  In examining the relationship between the number of points over
$\mathbb{F}_p$ on certain Calabi-Yau manifolds and hypergeometric series which
correspond to a particular period of the manifold, Rodriguez-Villegas
identified 22 possible supercongruences. We provide a framework of congruences
covering all 22 cases. Using this framework we prove one of the outstanding
supercongruence conjectures between a special value of a truncated ordinary
hypergeometric series and the $p$-th Fourier coefficient of a modular form. In
the course of this work we also establish two new binomial coefficient-harmonic
sum identities.
