Research: independent corroboration of the B509/source-22 dual-frame obstruction (no new kappa)

[navinor]

Change and mathematical scope

Independent corroboration; no priority claim and no new kappa. This package applies the all-length inverse-column frame invariant of #1511 (Andrey Mas) to the separately pinned R439 block-509 boundary — the second exceptional source left open by #1368 (Arham Tahir) and requested in the handoffs thread.

For the fixed eleven-wire F509 map on registers [17,22,33,38,50,60,67,77,87,92,468] (dirty helper 468), source 22's inverse-column mask is 1423, support [17,22,33,38,77,87,468]. Wires 17 and 468 enter on the full block frame F509, so the invariant forces W_22^exit = F509 for every legal replacement circuit (arbitrary finite length, temporary writes, cancellation, carriers). PR1368's forward bounds force the other ten exits; the complete forced-exit table is in the README. Entry ranks (4,2,2,2,1,1,2,2,2,2,4) give the single-climb invoice {2:7, 3:2}, block moment 7·2^q + 2·3^q at q = 1-a, minimal for 0 < a < 1 by the concavity step t^q >= t; the unchanged continuation and the literal inverse cleanup cannot turn a replacement into a complete paid-frame improvement. Source 22's first later visit is C[293] at the full cleanup frame; all eleven first later visit frames contain F509.

This is a scoped obstruction in the PR1368 model (original wires, reversible XORs, retained monotone common-frame promotions inside F509, fixed continuation and cleanup). It is not a new kappa, supplier, or multiplication theorem.

Concurrent work (read this first)

The pre-submission overlap refresh found the same question answered concurrently while this session was working:

• Discussion 1515 posted the same corollary with the same constants (1423, same support, same {2:7, 3:2} conclusion).
• Research: independently certify the B509 inverse-frame obstruction #1535 (CubeJerry) certifies the same obstruction with two exact implementations, full 661-column scalar replays across three current-main words, and its own registered package.

#1535 is the stronger submission. This PR claims neither priority nor a different proof method; it is a third independently written data point, offered so the maintainers can pick whichever checker style they prefer. What it adds relative to the summary of #1535 is narrow: (i) an explicit orientation control — the inverse row of source 22 has label rank two and does not close the case, only the inverse column does (the trap PR1511 also guards); (ii) the recorded continuation boundary (C[293], full cleanup frame, all eleven first later visits); (iii) a dependency audit of both invariants at every prefix of the constructed fixture, mirroring the PR1511 checker discipline; (iv) a single-file self-contained stdlib checker with no generated artifacts. None of this changes the theorem. Closing this PR as a duplicate of #1535 loses no mathematics.

Task card, assignment and exact heads

• Drawn assignment: OS nonce 739c0098274f69cfc25fd435de0a325c, track bit-mechanisms, priority revision 2; cards bit-new-register-model and bit-helper-contract.
• Scope changed (recorded in TASK.json): bit-new-register-model is heavily overlapped (open PRs PR 1414, PR 1491, PR 1495, PR 1496, discussion 1317) and bit-helper-contract's semantic-D question is covered by Prove a semantic zero-frame D contract for a fixed R439 word #1194 / Research: independently check semantic-D bridge for composed R439 word #1311. The concrete object is the open handoff request above.
• Base commit: ef5f39403610d231a0c27e8a6b4f08c10209bcd6; branch research/agent-19-b509-source22-dual-frame-739c0098.
• Predecessor heads: Research: a lower-frame obstruction for eight R439 phase-B blocks #1368 head 6ae784908c57f3aa5a2165d382b21a40accdf7a6; close source19 frame exception with inverse column invariant #1511 head f247c4e17b19e55c0db0ec8a1b660fd118adf014. Concurrent: Research: independently certify the B509 inverse-frame obstruction #1535 head 274dc01bbe537da6b3173fd8da2512860b5e0626 (reviewed before submission only through its PR body; no code imported).
• The local task card is notes/task-card-agent19-b509-source22.md.

Evidence and reproduction

Standard library only, from the repository root:

python3.12 scripts/research_package.py --package research/r439-source22-dual-frame-obstruction

Expected:

PASS_R439_F509_SOURCE22_DUAL_BARRIER
failure_controls=11 inverse_column=[17, 22, 33, 38, 77, 87, 468] all_exits=F509 bill={2:7,3:2}
PASS_REGISTERED_RESEARCH_PACKAGE research/r439-source22-dual-frame-obstruction outcome=negative-result

Also run directly: python3 -I -O -B research/r439-source22-dual-frame-obstruction/verify.py --word research/e8-bit-p111-tuned/tune/bitE8mut-p111-tuned.json.gz. Both forms were executed locally (CPython 3.12.14, Windows, normal and optimized): the exact rational spans and Gram determinant, both binary products, both inverse orientations, the full forced-exit table, essentiality of all wires, the invoice and exact integer concavity samples, a 32-gate Gaussian fixture audited at every prefix and replayed on all 2,048 dirty assignments with reversed-gate cleanup, and eleven failure controls (rank-two and rank-three source-22 exits, corrupt inverse bit, singular map, self ADD, extra register, one-sided hosting, frame descent, truncated circuit, omitted inverse gate, corrupted source bytes). The --word adapter is read-only and binds the constants to the pinned gzip (SHA-256 e3e301e62bc2b41dbf1ceac0acf3d35824ebeab1848c5a2142d4577b109da52f, Git blob 85a4499bf9e4911a705d50567a2c2ef6cf23739a): entry frames after D, A, B[:283], slice B[283:314] (31 ADDs), endpoint matrix, {2:7,3:2} bill, continuation visits, and the literal full-frame cleanup shape. scripts/research_package.py --check-only passes (PASS_PACKAGE_METADATA_AND_PINS).

Not checked: a whole-word 661-wire dirty replay by this package (the adapter is slice-level; #1535 provides full-word replays), native/COPY-ERASE physical replay, the selected cold replay, hosted CI, Lean or independent human proof review, and any hosting/precision/tape/all-size/analytic admission. The invariant's universal quantifiers rest on PR1511's written induction, not on the finite controls.

Limitations and open next questions

Confined to the fixed block-509 map and interface above; not enlarged seams, new registers, nonmonotone reuse, changed gate rules or continuation compilers. With source 19 closed by #1511 and source 22 closed here (and independently by #1535), all ten blocks of the #1368 handoff are covered in this model. Structured next questions are in TASK.json and the README: the same audit on phase-A/D boundaries; scalar resynthesis at the now-minimal frame invoice; a Lean formalization of the invariant. The next-question suggestion of #1535 (enlarge the seam to change donor entry frames) is complementary and not repeated here.

Credit and disclosure

Predecessor credit: Arham Tahir (substantial OpenAI Codex assistance) for #1368 — block data, entry labels, forward bounds, the two named exceptions and the prefix inverse-matrix calculation; Andrey Mas (substantial GPT-6 Pro assistance through ChatGPT) for #1511 — the inverse-column invariant used unchanged here. Concurrent: discussion 1515 and CubeJerry / #1535. Retained lineage: Aaron Wang / #1015; Ross Richardson / #923; Sagar Thakrar / #1062; Sricharan Vagvala / #967; Gareth Davidson / #915 and #926; DreamingOfClouds / #589; eumemic / #555 and #543.

Contribution by Aaron Wang / navinor, with help from opencode (substantial AI assistance in the mathematics layout, verifier, packaging and writing). No predecessor implementation is imported. Apache-2.0. upstream/, frozen sources, pinned evidence and the selected frontier are unchanged.

Workflow feedback

One friction item: python3 -B -m unittest discover -s tests -p 'test_research_*.py' has six pre-existing failures on Windows (test_research_onboarding): the fixture's Path.write_text("...\n") is newline-translated to CRLF while git show returns the LF blob, so new_research_package.create raises "source has uncommitted changes or differs from chosen base: input.txt". Unrelated to this package; suggest writing fixture bytes with newline="" or comparing normalized newlines.

[Mister-Meeseeks]

Batch review at 7fdf558a8e4bcf9e98642e9ba688bc66b6629e86.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Independent source-22 inverse-column certificate corroborates PR1535 and credits PR1511. The endpoint frame and fixed-continuation invoice are forced; integration corrects a sentence to preserve the documented lower initial frame.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.