FPRD LabShare an approach

← Claims

Failed approach

FPRD-QA-MG-FAIL01

Simple-edge collapse is unsafe

Exact statement

Merging parallel quotient edges can preserve reachability while destroying the receipt needed for closed-walk lifting.

StatusRefuted by C4
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

FPRD-QA-MG-X02 is the minimal witness.

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

Use a multigraph or dart quotient.