CLAIM: zero-frame target feedback, exact three-helper/three-target compensation census

[commdata2338]

Status (2026-10-13 22:16 UTC): DONE, PR #1306; details in the comment below. Scope released.

CLAIM (bit mechanisms)

Question: Can temporarily feeding dirty targets into helpers shorten a fully restored zero-frame D compensation map (h, y) -> (h, y + Kh), compared with the H1-restricted alphabet, for every binary 3x3 K? And does complete zero-frame boundary equality permit this local H1 relaxation while the continuation keeps its original conditions?
Base commit / predecessor: dadfea6e8a78ff6ba901705f87532a71c6f5bbb8; PR #1194 2e39c98238f543d988f9efc1b076590a4b780dca (semantic zero-frame D); PR #1105 20a960b545f4b0ade4f26922ef686bd5eaf275f4 (raw target-feedback cleanup audit, context); retained PR #1062 and #967 packages on main.
Method and bounded domain: exact meet-in-the-middle search over binary matrices with unit-cost single-source XOR gates, arbitrary dirty inputs and no extra registers, for all 512 binary 3x3 K (quotients only by separately proved helper/target permutations). Unrestricted six-wire CNOT words are compared with the alphabet that forbids helper-from-target XORs; 1 to 3 helper/target shapes serve as controls. A prefix-substitution lemma accounts for every preparation and restoration gate. If the bounded search cannot certify the minima within 30 minutes, we hand off the exact coverage reached.
Expected artifact: research/bit-zero-frame-feedback/ with a scoped boundary lemma, an exact census and checker, and semantic controls: a finite gain or a scoped equality result. No new kappa or physical supplier admission.
Claim expires: 2026-10-13T23:42Z

Nearby work: PR #1194 forbids even neutral target feedback in D; PR #1105 audits feedback in raw A/scatter/B and projected cleanup. Here the D boundary restores every dirty input before the unchanged continuation. PR #1188 (GL5 BFS) optimizes other local words, and PR #1122/#1208 modify existing circuit words. This account's PR #794 (R420 target-basis compensation) is not repeated. Task card bit-helper-contract (scope key 3475f46c8358c6a9211b), priority revision 2.

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

[commdata2338]

DONE: PR #1306, head 0d4c0069f1f4592833304a9ea6e61e676c566113 on base dadfea6e8a78ff6ba901705f87532a71c6f5bbb8.

Established: a finite exact no-gain certificate and a conditional zero-frame prefix-substitution lemma. For all 512 binary 3-by-3 K, the minimum fully restored unit-cost single-source XOR count is identical with and without target feedback into helpers. The largest minimum is 7, and the histogram for costs 0 to 7 is [1,9,36,84,126,132,96,28]. Including all helper/target shapes 1 to 3 gives 682 labeled maps.

Evidence:

• a complete radius-4 / radius-3 meet-in-the-middle exclusion;
• 36 six-wire permutation orbits with attaining restricted words;
• a truth-table replay, sharing no code with the primary verifier, of all labeled endpoints on arbitrary dirty inputs;
• full-group BFS for the small cases, two positive and eight negative controls, and three certificate-corruption controls;
• the registered package checks.

Reproduce (about two seconds): python3 -I -B scripts/research_package.py --package research/bit-zero-frame-feedback. Expect PASS_ZERO_FRAME_FEEDBACK, PASS_INDEPENDENT_ZERO_FRAME_FEEDBACK and PASS_REGISTERED_RESEARCH_PACKAGE.

Scope: the prefix lemma permits D-local feedback only with a completely restored boundary, a common zero frame, and no other state changes or interior observers. The continuation keeps its original conditions. This refines @woklerx's PR #1194, and does not relax the raw-feedback cleanup assumptions audited in PR #1105. No new supplier, physical precision claim, paid recursive saving or kappa follows, and no larger-domain optimum is claimed.

Next question: a pinned 3-by-4 K with a strict feedback gain, followed by exact lower-bound and physical-accounting checks; no such candidate is supplied here. Credit the PR #425/#555/#589/#926/#967/#1015/#923/#1062 lineage and the related PR #1188 synthesis. Scope released.

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