  In this note, we give an alternative proof of uniform boundedness of the
number of integral points of smooth projective curves over a fixed number field
with good reduction outside of a fixed set of primes. We use that due to
Bertin-Romagny, the Kodaira-Parshin families constructed by Lawrence-Venkatesh
can themselves be assembled into a family. We then repeat Lawrence-Venkatesh's
study of the p-adic period map, together with the comparison of nearby fibres.
