Generic Newton polygon conjecture for T-adic C-functions

Let $C_f(s,T)$ be the $C$-function of the $T$-adic exponential sums associated with a polynomial $f$, and let its absolute $T$-adic Newton polygon mean the $T^a$-adic Newton polygon of $C_f(s,T;\mathbb{F}_{p^a})$. A generic $f$ means a polynomial in the generic locus for which this polygon is constant. Generic Newton polygon conjecture. If $p$ is sufficiently large, then the absolute $T$-adic Newton polygon of $C_f(s,T)$ is constant for a generic $f$; this polygon is called the generic Newton polygon of $C_f(s,T)$. This predicts eventual generic constancy of the absolute Newton polygon as the prime $p$ grows; the supplied text gives no resolution status.