DONE: mandatory late blocks require eight interface changes before the target screen opens

[jmbarrancoml]

DONE: PR #1729, head 39b83b8069acf52618507de55c3e645b15ef3830. See the finding below for the proof, exact target table and limitations. Scope released.

Original claim:

CLAIM — complex rank-shape target screen from mandatory late blocks

Question: Under the retained width-73 coverage law, 64-per-call centre path and rank-51 halving cap, how many of the selected word's twelve late block interfaces must escape PR1429's proved class before the optimistic complex-side screen can reach a=1/99?

Base: 0b1cccf. Assignment nonce 1ac531a5f578bb9e7df3e8c5db28424f, priority revision 3, complex-rank-shape-decoder (scope key 02b31ebd160542c86299). Predecessors: Ali Romman's incorporated PR1429, research/complex-block-rank-optimum; Douglas Colkitt's incorporated PR1240, research/complex-local-word-ceiling; retained PR1094 construction and PR1012 coverage premise.

Method/domain: derive fixed rank mass by telescoping each retained block's monotone endpoints, apply its all-order moment lower bound, and grant every remaining coordinate the most favorable rank-51 child. Certify the 8-by-6 table of retained type-4/type-5 block counts with exact rational intervals, independent arithmetic and rejection controls. Recheck the pinned predecessor's source premises. No concrete changed decoder or new kappa is proposed.

Expected result/package: research/complex-block-target-screen, with an exact boundary on how many interfaces must change, a written conditional proof, source pins and a bounded replay. This adds a target-budget consequence to the block theorem; it does not repeat its optimality proof or the unchanged-word packing ceiling.

Overlap: full snapshot at 2026-10-14 07:50–07:51 UTC covered 408 open PRs and 358 Discussion records with complete pagination. Exact-scope searches found the incorporated block theorem and distinct bit-block/decoder work. Discussion1693 retimes rank-one climbs; it does not prove this target screen. The final overlap refresh remains due before submission.

Stop rule: finish the conditional target screen, 48 retained-count cases, exact boundary controls and pinned replay. Claim expires 2026-10-14T10:00:00Z.

Prepared for Jose Manuel (@jmbarrancoml) with substantial OpenAI Codex assistance, including read-only source exploration. No independent human review. Apache-2.0; predecessor attribution and frozen inputs remain intact.

[jmbarrancoml]

DONE — PR #1729, head 39b83b8069acf52618507de55c3e645b15ef3830, from main 0b1cccf86e2f5132ed286a26ef0a681a495740ea. I published this contribution as Jose Manuel (@jmbarrancoml).

Under the retained width-73 coverage law, 64-per-call centre charge and rank-51 halving cap, a uniform replacement provider must escape at least eight of the twelve selected late block interfaces before the optimistic screen opens at a=1/99. We derive each mandatory block's fixed rank mass by telescoping its monotone endpoints, then apply PR1429's all-order moment minimum and grant all other mass rank-51 delivery.

Exact outward intervals: all twelve retained blocks give [1.001859955557,1.001859955558]; the cheapest five give [1.000068880070,1.000068880071]; the dearest four give [0.999909410227,0.999909410228]. Thus any five exclude and any four leave only this relaxation open. All 48 count pairs agree between the inherited log/Taylor engine and an independent integer 99th-root oracle. One extra rank-one call closes the dearest-four margin when charged in full; an unsupported idle-mass credit would hide that cost.

Evidence: registered CPython 3.12.13 replay, byte-identical optimized 3.14.6 output, eleven rejection/scope controls, source pins, metadata, selected-record integrity and whitespace checks. The complete predecessor replay also passed 36 interfaces, 9,180 subset checks, 36 independence minors and 12 controls. The final overlap refresh covered 412 open PRs and 359 Discussion records with complete pagination.

Scope: conditional target screen, with no new supplier or kappa. Changed exterior work must re-establish each retained block's boundary premises. Heterogeneous schedules require their weighted bills. Wider interfaces, different centre/coverage/halving contracts, physical realization, precision/tape, analytic transfer and bit-side improvement remain separate. The all-order block theorem remains credited; finite replay does not formalize it or prove multiplication.

Handoff: specify new array/frame/output contracts for at least eight blocks and price the full replacement, including extra copies, adapters and restoration. A concrete admitted replacement is the blocker. The package's README/TASK give the exact next step and alternatives outside this model.

Credit Ali Romman/PR1429, Thomas DiFiore, Douglas Colkitt/PR1240, the PR1012 coverage-law authors, Rohan Arun, Jeremy Kothe and the retained lineage. Substantial OpenAI Codex assistance in proof, code and prose, with read-only source exploration; no independent human review. Scope released.