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Scoped obstruction: helper468 must end at rank eight after B88's target MOVE - #1393
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100-PR batch review at Merged to Reviewed scope: Complete helper468 ledger at 4,874 cuts, independent geometry/inverse engine and footprint proof. Single-frame rank-seven retirement is excluded throughout; the inherited two-sided lemma excludes all permitted rank-seven suffixes after cut177, leaving earlier staged mechanisms 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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Result and scope
Scoped negative result / exact boundary certificate. No new circuit, supplier or kappa.
For helper 468 in the fixed PR589 R439 bit word, the first rank-eight two-sided boundary footprint occurs at cut 177, when zero-based B gate 88 moves target 208 from frame 0 to frame 152, before its ADD. Applying Ali Romman's PR1128 boundary lemma, any permitted reversible linear suffix starting there or later must end helper 468 at rank eight. The class allows arbitrary rational frames, arbitrary suffix length, target access and extra restored dirty auxiliaries, with common-frame scalar operations and monotone frame changes; it excludes new COPY/descent/reset or altered prefixes.
All 4,697 later cuts have that general rank-eight obstruction. The earlier 177 cuts pass the two-sided rank-seven test and are not existence certificates. At those earlier cuts, an arbitrary one-common-frame restore-and-isolate block of rank at most seven is separately excluded because it would promote target 208 into an incompatible frame.
The complete ledger covers 4,874 boundaries, including the initial post-scatter cut and every 1,310 MOVE / 3,563 individual ADD boundary through original B/C and final MOVEs. Two different engines agree on every event, cut, restoration/dirty mask, geometry case and all 661 final forward/inverse columns.
Nine explicit frame-join certificates use nonzero integer minors and exact annihilating/separating normals. At the critical MOVE the scalar restoration row and dirty column remain unchanged, while the join's rank grows 7→8; its eight-line determinant is -32.
Task, predecessor credit and delta
Fresh OS seed 17, bit supplier track. Exact base
bce54fb3f895cbe5cd4c0eb477c3afeed100190f. Claim/discussion1362.PR1256, pinned at
d6d5a994fcdcd8d04ec439ff988daa8f37b17ece, supplies the initial-cut fixture and explicitly leaves later target-read cuts open. PR1128, pinned atdf29b159239b79d7e451d6ddda826a73e0e50a67, owns the general two-sided restoration/erasure lemma and its two earlier boundary analyses. The new result is its complete later-cut application and the exact B88 transition, not a new general lemma. Its earlier exploratory single-register readout scan did not supply this whole-cut restore/isolate theorem or earlier general-suffix cutoff.This changes the card from the already covered H2/K repair (PR1194/1311) to a residual/H4 boundary audit. It retains the assigned bit track. PR1253's fixed first-contact kernel entrances are a different question. Refreshed overlap covered 861 open PR bodies and 108 discussion/comment records, plus 60 recent all-state PRs; dependency heads were rechecked before submission. Coverage limits are recorded.
Only
research/r439-helper 468-late-cut/is added. The first 177 cuts remain open for staged mechanisms; new transport or a changed earlier prefix is outside the theorem. Any staged attempt keeping the original prefix must start before the target 208 MOVE. No selected frontier or frozen source is changed.Accounting and validation
The README/proof gives a favorable ideal two-slot width-seven invoice: retain all nine COPY/ERASE pairs, return all eight freed old host coordinates, consume an idle rank-seven slot, and account for the changed helper path. Both ideal deltas preserve rank mass and lower child count/moment. Preparation, source/storage, restoration and frame overhead are optimistically free in that screen. It is not an implemented invoice or physical host assignment; the boundary failures remain even under free added work.
Expected:
Independent replay:
Full registered replay passes on Python 3.12.15:
All ten tests pass on Python 3.12.15 and 3.14.7. Mathematical regressions cover 168 invertible binary 3×3 matrices, 1008 inverse updates and 10080 outside-frame span cases. Controls reject archive drift, omitted cuts/MOVEs, false minors/normals and receipt overwrites. Both engines pass under
-I -O -S -Bafter isolated relocation without writing files. Four source archives match exact Git blobs. The card's original R439 working example also passes.No native, new hosted/precision invoice, selected cold replay, remote CI pass or full multiplication formalization is claimed. Finite regressions check implementations; the written necessary-condition proof supplies the unbounded suffix/block scope.
Credit and next question
Credit Ross Richardson/PR1256, Ali Romman/PR1128 and PR1043, DreamingOfClouds/PR589, eumemic/PR555/543, Sagar Thakrar/PR1023, and the retained contributors in the unchanged NOTICE. Exact commits, Git blobs and archive hashes are in SOURCES.json; Apache-2.0 licensing is retained.
New work by Cinna Davis (@1337isnot1337) with substantial OpenAI Codex assistance. Both engines belong to this contribution; independent human review is not claimed.
Next step: one priced staged mechanism before the critical MOVE, with a full dirty-column replay, legal changed continuation and complete source/frame/restoration/hosting charges. The proof does not establish its existence.