2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/15835We investigate the existence of a class of ZFC-provably total recursive unary functions, given certain constraints, and apply some of those results to show that, for $Σ_1$-sound set theory, ZFC$\not\vdash P<NP$.LaTeX, 16 pages, no figures. This paper was submitted to a major journal in the field and rejected. The referee somehow misundesrtood Corollary 3.8 and wrongly concluded that the proof had either a gap or an error. Can you find whether that error exists?Computation and Languagetext