κ = 7.77947425336102317479703e-4: restore ten terminal caches in original registers

[eumemic]

κ = 7.77947425336102317479703e-4

Exact value: 777947425336102317479703/1000000000000000000000000000.

Ten terminal helpers blocked by early reads become restored caches in their original dirty registers. The transform retains the early contribution, feeds the pivot after the final centre ERASE, then restores each register using the changed source and its intervening correction. Six helpers finish at rank 5 and four at rank 6. The resulting 146 endpoint-rank reduction is priced together with the five kernel ranks lost by protecting these helpers. Every data endpoint, COPY lifetime, correction and late scalar write remains accounted for.

This uses the immutable source023 orientation construction underlying #338, with fresh protected-kernel selection, 240 early restorations, fifteen ordinary sink removals, ten caches, 115 reorderings and 50 final constructed-frame retimings. It is a separate construction from the selected-carrier sixteen-sink releases. Complete native pricing, rather than a local discovery score, determines the displayed bound.

The final word has 10,005 registers, 8,085 independent dirty helpers, 324,389 ADDs, 47,812 paid calls and rank mass 177,714. At 300 replicas the literal stock is 3,265,110, with 1,918,663,827,000 paid selectors and primitive coefficient 125,785,307,842,628,501. Eight bootstrap levels yield the exact bound above.

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 406 committed package files plus the outer manifest matched before push. The source-bound cache stage checks all signed integer and F₂ formal columns, both reflected ledgers and twelve omission controls. A distinct final-word audit checks every F₂ forward/inverse column, arbitrary helper dirt, COPY lifetimes, both reflected paid ledgers, independent exact bank tiling, all 27,836 basis and annihilator minors, and closed-form assembly. The independent final operator replay is over F₂; integer inverse semantics follow the actual signed elementary shears and retain the signed decoder/recovery assumptions.

Word SHA256: f99a64ba36393aa9d0dd04f10dcab19d688782137d89bc27711bf654dd4711f2.
Package manifest: cbd40affd1d4d820394283f56f5ab735a8c59a9b74b04f9128da165dfe70690b.

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. Cache research, integration, independent auditing and publication used substantial OpenAI Codex assistance. All inherited licenses, provenance and AI disclosures are preserved.

A dedicated Linux workflow replays the full package. The repository-wide inherited 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: Restoration of terminal caches in their original registers.

Review and limits: Actual restoration and owner/bank accounting are checked; cache reuse is not treated as free workspace.

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: da0c805eab7e88d8b9fcce112ff8ed4b720bea8a. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.