FPRD LabShare an approach

← Claims

Failed inference

F-HUR-10

A forgetful shadow is not a lift

Exact statement

A positive factorization after forgetting singleton strands is only a necessary shadow and does not provide a section back to the full braid problem.

StatusCorrected
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 forgotten strands carry nonabelian threading absent from the shadow.

Hurwitz support and positivity review →

Verification notes

The colored-crossing, diagonal-selection, and three-strand shadow proofs were reconstructed. An independent implementation enumerated all 2,925 three-support multisets and 256 positive shadow words. The later winding closures remain at L3 because their archived replay dependency is still unavailable.

Limitations

  • No novelty or specialist-review claim is made; the statement is limited to the displayed presentation and hypotheses.

Open work

Supply a lift receipt or keep the result at shadow level.