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Theorem · sewing receipt

QA-BUCK-DIAG-012

Internal crossing equation

Exact statement

Each endpoint component obeys an exact internal crossing equation, completing the colored abelian receipt omitted by cross-linking alone.

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

Diagonal crossing counts are additive and pinned by 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

  • The complete colored abelian receipt remains weaker than the nonabelian braid lift problem.

Open work

Use it to remove false positive occupancy types.