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I will present an all-order argument for the leading-power factorization of inclusive hadron production at high transverse momentum in hadron-hadron collisions. The key improvement over previous literature is an explicit local unitarity argument formulated in a covariant gauge, applied consistently to both the collinear and the soft sectors. When applied to inclusive hadron production, it reduces the pinch surfaces to those familiar from the Drell-Yan factorization. The same approach extends naturally to inclusive hadron production in lepton-lepton and lepton-hadron collisions, thereby demonstrating the universality of fragmentation functions.