FPRD LabShare an approach

← Claims

Theorem · linearization

QA-HUR-FIB-T02

One-step congruence kernels linearize

Exact statement

A one-step pp-power congruence kernel is an Fp\mathbb F_p-vector space, and multiplication linearizes in its top layer.

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

Cross terms vanish modulo the next power.

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

  • Comparing complete first-layer solution families introduces quadratic dependence one level later.

Open work

Track the first nonvanishing cross term explicitly.