Curvature of the Normalized Totient Function and Prime Gap Structures

This work analyzes the normalized Euler totient function I(n)=φ(n)/log⁡nI(n) = \varphi(n)/\log nI(n)=φ(n)/logn and its second discrete differences to study prime gap structures. Computational results show that primes tend to correspond to local minima of curvature, suggesting new heuristic models of prime distribution stability. This curvature method complements probabilistic prime gap theories and provides a testable classical framework for prime regularity analysis.