Zilber–Pink in a product of modular curves assuming multiplicative degeneration

We prove the Zilber–Pink conjecture for curves in Y(1)n whose Zariski closure in (P1)n passes through the point (∞,…,∞), going beyond the asymmetry condition of Habegger and Pila. Our proof is based on a height bound following André’s G-functions method. The principal novelty is that we exploit relations between evaluations of G-functions at unboundedly many non-Archimedean places.