helpers can be removed entirely by splitting an intervening source read and deferring the source update until after the final centre ERASE. The other four remain restored rank-6 caches in their original dirty registers. This saves 176 endpoint ranks while preserving all data input/output frames, compared with 146 for the ten-cache construction. Every split read, dirty correction and deferred update is charged in the actual word.

The immutable source023 construction underlying #338 is regenerated before fresh protected-kernel selection, 240 early restorations, fifteen ordinary sink removals, the six-direct/four-cache transform, 115 reorderings and 456 final frame retimings plus three second-round reorderings. The final word has 9,999 registers, 8,079 independent dirty helpers, 324,353 ADDs, 47,792 paid calls and rank mass 177,684. At 300 replicas the literal stock is 3,264,660, with 1,917,245,877,000 paid selectors and primitive coefficient 125,725,705,474,676,501. Eight finite bootstrap levels yield the displayed bound.

The full operational complex supplier remains #327 at 40ed0456ab1990beb3440e61bb883ccf95fdcea4, with full-fallback saving 779597612622781/10^18; the bit side still binds. The all-size compiler, weighted selector, common-ancestor chart, restored-row, routing, prime-supply, precision/recovery, complex-symbolic and analytic interfaces remain inherited assumptions. This is a conditional sufficient construction.

Two complete immutable 22-stage replays on Python 3.11 and 3.12 actually exited 0 with matching mathematical certificates. Every receipt hash, both complete five-file producer regenerations, and all 419 committed package files plus the outer manifest matched before push. The hybrid stage retains all 10,005 original signed integer and F₂ columns, verifies removed-input/output identities, binds the exact six-role compaction map, and rejects sixteen omission controls. A distinct final-word audit checks all F₂ forward/inverse columns, arbitrary dirty restoration, COPY lifetimes, both reflected paid ledgers, an independent exact tiling, all 27,868 basis and annihilator minors, and closed-form assembly. Its numerical operator replay is over F₂; integer inverse semantics follow the actual signed elementary shears and retain the signed decoder/recovery assumptions.

Word SHA256: 9c99e3e6ac6058132bec486425ecf078489edb23f018e395831358111f501297.
Package manifest: f2bad40ac05272f0e5efa931b8b97771a2b1fe4f9a3d2fff70467368525f4c2a.

Credit includes DreamingOfClouds for #325 and #327, Chafik Boukhalfa for transcript transforms and p10 adaptations, Rohan Arun for frame optimization and arithmetic refinements, the credited #283 terminal-sink mechanics, and every contributor in inherited notices. The independently implemented frame search, hybrid integration, independent auditing and publication used substantial OpenAI Codex assistance. All inherited licenses, provenance and AI disclosures remain preserved.

A dedicated Linux workflow replays the complete package. The inherited repository-wide joint-dual Makefile pin failure remains separate, addressed by #318. Previously published PR heads and claims remain frozen.

[Mister-Meeseeks]

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

Contribution: Transfer of compatible frame components from a parallel word.

Review and limits: Only source-compatible components are transplanted; full exact scalar/frame/prime and bank checks remain mandatory.

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: 9e15e4d5ed41f8df20bd8393ece9f62e910cd49c. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.