2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/54358I present a criterion for all-order finiteness in $N=1$ SYM theories. The structure of the supercurrent anomaly, the Callan-Symanzik equation and the supersymmetric non-renormalization theorem for chiral anomalies are the essential ingredients of the proof.6 pages, no figures, plain LATEX fileHigh Energy Physics - TheoryHigh Energy Physics - PhenomenologyAll-orders finite $N=1$ super-Yang-Mills Theoriestext