Curvature of the Riemann Zeta Modulus Near the Critical Line

This study investigates the curvature of the modulus of the Riemann zeta function ∣ζ(s)∣|\zeta(s)|∣ζ(s)∣ in the critical strip. We analyze the second discrete difference of ∣ζ(σ+it)∣|\zeta(\sigma + it)|∣ζ(σ+it)∣ for t≤50,000t \leq 50,000t≤50,000 and find that curvature achieves local minima at the critical line σ=1/2\sigma = 1/2σ=1/2. This supports the idea that the critical line represents a minimal distortion path in the modulus landscape, offering a structural heuristic for understanding the special nature of the Riemann Hypothesis.