Research · Papers · What rank-one constraints can express · ML-041
An impossibility result for affine third factors of the named JSC-12 witness
For JSC-12 with q = current1 * middle2, no affine M makes qM vanish on honest {q=1} while rejecting the false point on K10, K11, K1x, all-K
Published 2026-08-29
For everyone
Plain summary
ML-041 rules out an affine repair route for the named JSC-12 witness. When taking q = current1 * middle2, no linear-plus-constant third factor M allows qM to vanish on all valid points while rejecting the named false point across the K cases. Small modifications still leave at least 2^19 valid k0=1 mismatches. A 36-term degree-three companion outside the affine class remains viable. This result applies strictly to this witness and affine third factors. The register records no prior-art position.
Result
For the named JSC-12 witness with q = current1 * middle2, no affine M makes qM vanish on honest {q=1} points while rejecting the named false point across K10, K11, K1x, and all-K. K00/K01 recover M = σ₁ + final1 + final2 at rank 30; K10, K11, K1x, and all-K have rank 36 / 42 and contain the false point. A viable k0=1 companion exists as a non-affine 36-term flip-support cubic.
Setting and definitions
q = current1 * middle2; M is the affine third factor. Labels K index the witness cases. Honest {q=1} points serve as interpolation points, and the named false point is the rejection target. M0 denotes the baseline companion.
Method
Exact interpolation across 42 features evaluates vanishing on honest {q=1} points, case ranks, and false-point containment. Non-zero weight-1 and weight-2 enlargements of M0 leave at least 2^19 honest k0=1 mismatches. Raw output and computation receipts are available in this paper's downloadable evidence pack.
Discussion
Scope is strictly limited to the named witness and affine candidate class. The 36-term non-affine cubic associated with MF-067 lies outside this closure. Corrections: none. Prior-art position: the register does not record this.
For everyone — the takeaway
What this means
A simple affine fix does not work for this specific witness. Multiplying current1 and middle2 by a linear-style third factor fails: every candidate either accepts the bad point or breaks on at least 2^19 valid cases. A 36-term cubic formula still works, so third-factor repairs remain possible in higher degrees. Apply this negative result only to the named witness and the affine class.
Register references
- Entry: ML-041.
- Receipts:
jsc_k1_companion_affine.log;jsc_k1_companion_cubic.json;ZKGOLF-FINDINGS-JSC-CUBIC-ALLK-2026-08-13.md. - Prior art: the register does not record this.
Every artifact named above is bundled in, or hashed by, this paper's evidence pack below.
Evidence pack
Everything needed to check this entry against its receipts: the register text, a manifest with a SHA-256 hash for every named receipt, and 3 of 3 receipt files bundled (6 KB). Anything not bundled is still hashed in the manifest and lives in the compute-box working trees.
Changelog
Last reviewed 2026-08-29
- 2026-08-29Published on this site.