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Corollary · orbit obstruction

QA-HUR-FIB-C08

Product-cokernel data separates quotient orbits

Exact statement

In a square-zero layer, product-image dimension, target membership, and the product-cokernel class are invariants of the quotient Hurwitz orbit.

StatusProved
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

It follows from the product-set bijection and affine linearization.

Hurwitz fibre theorem core and independent audit →

Verification notes

The ordered-product proof was reconstructed with its square-zero and mod-eight domains explicit. An independent implementation checked 69,632 affine/quadratic matrix identities and 1,625 relative Nielsen and split-central identities, including an order-reversal hostile control.

Limitations

  • The invariant may be incomplete.

Open work

Compare its discriminatory power with relative Nielsen stabilizers.