Dwork's log-growth Newton polygon conjecture

Let $D y=0$ be an ordinary linear $p$-adic differential equation of order $\mu$ whose coefficients are bounded analytic functions on the unit disc and whose solutions are analytic there. Assume that $D y=0$ admits a Frobenius structure. Write $\mathrm{NP}_{\log,0}(D)$ and $\mathrm{NP}_{\varphi,0}(D)$ for its special log-growth and Frobenius Newton polygons, and, at a generic point $t$, write $D_t y=0$ for the pulled-back equation and $\mathrm{NP}_{\log,t}(D_t)$ and $\mathrm{NP}_{\varphi,t}(D_t)$ for the corresponding generic polygons.

Dwork's conjecture.

$$\mathrm{NP}_{\log,0}(D)=\mathrm{NP}_{\varphi,0}(D)$$

and

$$\mathrm{NP}_{\log,t}(D_t)=\mathrm{NP}_{\varphi,t}(D_t).$$

The conjecture identifies the log-growth Newton polygons with the Frobenius Newton polygons, both at the special point and generically. The generic equality was proved without additional assumptions, so this statement is recorded as solved.