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Theorem · classical adapter

FPRD-QA-MG-T03

Voltage is the closed-walk receipt

Exact statement

A free action without edge inversion gives a regular cover; the product of edge voltages is the monodromy that determines the lifted endpoint and component structure.

StatusProved and calibrated
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 packet gives a self-contained lift proof and the C4 control separates voltages zero and one.

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

  • Free action on vertices alone does not exclude edge inversion.

Open work

Use dart or edge-orbit quotients when parallel edges carry different voltages.