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Finite theorem · nonzero sewing obstruction

QA-GR-T02

The two-P3 synchronization obstruction

Exact statement

The deck of 2P32P_3 has 18 type-slot synchronizations in two symmetry orbits; precisely the six-element P=QP=Q orbit sews, while the twelve-element P≠QP\ne Q orbit does not.

StatusProved and independently reproduced
External reviewNo documented external or specialist review of this Quotient Arsenal result is recorded.

Context

Anonymous overlap types can all agree while the cards still fail to share one coherent naming. The smallest computed witness converts that mismatch into an equivariant matching defect.

Proof or evidence

Every synchronization has 4,096 candidate row namings. All 4,096 are coherent for each of the six P=QP=Q synchronizations, and none is coherent for any of the twelve P≠QP\ne Q synchronizations.

Graph-deck synchronization proof and independent audit →

Verification notes

An independent implementation reconstructed all 18 type-slot synchronizations, all 73,728 candidate row namings, the two symmetry orbits, all 864 S2 x S4 equivariance actions, and the 52-graph marked-orbit control through order five.

Limitations

  • The theorem concerns the declared type-slot quotient, not the full reconstruction conjecture.

Open work

Test receipts stronger than anonymous overlap types.