Monotonicity of Mahler measure along the Mahler flow

Let $P(z,w)=k-p(z,w)$ be a Newton polynomial undergoing the Mahler flow, with Mahler measure $m(P)$ and flow parameter $k>0$. Mahler-flow monotonicity conjecture. The Mahler measure monotonically increases as $k$ increases along the Mahler flow, from $k=0$ to $k\rightarrow\infty$. This is motivated by the observed numerical behavior for the Newton polynomials considered in the paper; no general proof is given.