Each ambiguous 5-by-5 center move needs one bit

Exact statement

Under half-turn symmetry, each of four outgoing dart orbits from the fixed center has two lifts, so one bit is required per chosen outgoing orbit.

StatusReproduced

External reviewNo documented external or specialist review of this Quotient Arsenal result is recorded.

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 independent verifier recovers all four stabilizer-coset choices.

Move-graph lifting and monodromy review →

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

This does not solve a knight-tour instance.

Open work

Use as the local nonfree-action regression case.