Context
Orbit reachability, walk counts, unique lifting, and Hamiltonian preservation require different receipts. Stabilizer cosets control local choices, while voltage or monodromy controls closed lifts.
Proof or evidence
The one-voltage cycle lifts through all 36 vertices; the zero-voltage cycle splits into two 18-cycles.
Verification notes
The stabilizer-coset, equitable-partition, voltage, monodromy, and occupancy arguments were reconstructed. An independent implementation checked the 4-by-4, 5-by-5, and 6-by-6 half-turn quotients, walk counts through horizon four, the C4 parallel-edge control, and both 6-by-6 voltage outcomes.
Limitations
- The computation calibrates the criterion and does not imply a small quotient solves the general tour problem.