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
Arbitrary conjugation collapses the mod-three atom classes and later alternate lifts survive.
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.