Newton non-degeneracy conjecture for Weierstrass inflectionary curves

Let $n=2\ell$, assume that $\operatorname{char}(F)$ is zero or sufficiently positive, and let $P^{\ell,*}_m$ be the atomic inflection polynomial of $y^n=x^3+\lambda x+2$. For even $m$, consider its restriction to the edge $[v_m^1,v_m^4]$ of the local Newton polygon; for odd $m$, consider the restriction to $[v_m^3,v_m^4]$. Weierstrass Newton non-degeneracy conjecture. These restrictions are Newton non-degenerate for every $m\geq6$. Newton non-degeneracy would control the embedded toric resolution and local singularity type, but the supplied text gives no resolution of the assertion.