2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113014This paper is the first in a series whose goal is to understand the structure of low-volume complete orientable hyperbolic 3-manifolds. Here we introduce Mom technology and enumerate the hyperbolic Mom-n manifolds for n <= 4.29 pages, 6 figures, 2 tables; added citations and updated introductionGeometric Topology57M50 (Primary) 51M10, 51M25 (Secondary)text