Corollary: Exact predecessor comparison

The action and full BV differential agree with X-H-ST's stated relative construction through order two. At $\lambda =0$, the present action is its explicitly specified reference continuation through order three. At $\kappa =0$, Theorem prop:freecausal and Proposition prop:tadpole give the precise free-limit statements.

Proof. The additional vertex starts at order three, and (eq:Ij) reproduces the predecessor coefficients for $j=0,1,2$. The remaining assertions are direct substitutions.