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 canonical patterns are enumerated and rejected in the pinned finite model.
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
- Arbitrary winding changes the lift fibre, so the result is not a global nonexistence theorem.