2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130503Possible reasons for the uniqueness of the positive geometric law in the context of stability of random extremes are explored here culminating in a conjecture characterizing the geometric law. Our reasoning comes closer in justifying the geometric law in similar contexts discussed in Arnold et al. (1986) and Marshall & Olkin (1997) and also supplement their arguments.11 pages, in the published journal format, presented at the International Conference on Order Statistics and Extreme Values: Theory and Applications, December 18-20, 2000, University of Mysore, IndiaProbabilityStatistics Theory60G70, 62H05, 62H10, 60E10text