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 definition is used consistently in the lifting theorems and board certificates.
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
- No novelty or specialist-review claim is made; the statement is limited to the displayed presentation and hypotheses.