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Negative result · quotient saturation

F-HUR-13

More winding can make a quotient less selective

Exact statement

Enlarging the winding fibre saturates the mod-three image rather than sharpening it.

StatusStored exact computation
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 40-element class has full eighth power in the archived certificate; replay dependency is incomplete.

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

  • Finite-image saturation does not imply an integral lift.

Open work

Change the receipt doctrine instead of enlarging the same quotient.