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Finite counterexample · orbit separation

QA-BUCK-FIB-X04

Same residual product, different Hurwitz orbits

Exact statement

Two residual-two quotient words with the same degree-three product lie in different quotient Hurwitz orbits because their degree-four product receipts have ranks seven and ten and opposite target-lift decisions.

StatusStored exact certificates; replay dependency incomplete
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 rank and membership certificates invoke FPRD-QA-HUR-T08; import-time full replay is blocked by the missing helper.

Quotient Arsenal synthesis →

Verification notes

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

Limitations

  • This is a finite-model separation, not a B5 factorization classification.

Open work

Repair the verifier before checked status.