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Research: independently certify the B509 inverse-frame obstruction - #1535
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Batch review at Merged to Reviewed scope: Independent B509 inverse-column footprint certificate across three source words closes the source22 exception and proves the retained fixed-boundary climb floor. Full scalar/frame replays and exact minor witnesses pass; concurrent invariant work is credited and changed seams remain open. 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. |
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This adds an independently checkable certificate for the fixed R439 B509/source-22 boundary. Although source 22 finishes unchanged, inverse dependencies force it to reach the full rank-four frame. The package supplies a scoped written proof, two separate exact implementations, pinned evidence, and failure controls.
No new κ. The selected conditional κ remains 0.001672660197076918.
Exact result and scope
For the fixed B509 map on the original 11 wires, all 11 exit frames must equal F509 under exact reversible common-frame operations with monotone rational frames contained in F509.
Source 22's inverse-column support is [17,22,33,38,77,87,468]. Registers 17 and 468 already enter on F509; either forces source 22 to reach F509. Forward dependencies already force the other ten exits.
Entry ranks are [4,2,2,2,1,1,2,2,2,2,4]. Consequently the existing frame bill, 7H2 + 2H3, is minimal for every supplier exponent 0<a<1: nine nonzero children, rank mass 20. Splitting climbs cannot improve this moment. This is a frame-cost result with the surrounding contract and external charges fixed, not scalar-circuit optimality.
The written invariant covers arbitrary finite circuit length and rational subframes outside the existing catalogue. Finite replays corroborate its instance data; they are not formal verification of the full multiplication theorem.
Added evidence and concurrent work
PR1368 identified the B509/source-22 exception left unresolved by forward-only dependencies. PR1128 provides related two-sided boundary reasoning.
The publication refresh found Andrey Mas/an664's PR1511 proving the same general inverse-column invariant for B508/source19, followed by Discussion1515 claiming the B509 corollary. Both are credited. This submission claims neither priority for the invariant/corollary nor a different mathematical proof method.
Its additional contribution is:
The full-word replay recovers rank mass 5,129 and nine rank-seven COPY charges. It models scatter as its exact additive map; it does not replay physical COPY/ERASE operations.
Both implementations were written in the same assistant session. No predecessor implementation is imported.
Base and pinned dependencies
Starting commit:
ef5f394
Runtime inputs, pinned by Git blob and SHA256 in SOURCES.json:
Git blob 85a4499bf9e4911a705d50567a2c2ef6cf23739a
Git blob d95fc2bf795fd9ef8d8bae9d70693c5e64948cec
Git blob 9a17b4920334878d6c949191f6931bd97126fe3c
Context references:
These pending-PR references are credited context, not runtime dependencies or accepted-frontier substitutions. Python 3.12 standard library only; tested with CPython 3.12.14.
Reproduction and executed checks
From the repository root:
Expected final result:
Executed successfully:
Controls reject rank-two and rank-three source exits, omitted/reversed gates, a missing inverse donor, frame descent, dirt leakage, and a dependent rank witness. Both engines reject corrupted inverse data, understated carrier cost, a false rank-three receipt, and changed source bytes. Actual-word tests reject an illegal lower-frame gate and an endpoint-preserving cleanup corruption.
Limitations and handoff
The result excludes extra wires, COPY/ERASE inside the replacement, noninvertible operations, frame descents, frames outside F509, changed entry contracts, and cross-block rewrites. It does not establish a new supplier or outer assembly.
Native physical-address/COPY/ERASE replay, the selected full cold replay, and proof-assistant verification were not run. Inherited all-size/compiler, common-label, mutable-source, hosting, precision/tape, and analytic obligations remain. PR1062's semantic-D H2/K adoption gap is unchanged.
A useful next investigation would enlarge the seam to change the entry frames of donors 17 or 468, then recompute exact dependencies and price every resulting operation. More synthesis inside the closed fixed interface is not proposed.
OS assignment seed: 19, bit-supplier track. TASK.json records three candidate tasks, the local claim/result, stopping rule, and overlap coverage. Public HTML checks were partial; API/posting access was unavailable, so the coordination update remains local. No synthesis search or search-exhaustion claim is made.
Attribution and disclosure
Contribution by @CubeJerry with substantial OpenAI Codex assistance in research, proof, implementation, verification, and writing. No subagents or independent human review.
Credit Arham Tahir/PR1368; Ali Romman/PR1128; Andrey Mas/an664/PR1511 and Discussion1515; Aaron Wang/PR1015; Ross Richardson/PR923; Sagar Thakrar/PR1062; Sricharan Vagvala/PR967; Gareth Davidson/PR915/926; DreamingOfClouds/PR589; eumemic/PR555/543; and their retained compiler/frame/hosting/checker lineage.
New work is Apache-2.0. Upstream files, frozen predecessors, and the selected frontier are unchanged.