6 problems

Let $C(n)$ range over the Apéry-like sequences listed in Tables 2 and 3 of the source, including $(\eta)$ and the sequences $(\delta)$, $(\alpha)$, $(\epsilon)$, $(\zeta)$, and…

Kimoto–Wakayama's conjecture. For every prime $p\geq 3$,

Higher Apéry-like sum conjecture. For any odd prime $p$ and any integer $k\geq2$,

ASD-type congruence conjecture. For any odd prime $p$ and $m,r\in\mathbb{Z}_{>0}$ with $m$ odd,

Kimoto–Osburn conjecture. For any odd prime $p$ and any $m,r\geq1$,

Square-sum supercongruence. For any odd prime $p$,