FPRD LabShare an approach

← Claims

Theorem · necessary shadow

QA-BUCK-SHADOW-014

Rigid three-strand shadow lift

Exact statement

The eight-half branch has the rigid standard-alphabet shadow x4(yx2y)2=(xy)6x^4(yx^2y)^2=(xy)^6 after forgetting two singleton strands.

StatusProved
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 positive word identity and rigidity in the declared alphabet are checked exactly.

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

  • Forgetting singleton strands discards their nonabelian threading, so this is not a B5 lift.

Open work

Restore singleton threading through a relative Nielsen or nilpotent receipt.