2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/18061We respond to Sornette and Johansen's criticisms of our findings regarding log-periodic precursors to financial crashes. Included in this paper are discussions of the Sornette-Johansen theoretical paradigm, traditional methods of identifying log-periodic precursors, the behavior of the first differences of a log-periodic price series, and the distribution of drawdowns for a securities price.12 LaTex pages, no figuresCondensed Mattertext