Dwork's p-adic hypergeometric inversion conjecture

Let $s\geq 1$ be an integer and let $a_1=\cdots=a_s=a\in\mathbb{Z}_p$. Let $\mathscr{F}^{\rm Dw}_{a}(t)$ denote Dwork's $p$-adic hypergeometric function with all $s$ parameters equal to $a$. Let $l$ be the unique integer in $\{0,1,\ldots,p-1\}$ such that

$$a+l\equiv 0\pmod p.$$

Dwork's p-adic hypergeometric inversion conjecture.

$$\mathscr{F}^{\rm Dw}_{a}(t)=((-1)^s t)^l\mathscr{F}^{\rm Dw}_{a}(t^{-1}).$$

This transformation is stated for Dwork's $p$-adic hypergeometric functions. The paper proves the case $s=1$ for odd primes and gives a counterexample when $p=2$, so the unrestricted conjecture as stated is refuted.