Counterexample · quantifier correction

QA-BUCK-MOVING-017

Candidate rejection is not fibre obstruction

Exact statement

Canonical rejection, arbitrary-winding permission, one candidate rejection, and alternate-lift permission can coexist; rejecting a chosen lift does not obstruct the whole fibre.

StatusExact finite realization; replay partly blocked
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 stored full-fibre certificates distinguish selected candidates from the complete allowed lift set.

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

  • Several exact replay scripts need a missing helper module.

Open work

Preserve the existential quantifier over complete lift fibres in every obstruction claim.