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Failed finite-quotient approach

F-HUR-15

Burau modulo four does not repair the quotient

Exact statement

Both squared packet types are invisible modulo four, and the length-eight active product set contains the identity.

StatusExact stored 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 archived finite product set has 192 elements and contains the target.

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

  • This does not prove all Burau-type quotients fail.

Open work

Do not continue the same low-layer quotient without a structural reason.