A uniform sub-three-fifths bound for exceptional abc triples

Abstract

GPT 5.6 Sol discovered the result and proof presented in this paper. We establish a new uniform upper bound for the number of exceptional abc triples throughout the full subcritical range. The proof combines an anatomic decomposition with Fourier analysis, geometry-of-numbers estimates, and a new primitive-slope argument, followed by an exact computer-assisted verification using rational arithmetic. The resulting exponent is strictly below three-fifths and improves the previous uniform bound near the critical abc threshold. Preprint, version dated August 2026, not peer reviewed