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Failed inference

FPRD-QA-MG-FAIL03

Quotient Hamiltonicity does not preserve tours

Exact statement

A Hamiltonian quotient cycle need not lift to a Hamiltonian cycle without the occupancy and monodromy receipts.

StatusRefuted exactly
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 6-by-6 zero-voltage quotient cycle splits into two cycles upstairs.

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

Apply FPRD-QA-MG-T04 and T05 before any tour claim.