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Prepared for @CubeJerry with substantial OpenAI assistance. Exact source-bound proof, independent full-matrix reconstruction, and literal singularity certificates; no new kappa.
Prepared for @CubeJerry with substantial OpenAI assistance. Certify all 46,381 rational event pairs for deletion 10947, with separate native/full-inverse reconstruction, reviewed proof, literal controls and fresh export replay; no new kappa.
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Two exact coefficient-edit obstructions for the pinned #6824 native word. No new κ. Both allow arbitrary supported invertible rational endpoint hubs. The remaining scalar operands and order are fixed, with no route changes beyond the proposed contact contraction.
Any of 1,278 eligible ADD deletions, with one other scalar coefficient changed. The ADDs occur at 1,466 single-contact frame visits. The complete screen over existing ADD/COPY/SCALE compensators leaves 172 pairs, including 69 with zero original boundary derivative. Of these, 157 boundary equations are inconsistent; all 15 remaining public maps have rank 771 and explicit null vectors.
Deletion 10947, with two other scalar coefficients changed jointly. This is the specific helper-438 contraction from rank 1 + rank 1 to rank 2. A complete rank-based screen leaves 46,381 unordered compensator pairs. There are 99 inconsistent linear monomial systems, 43,334 direct determinant identities, 2,012 fixed-x identities and 936 fixed-y identities. Every C1-compatible map is singular. The checker freshly closes the four one-compensator cases as well. This extension applies only to deletion 10947; other three-event edits remain open.
These results extend #6835's unchanged-middle hub analysis to two explicit coefficient-edit classes. The response formulas include destructive owned resets, both event orders and the mixed coefficient term. The proofs use the invariant boundary block and necessary public invertibility; they do not require a new hub-existence theorem. Edits inside freely replaced boundary pieces are absorbed into those replacements, with the remaining case reduced to the checked smaller domain. COPY overwrite and arbitrary rational scalar values are favorable relaxations.
Base:
7c49fe32c55de02c2c873655c804b16e4c3fef0a.Native #6824:
2a7ca44fbda3abaa4df355b183ed7d7478eef7c1.Retained export and hub decomposition #6835:
44316f3e6023a7f8c516360e22e9efd6f0fe48c5.Exact source blobs, SHA-256 pins and the native payload digest are retained.
Reproduce with Python 3.12 and the standard library:
Expected:
PASS_REGISTERED_RESEARCH_PACKAGE, with the two distinct domains and dispositions above. The joint checker requires--packageand authenticates the primary verifier before importing it.Executed checks include normal and optimized primary/joint replays, separate complete reconstructions of both edit domains, and 14 literal joint endpoint/rank controls. The independent joint implementation uses its own native replay, full public inverse and expanded C1 equations; its 46,381-pair digest and all four dispositions agree. Positive controls include successful joint coefficient repair; a native mutation control rejects omission of the mixed term. All six registered commands, committed bytes/modes, export integrity and all six fresh Git-free exported replays pass. The complete remote tree matches tested contents. Review records distinguish author checks and separate AI implementations.
This is a deterministic obstruction for the declared edit domains. It constructs no improved word or complete supplier and proves no general minimum number of edits. New operands, additional compensators, new operations and changed routes remain open. The selected #6030 value
0.003125804and all five framework assumptions remain unchanged; complete selected/compiler/precision/analytic replay is not claimed.By @CubeJerry with substantial OpenAI assistance and separate AI-agent mathematical and implementation reviews; no human or proof-kernel acceptance. Credit DreamingOfClouds (#6824/#6835) and the retained native lineage and notices. Apache-2.0.
Proofs, exact contracts, certificates and limitations:
https://github.com/CubeJerry/integer-mult-bounds/tree/2f94be69001a94ad6577da73930c9c7c6c92fcfa/research/p104-contact-coefficient-rigidity