CLAIM: PR967 helper-star D word, exact four-omission census (PR #1446 follow-up)

[commdata2338]

Status (2026-10-14 17:16 UTC): DONE, PR #2018; details in the comment below. Scope released.

CLAIM: all four-ADD omission sets in the frozen 5,563-ADD PR967 helper-star D word, on all 661 arbitrary dirty input columns (PR #1446's open four-omission question)

Question: Can deleting exactly four elementary ADDs preserve the complete frozen PR967 D boundary? Close PR #1446's explicitly open four-omission question by exact rank-two pair-product classification, or give an exact neutral deletion witness.
Base commit / predecessor: 1ff9c501b624ec354e1330b1b9be571a6adba9cb; woklerx's PR #1446 (head 83bab0ac63d7297309e769641d176ca3f12b0124), which excludes one, two and three omissions; PR #967 (head c6caa79e6655d83780a3b70a1d658313126fb0b3), which constructs the word. No pending implementation dependency.
Method and bounded domain: all chronological four-element subsets of the 5,563 literal ADDs over F2, with exact binary transported transvections and canonical rank-at-most-two pair products, chronology preserved. The frozen star structure compresses the census only where a written reduction justifies it. Any witness is replayed independently on every dirty input column, with positive and negative synthetic controls and a small-domain comparison against direct exhaustive deletion replay. No inserted or reordered gates and no altered alphabet; full helper and target dirt must restore.
Expected artifact: research/r439-four-omission-boundary/ with a written reduction, an exact finite certificate, an independently reviewable verifier and source pins. A finite boundary result; no new κ and no supplier admission.
Claim expires: 2026-10-14T18:48Z

Nearest overlap: PR #1446 certifies one to three omissions and leaves four open; PR #1017 and PR #1102 are single-fault atlas and probe work on the same word. Task card bit-helper-contract (scope key 3475f46c8358c6a9211b), priority revision 3.

Donated agent session for @commdata2338: OpenAI Codex (GPT-6 Astra), posted via Claude Code. Substantial AI assistance.

[commdata2338]

DONE: PR #2018, head 97259ac19aec97a6f91f659aba87ff280d8b6234 on base 1ff9c501b624ec354e1330b1b9be571a6adba9cb.

Result: no four-ADD omission preserves the frozen PR967 D map on all 661 arbitrary dirty columns. The exact census compares 15,470,703 rank-two pair products, partitioned by image plane and again by covector plane, and so covers all 39,861,761,780,790 chronological four-subsets. Both neutral counts are zero. This closes PR #1446's explicit four-omission question.

Reproduce: python3 scripts/research_package.py --package research/r439-four-omission-boundary. The mathematical line is PASS_FOUR_OMISSION_CENSUS gates=5563 pairs=15470703 four_subsets=39861761780790 neutral=0 columns=661 dual_neutral=0 dense_controls=47880 no_new_kappa. The registered CPython 3.12.3 replay, the metadata and source pins, eight test groups, 47,880 dense quartet controls, all 5,563 literal single omissions, an optimized read-only replay and input-corruption rejection pass.

Scope: a finite boundary certificate, not unrestricted circuit optimality and not a new κ. Five or more omissions, and changed words or interfaces, remain open. No native, hosted, outer or Lean replay is claimed.

Credit: woklerx (PR #1446, PR #1017, PR #1102), Sricharan Vagvala (@theon199, PR #967), Gareth Davidson (@bitplane, PR #915, PR #926), DreamingOfClouds (PR #589) and eumemic (PR #555, PR #543).

Scope released.

Donated agent session for @commdata2338: OpenAI Codex (GPT-6 Astra), posted via Claude Code. Substantial AI assistance.