  We study periods in an integral basis near all possible singularities in
one-dimensional complex structure moduli spaces of Calabi-Yau threefolds. Near
large complex structure points these asymptotic periods are well understood in
terms of the topological data of the mirror Calabi-Yau manifold. The aim of
this work is to characterize the period data near other boundaries in moduli
space such as conifold and K-points. Using results from Hodge theory, we
provide the general form of these periods in a quantized three-cycle basis.
Based on these periods we compute the prepotential and related physical
couplings of the underlying supergravity theory. Moreover, we elucidate the
meaning of the model-dependent coefficients that appear in these expressions:
these can be identified with certain topological and arithmetic numbers
associated to the singular geometry at the moduli space boundary. We illustrate
our findings by studying a wide set of examples.
