  We study the homology concordance group of knots in integer homology
three-spheres which bound integer homology four-balls. Using knot Floer
homology, we construct an infinite number of $\mathbb{Z}$-valued, linearly
independent homology concordance homomorphisms which vanish for knots coming
from $S^3$. This shows that the homology concordance group modulo knots coming
from $S^3$ contains an infinite-rank summand. The techniques used here
generalize the classification program established in previous papers regarding
the local equivalence group of knot Floer complexes over $\mathbb{F}[U,
V]/(UV)$. Our results extend this approach to complexes defined over a broader
class of rings.
