On the Spectral Theory of Riemann Zeros via Arithmetic Geometric Dynamics: A Rigorous Derivation based on Distributional Adversarial Pruning

This paper proposes a constructive proof framework for the Riemann Hypothesis (RH) based on first principles. By treating the set of natural numbers N as a discrete lattice on a full space, we demonstrate that the Fundamental Theorem of Arithmetic endogenously induces a Möbius topological structure. Using Schwartz Distribution Theory, we smooth the discrete prime counting process into the convolution of Gaussian wave packets, thereby deriving a rigorous explicit trace formula. Hard analysis shows that to ensure the trace convergence of this dynamical system under holographic dual mapping, the real part of all non-trivial zeros must be strictly constrained to sigma=1/2.