κ = 7.776299656948249002253e-4: exact-subspace grouping and sixteen carrier switches

[eumemic]

κ = 7.776299656948249002253e-4

Exact value: 7776299656948249002253/10000000000000000000000000.

This construction builds on frozen #335 with exact-subspace endpoint grouping and sixteen source-bound carrier switches. Fresh matching, two physical reuse/descent passes, and fresh downstream discovery produce a concrete word with a better paid rank distribution. The standalone grouping control ties #335 after final retiming, so its apparent source gain is not counted twice.

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

The final word has 10,006 registers, 8,086 independent dirty helpers, 324,628 ADDs, 47,817 paid local calls and rank mass 177,874. Fresh stages comprise 480 first retimings, 120 target groups, 1,242 entrance families of rank 1,246, 240 early restorations, 14 terminal sinks, 126 reorderings and 14 final retimings. The second reorder is empty. At 300 physical replicas the literal stock is 3,267,510, with 423,102 complete banks per stage, 1,918,907,127,000 paid selectors and counted primitive coefficient 125,797,874,249,792,501.

Word SHA256: be44db315647bf12789b1efdcad87a0980c063159587e9de565a134a0b493d15.
Package manifest: 094ff309628d60d62628a3065078ef2acc6149e97327f1c74447a263231296de.

Both immutable 22-stage replays actually exited 0 (Python 3.11 and 3.12). Their complete mathematical certificates match, excluding only top-level timing-dependent receipt hashes. Every receipt hash and both complete five-file source regenerations passed. The separate literal audit has already passed the actual forward/inverse scalar operators, arbitrary dirty restoration, COPY lifetimes, both reflected ledgers, alternate exact bank tiling, all 27,814 basis/annihilator minor witnesses, and an independent closed-form assembly. Omitting kernel restoration corrupts 953 formal rows. The final pre-push gate also checks all 404 committed package blobs and the outer manifest, including every nested manifest.

Credit includes DreamingOfClouds for the #325 bit construction and #327 complex supplier, Chafik Boukhalfa for transcript transforms and p10 adaptations, Rohan Arun for frame optimization and arithmetic refinements, and every contributor named in inherited notices. The new source grouping and carrier search, selections, integration, independent auditing and publication used substantial OpenAI Codex assistance. All inherited provenance and AI disclosures are retained.

The repository-wide inherited joint-dual Makefile pin failure remains separate and is addressed by #318. A dedicated Linux workflow replays this complete new package. All previously published PR heads and claims remain unchanged.

[Mister-Meeseeks]

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

Contribution: Exact-subspace grouping and carrier switches.

Review and limits: Changes the carrier matching and frame itinerary, not just an arithmetic parameter. Preserve all dirty-state and complete bank checks.

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: f566fe33384cd295fc1416cf3ed882500135a1f2. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.