The Riemann Zeta Function as a Conservative Dynamical System: A Heuristic Demonstration of the Riemann Hypothesis via Unitary Invariance

Since 1859, the Riemann Hypothesis has been primarily approached through analytic number theory. This paper proposes a paradigm shift by redefining the Riemann Zeta function no longer as a static series, but as a dynamic evolution operator acting on the phase space of prime numbers. By applying the Central Limit Theorem to lacunary trigonometric sums, we establish a Stochastic Dispersion Lemma square root of N. We demonstrate that to admit stable non-trivial zeros, the Zeta operator must satisfy a strict unitarity condition, leading to the unique energy conservation equilibrium sigma=1/2. This result formally connects arithmetic to quantum chaos and redefines cryptographic complexity as a geometric magnitude (artificial entropy). Files included : Full Manuscript (English) PDF Python Source Code for Graphical Proofs (Vortex, Dispersion, Potential Well)