Arithmetic Function Chaos Filtered by Curvature: A Classical Analysis

In this study, we introduce a curvature-based framework to filter and analyze chaotic behavior in classical arithmetic functions. By measuring the second discrete difference Δ2f(n)\Delta^2 f(n)Δ2f(n), we identify zones of local stability and irregularity in functions such as τ(n)\tau(n)τ(n) (number of divisors), σ(n)\sigma(n)σ(n) (sum of divisors), and φ(n)\varphi(n)φ(n) (Euler’s totient function). This document proposes the Arithmetic Curvature Stability Filter as a classical analytical tool for understanding informational stability and chaos in number-theoretic landscapes.