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Negative result · missing hypothesis

FPRD-QA-MG-FAIL02

Free vertices do not rule out edge inversion

Exact statement

A group action free on vertices may still invert an undirected edge, so regular-cover conclusions require a no-inversion hypothesis.

StatusExact
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 edge-stabilizer analysis isolates the missing condition.

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

  • No novelty or specialist-review claim is made; the statement is limited to the displayed presentation and hypotheses.

Open work

Check darts or barycentrically subdivide before invoking cover theory.