Counterexample · finite observation loss

QA-BUCK-FIB-X01

Degree-three agreement can fail at degree four

Exact statement

A selected nonexact word agrees with its target through degree three of the integral Magnus expansion and first differs in degree four.

StatusExact certificate; imported conservatively
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 stored faithful Artin and Magnus transcript pins the first differing degree.

Verification notes

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

Limitations

  • Rejecting this word does not reject other lifts in its quotient fibre.

Open work

Compute the full fibre product image before drawing an obstruction conclusion.