A complete quadratic fibre can have zero obstruction

Exact statement

For the selected residual-zero word, the vector-valued quadratic obstruction vanishes on all $2^{32}$ first-layer solutions, so every one lifts modulo eight in the pinned Magnus model.

StatusCertificate independently audited

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

All 529 quadratic coefficients vanish; the certificate-consistency verifier passes eight hostile checks.

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

Certificate consistency was rerun; the full orbit generator still depends on a missing helper.

Open work

Restore full recomputation before checked status.