I will report on work in progress with M. Groechenig and P. Ziegler where we aim to express certain enumerative invariants, so called refined BPS-invariants, in terms of integrals on p-adic analytic manifolds naturally associated with the enumerative problem. In the case of 1-dimensional sheaves on a K3 surface, our work implies that these invariants are independent of the Euler-characteristic, confirming a conjecture of Toda.