Proof of `Assignment moves, pass moves, and deviations` (1st statement)
What this proof establishes
Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.
Description
Classify the nonregular edges. Removing the central vertex directly leaves a nonzero value. A move incident to a clause vertex permits a zero-valued central reply. Opening a clause with a surviving literal permits one of two zero-valued replies, according to parity.