  Using an intrinsic $q$-hypergeometric strategy, we generalise Dwork-type
congruences $H(p^{s+1})/H(p^s)\equiv H(p^s)/H(p^{s-1})\pmod{p^3}$ for
$s=1,2,\dots$ and $p$ a prime, when $H(N)$ are truncated hypergeometric sums
corresponding to the periods of rigid Calabi--Yau threefolds.
