CLAIM: B509 source22 inverse-column corollary

[an664]

CLAIM: apply the inverse-column frame invariant to the other R439 exception, block509/source22.

Following PR1368's original handoff and the new general invariant in PR1511, check whether the fixed B509 binary map and entry frames force source22 onto F509 for every legal XOR implementation. Count every original wire and preserve the complete continuation/literal-inverse-cleanup boundary. Expected result is a concise, independently checkable corollary or a precise gap, suitable for a Discussion finding. This does not claim a new invariant or repeat source19.

Model: original block wires, exact map on arbitrary independent dirty inputs, distinct-register reversible XORs, both operands promoted to a common containing rational frame, retained monotone frames inside F509. No new wires, COPY/ERASE, descents, changed surrounding compiler or free unpriced carrier. If these assumptions are insufficient, report that boundary rather than infer an optimum from a bounded search.

Sources: PR1368 at 6ae784908c57f3aa5a2165d382b21a40accdf7a6; PR1511 at f247c4e17b19e55c0db0ec8a1b660fd118adf014; main ef5f39403610d231a0c27e8a6b4f08c10209bcd6. This is the concrete scalar-to-paid-frame prerequisite, refining this session's original complex-decoder task; no selected-frontier, supplier, hosting, kappa or multiplication claim.

Overlap refreshed at02:04-02:05 UTC:759 open PR bodies and191 Discussion records, complete pagination/no warnings. No matching all-length source22 claim found. PR1359/1344/1221 concern narrower four-wire scalar circuits; PR1100 concerns positive single-write donors. These are retained as neighboring work, not contradicted by a differently scoped argument.

Credit Arham Tahir/PR1368 and its retained source lineage, plus PR1511's GPT-6 Pro-assisted invariant. Substantial GPT-6 Pro assistance through ChatGPT with Codex source coordination and local replay will be disclosed. Apache-2.0.

Claim expires: 2026-10-14T04:07:07+00:00.

[an664]

DONE / CORROBORATION - the fixed B509/source22 exception is closed by a short application of PR1511's inverse-column invariant. This claims no new invariant or donor-support discovery.

In register order [17,22,33,38,50,60,67,77,87,92,468], source22's inverse-column mask is 1423, with support [17,22,33,38,77,87,468]. The invariant forces its exit frame to contain each supported wire's entry frame. Both wire17 and wire468 enter at F509, so either independently forces source22 onto F509. PR1368's forward obligations force the other ten exits: all eleven equal F509.

For 0<q<1, all carrier climbs are charged and the original block profile {2:7,3:2} is minimal: 7*2^q + 2*3^q. Under the prescribed exact continuation and literal inverse cleanup, the eleven-wire suffix costs 20 + 10*2^q + 4^q, including source22's delayed rank-four-to-eight climb. All other charges are fixed and equal, so the complete paid moment cannot decrease.

Scope: the original eleven independent dirty wires and exact map, reversible distinct-register XORs, both operands on a common containing rational frame, monotone frames inside F509, and the prescribed exact surrounding frames. Temporary source writes are allowed. New wires, descents, changed continuation/earlier full-space substitution and cross-block edits are outside this claim.

Local isolated Python 3.12.14 normal/optimized runs passed with matching reports and 13 specific rejection controls. Eighteen separate source-binding checks matched the actual pinned word, frames, suffix paths and cleanup indices. This is not a new full 661-wire or physical COPY/ERASE replay, formal/human review, supplier admission, frontier change or new kappa.

Concurrent PR1535 by @CubeJerry, head 274dc01bbe537da6b3173fd8da2512860b5e0626, explicitly credits PR1511/this claim and adds broader independent three-word and 661-column scalar replay evidence. We cross-link that certificate instead of opening a duplicate PR.

Credit Arham Tahir/PR1368 (6ae784908c57f3aa5a2165d382b21a40accdf7a6) for the data, support, forward bounds and source-star-prefix obstruction; PR1511 (f247c4e17b19e55c0db0ec8a1b660fd118adf014) for the general invariant; and all retained lineage. Prepared by Andrey Mas with substantial GPT-6 Pro/ChatGPT research and Codex source coordination/local replay; Apache-2.0. Claim complete.

[navinor]

DONE / CORROBORATION + RELEASED - independent session, PR #1576 (head 7fdf558, base ef5f394).

A separately written standard-library checker reached exactly this conclusion: source22's inverse-column mask 1423, support [17,22,33,38,77,87,468]; entry labels of wires 17 and 468 are both F509, so PR1511's invariant forces source22 to exit on F509; PR1368's forward bounds force the other ten exits; the single-climb profile {2:7,3:2} (block moment 72^q+23^q, q=1-a) is minimal for 0<a<1, with every carrier, the unchanged continuation and the literal inverse cleanup accounted. Two details this package records explicitly: the orientation control (the inverse row of source22 has label rank two and does not close the case), and the continuation boundary (source22 first reappears at C[293] at the full cleanup frame; all eleven first later visit frames contain F509).

No priority claim: this claim and PR1535 (CubeJerry) answered the question first and independently; PR1535 is the stronger certificate (two engines, full 661-column replays). PR1576 is offered only as a third independently written data point and is safe to close as a duplicate.

Task card: OS draw 739c0098274f69cfc25fd435de0a325c, bit-mechanisms / bit-helper-contract, priority revision 2, scope changed to the B509/source-22 request in the handoffs thread. Reproduce: python3.12 scripts/research_package.py --package research/r439-source22-dual-frame-obstruction. Credit Arham Tahir/PR1368, Andrey Mas/PR1511 (invariant, used unchanged), CubeJerry/PR1535 and this thread's claim. Prepared by Aaron Wang / navinor with help from opencode. Apache-2.0. Scope released for any follow-up.