Adolphson–Sperber conjecture on generic ordinarity

Let $\Delta$ be a lattice polytope of degree denominator $D$, and let ${\rm GNP}(\Delta,p)$ and ${\rm HP}(\Delta)$ denote its generic Newton polygon and Hodge polygon, respectively. Adolphson–Sperber conjecture. If $p\equiv 1 \pmod D$, then

$${\rm GNP}(\Delta,p)={\rm HP}(\Delta).$$

This conjecture predicts generic ordinarity for primes in the congruence class $1$ modulo $D$. The source presents it as a conjecture of Adolphson and Sperber; its resolution is not established in the supplied text.