Failed approach · relational obstruction

F-HUR-02

Unary receipts do not decide Hurwitz equivalence

Exact statement

Equal endpoint, length, atom type, factor conjugacy classes, and abelian receipts can still leave positive factorizations in distinct Hurwitz orbits.

StatusRefuted by exact B3 witness
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 already-published QA-BK-T05 witness has generated permutation subgroups of orders two and six.

Verification notes

The exact written argument and available certificate were inspected; the public maturity level reflects whether import-time replay was complete.

Limitations

  • The witness is not itself a boundary multitwist factorization.

Open work

Use relational or subgroup receipts only within their proven scope.