Stirling-Based Asymptotic Reformulations of Baker’s Explicit ABC Bound

This paper presents a novel simple proof of inequalities for the ABC conjecture using Stirling series. This approach bridges Stirling’s approximation with the radical function, producing explicit, computationally testable bounds. Specifically, for any ε > 0, there exists Cε such that for coprime a +b= c, c ≤ Cε·rad(abc)1+ε. Furthermore, this approach turns an abstract conjecture into verifiable numerical inequalities.