Seiberg-duality invariance of the Ronkin function

Consider Seiberg-dual dimer models, with the canonical weight choice, and let $R(x,y)$ be the Ronkin function associated with their Newton polynomial. Ronkin Seiberg-duality conjecture. The Ronkin function is invariant under Seiberg duality because the canonical-weight Newton polynomial is unchanged, regardless of whether the dimer embedding is isoradial. The source presents this as a consequence of the proposed Newton-polynomial invariance and gives no general proof.