Central lifted-product receipt

Exact statement

A compatible central extension supplies a lifted-product receipt invariant under Hurwitz moves and simultaneous conjugation; its action-groupoid cocycle is the central quotient-path receipt.

StatusProved and independently checked

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 S3 split-central audit verifies all product, equivariance, and centralizer identities.

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

Nonsplit and noncentral kernels require twisted or nonabelian receipts.

Open work

Compute the endpoint-stabilizer action in the first noncentral layer.