The Dynamic π and the Proof of the Riemann Hypothesis - Quadrant Phase Model and a New Mathematical Synchrony

This document presents a novel dynamic model of π as a field-based resonance function rather than a static ratio, and connects this to a physical-mathematical proof of the Riemann Hypothesis.

Through the quadrant phase model, the periodic modulation of π(t) is used to derive a symmetric phase-closure condition, which naturally leads to the non-trivial zeros of the zeta function lying on the Re(s) = 1/2 line.

This is not a reformulation but a structural extension of classical mathematics toward a cyclic, resonance-oriented logic.