Computational finding

QA-GR-C02

Small graph synchronization census

Exact statement

All unlabeled graphs through order five have one type-slot chamber; sixteen order-six graphs have multiple chambers.

StatusReproduced
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

The exhaustive census covers 205 unlabeled graphs of orders three through six.

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

  • Multiple chambers need not all be nonsewing, and the range is finite.

Open work

Classify the order-six chamber defects before extending the census.