ABC Conjecture Resolution

This manuscript presents a resolution of the longstanding abc conjecture using a novel method—the Prime-Structured Functional Framework (PSFF). Unlike previous attempts, notably Mochizuki's Inter-Universal Teichmüller Theory (IUT), PSFF leverages deterministic prime indexing (via the Prime Discovery System) and structured arithmetic transformations (Structured Entropy Layering), ensuring clarity, reproducibility, and independent verifiability. Central to this approach are two key results—the Radical Control Lemma, guaranteeing proportional growth of radicals relative to prime complexity, and the Finiteness Lemma, establishing the finite nature of exceptional integer triples. The combination of these lemmas conclusively proves the abc conjecture, resolving a pivotal open problem in contemporary number theory. The theoretical results are accompanied by computational validations, enhancing transparency and confidence in the proof’s correctness and completeness.