Failed inference

F-HUR-07

Cross-linking alone is incomplete

Exact statement

The 55 cross-linking support solutions are necessary quotient solutions, not realized braid factorizations, because internal braid and label-order data are lost.

StatusCorrected
External reviewNo documented external or specialist review of this Quotient Arsenal result is recorded.

Context

Finite quotient words do not lift one factor at a time independently. Local affine lift fibres must be transported through the ordered product; the target defect then lives in a product-image cokernel that is invariant under quotient Hurwitz moves.

Proof or evidence

The diagonal receipt already eliminates one occupancy type and later lift receipts separate more.

Verification notes

The colored-crossing, diagonal-selection, and three-strand shadow proofs were reconstructed. An independent implementation enumerated all 2,925 three-support multisets and 256 positive shadow words. The later winding closures remain at L3 because their archived replay dependency is still unavailable.

Limitations

  • No novelty or specialist-review claim is made; the statement is limited to the displayed presentation and hypotheses.

Open work

Treat support enumeration as a first-stage filter only.