DONE: PR1062 two-copy scatter saves 120 ADDs (#1704)

[RossRichardson]

DONE / HANDOFF — PR1704, exact tested/published head 7f14aa7285cf10a7be350472fab25a25ef898484. Claim complete and released.

The fixed PR1062 scatter has a two-live-copy construction with 120 fewer ADDs, including preparation/restoration: scatter 527→407; complete word 11,500→11,380. Exhaustion of all 2,620 disjoint pair/singleton partitions gives 105 optima. This is the stated pair-block class, not arbitrary two-temporary optimality.

Both full programs agree on all 661 dirty input columns in both directions. A separately written integer-column checker verifies equality of their full signed lifts, independently reproduces the optimum via subset DP, and recounts exact frame ranks. All 2,620 partitions pass the dirty scatter boundary; nine test groups cover chronological ERASE, all temporary-gate omissions, sign/role/accounting faults, receipt/source corruptions and read-only relocation. The committed-head registered Python3.12 replay, selected-record integrity and binding-only baseline check pass. Hosted CI has 61 queued checks at 07:25 UTC; no hosted pass is claimed.

Cost/remaining boundary: nine rank-seven COPYs and all persistent frame paths are unchanged; peak live copied slots rise 1→2 (sum of their ranks 7→14). The reverse positive bound rises 5,911,840→6,248,884; strict inherited algebraic guards still pass. The native single-copy/immutable-temporary checker is unchanged and does not admit this proposed contract. Next useful work is a two-slot native emitter plus complete physical workspace/hosting/precision admission. No new kappa, selected change, full cold replay, outer theorem or independent human review.

Reproduce: python3.12 -B scripts/research_package.py --package research/bit-two-copy-scatter. Proof, task, sources and evidence. Final overlap refresh at 07:22 UTC covered 389 open PRs and 346 discussion records with complete pagination and no warnings.

Credit Sagar Thakrar's PR1062, the PR967/926 and PR589/555 lineages, Dylan Crow's exporter, woklerx's live-copy/late-mixing and semantic-D work, and earlier restored-sharing mechanisms. Ross Richardson with substantial OpenAI Codex assistance; no subagents. The pair-sum identity is standard; this result is its scoped contract and source-bound application.

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Original claim:

CLAIM — PR1062 two-copy scatter contract

Question: can two simultaneously live retained-total copies share a zero-frame XOR, restore each original copied value before ERASE, and reduce the complete scalar scatter bill? Base 5e554ff58d01921747d27177045c0061f31e1ad1; input is the unchanged PR1062 candidate in research/r439-bsection-stars-seed01/candidate.json.gz.

Method/domain: prove the arbitrary-dirty boundary of one signed two-copy block, then exhaust all disjoint pair/singleton partitions of the nine retained totals. Include both prepare/restore ADDs, all COPY/ERASE ranks, the second live temporary, complete word replay and precision bounds. This changes the native single-copy/immutable-temporary contract; it does not disable the old checker or claim native admission. No recursive-moment or kappa gain is expected because the nine rank-seven COPY charges and persistent frame paths remain fixed.

Assigned bit-helper-contract, nonce ffd7509ee115bd599b3ebe2151ecdd39; scope explicitly changed from H2/K (covered by PR1194/1306) to mutable copied temporaries. First-step PR1062 replay passed. Fresh overlap covered 382 open PRs and 332 discussion records with complete pagination and no warnings; prior live-copy stabilizer and late retained-total mixing notes are credited. COPY outputs are at ZERO in the pinned exporter, so original-helper frame-mixing bounds do not directly settle this question.

Expected artifact: one source-bound finite package with a replacement boundary lemma, complete priced local word, exact restricted optimum and meaningful failure controls. Credit Sagar Thakrar PR1062, PR967 helper stars, DreamingOfClouds PR589, eumemic PR555, Dylan Crow's exporter, woklerx's live-copy and late-mixing audits, and the restored-sharing lineage. Prepared by Ross Richardson with substantial OpenAI Codex assistance. Claim expires 2026-10-14T08:58:00Z.