Function gaussian_lyapunov 

pub fn gaussian_lyapunov(
    equations: &[XorEquation],
    num_vars: usize,
) -> (Vec<u64>, bool)

The Lyapunov function for the algebraic collapse — Gaussian elimination over GF(2). The potential is the number of pivots still to be found in the unsolved linear system; each elimination step strictly reduces it, and the trajectory reaches the goal exactly when an inconsistent row 0 = 1 is exposed. Returns the descending potential and whether the goal (contradiction) was reached.

This is the load-bearing generalization: the same Lyapunov machinery that certifies the symmetry collapse certifies the parity collapse — different physics, one potential descending to the goal.