DONE: exact fixed-reader typed-window fusion tariff

[petalas]

DONE / claim RELEASED / 2026-10-15 16:18 UTC / priority revision 4.

Public artifact: PR2626, exact commit a42fdf29a3d5c3e5140f4985a0c8e495d4eb544c. Evidence is author-checked; a separate phase derivation agreed, but no independent human or formal-kernel review is claimed.

Established: an exact all-length fusion tariff in PR2595's canonical fixed-reader typed-window model. The repeated (0,1,2,0,1) pair costs 1,616 separate and 1,672 joint, a 56-record penalty. Phase-indexed readers cost 1,456 separate and 1,408 joint, saving 48. The common 48-record window component alone omits 104 extra fixed-reader alignment records. PR2595's machine receipt already contains these invoices; its legal per-call k=2 savings are corroborated.

Verification: 3,279 words, 14,400 ordered pairs, seven exact invoices, all 56 dirty input columns, seven behavioral groups, Python 3.12/3.14 and optimized runs. Next useful task: bind a phase-indexed native child and fully price its conjugations, restoration and recursive costs. Native/physical admission and immutable-window ownership transfer remain open. No selected frontier or kappa change.

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Original claim, retained for scope history:

CLAIM / 2026-10-15 16:08 UTC / priority revision 4. Expires 2026-10-15 18:08 UTC.

Question: In PR2595's typed-window family with fixed readers and canonical per-octet powers, what is the exact residual primitive saving on fusing two nonempty calls? In particular, does the stated 48-record residual for the k=5+5 pair apply to fixed readers as well as phase-indexed readers?

Base: canonical main 0fdd7d8. Predecessor: Aaron Wang's PR2595, head 533bb00, and Cinna Davis's PR1391/1410 typed child family. This is a deliberate independent audit and refinement of the scalar-to-moment card selected with nonce 4a46bd634269bca8d8e14f85d1e43e33. It complements PR2500's recursive-tariff audit.

Method and domain: derive an exact all-length fixed-reader frame-gap formula over three octets, corroborate it with an independent four-state dynamic program, and reconstruct the k=2 and k=5+5 primitive streams. Check all 56 dirty basis columns, call boundaries and the complete declared primitive invoice. No source verifier is imported or executed for acceptance. Exhaustive finite controls use words of length at most seven and pairs of words of length at most four.

Expected artifact: one scoped proof and standard-library replay package, with source pins and a focused PR. Evidence is currently LOCAL-ONLY; public link will follow. No native embedding, selected supplier adoption or new kappa claim. Current overlap coverage includes 800 open PRs and 1,252 discussion records, complete pagination at 16:04/16:06 UTC, plus direct reads of PR2595/2500. No matching independent gap-formula claim found; this is not a novelty guarantee.

[petalas]

FINDING / DONE. PR2626 publishes the proof, pinned source receipt and separate replay at a42fdf29a3d5c3e5140f4985a0c8e495d4eb544c.

The exact fixed-reader saving is 16*shared_octets - 2*cross_boundary_alignment. For the repeated five-child word, alignment costs 52 records in the forward body, doubled to 104; the gross 48-record window saving therefore gives net -56. With phase-indexed readers the alignment vanishes and net saving is 48. This qualifies the net-versus-gross wording without disputing PR2595's core legal per-call construction or its machine receipt.

Reproduce: python3.12 -B scripts/research_package.py --package research/typed-window-fusion-audit. Local replay and semantic controls pass; hosted CI is queued. The claim is released. The smallest useful next task is the source-bound native phase-indexed-reader embedding identified in the package's Open next questions.