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Theorem · occupancy obligation

FPRD-QA-MG-T05

Fibre occupancy is necessary for Hamiltonian projection

Exact statement

The projection of an upstairs Hamiltonian cycle visits each quotient vertex exactly as many times as the size of its fibre.

StatusProved
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

Counting vertices along the projected tour gives the exact obligation.

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

  • The occupancy vector is necessary, not sufficient.

Open work

Combine occupancy with local cosets and monodromy in tour searches.