Seiberg-duality invariance of the Newton polynomial and Mahler measure

Consider Seiberg-dual dimer models with canonical edge weights, and let $P_1(z,w)$ and $P_2(z,w)$ be their Newton polynomials. Let $n_i$ be the number of edges, equivalently multiplets, in each perfect matching or GLSM field. Seiberg-duality invariance conjecture. The duals have the same Newton polynomial after cancelling the overall factors. If the factors $2^{n_1}$ and $2^{n_2}$ are retained, then

$$P_2(z,w)=2^{n_2-n_1}P_1(z,w),$$

and their Mahler measures satisfy

$$m_2=m_1+\log(2^{n_2-n_1}).$$

Thus Mahler measure is invariant under Seiberg duality up to the stated normalization shift. The source reports this behavior for the duals checked and does not prove it in general.