2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/162280We introduce stable tropical curves and use these to count covers of the $p$-adic projective line of fixed degree and ramification types by Mumford curves in terms of tropical Hurwitz numbers. Our counts depend on the branch loci of the covers.14 pagesAlgebraic Geometry14H10$p$-adic Hurwitz numberstext