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 $({\mathbb{P}}^1{)}^n$ passes through the point $(\mathrm{\infty },\dots ,\mathrm{\infty })$, 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.