FPRD LabShare an approach

← Claims

Computational theorem · quotient collapse

QA-BUCK-COLLAPSE-016

Arbitrary winding collapses the mod-three quotient

Exact statement

With arbitrary winding, the three atom grammars become one 40-element mod-three conjugacy class, and its eighth power fills Sp⁡4(F3)\operatorname{Sp}_4(\mathbb F_3).

StatusExact certificate; imported conservatively
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

Stored orbit certificates and the written proof support the claim, but the imported replay scripts lack one helper module.

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

  • The finite image becoming indiscriminate neither proves nor refutes an integral lift.

Open work

Restore the missing helper and rerun the full closure.