Theorem: Even-occurrence blindness

For amplitudes multilinear in vertex occurrences,

A $V_3\times V_3$ bubble is blind to a common cubic-rule reversal. A two-copy ghost loop is similarly blind. For $B_{ga}=n_{ga}\mathrm{mod}2$, sign vectors in ${\ker }_{{\mathbb{F}}_2}B$ are invisible to these graphwise comparisons.

Proof. Multiply one factor $-1$ for each occurrence. The simultaneous parity condition is $Bs=0$.