Phase-Locking and Minimal Entropy at ℜ(s) = 1/2: A Dynamic Approach to the Riemann Hypothesis

This paper proposes a new structural perspective on the Riemann

Hypothesis by investigating the phase dynamics and high-order deriva-

tives of the Riemann zeta function ζ(s). We show that the critical line

ℜ(s) = 1/2 is the only location in the complex plane where the phase

angle θ(t) = arg ζ +it exhibits convergence to 90 arising from self-

conjugate symmetry, accompanied by stable high-order derivative behav-

ior and structural robustness. These observations suggest a deeper struc-

tural reason behind the distribution of nontrivial zeros along the critical

line, grounded in phase-locking and dynamic equilibrium principles.