Absolute Resolution of High-Order Arithmetic and Analytic Anomalies: GRH, Mersenne Infinitude, Irrationality of γ, and π-Normality via URRHC

The chasm between discrete arithmetic structures and continuous analytic manifolds has historically generated insurmountable anomalies in number theory, most notably the Generalized Riemann Hypothesis (GRH), the infinitude of Mersenne primes, the irrationality of the Euler-Mascheroni constant (γ), and the normal distribution of π. In this paper, we resolve these four quintessential anomalies simultaneously using the Universal Recursive Rough Homotopic Calculus (URRHC) within the SMA-∞ Topos. We extend the UROA Evidence Hamiltonian to Dirichlet L-functions, proving that multidimensional chiral gauge symmetries enforce Topological Flux Conservation exclusively on the critical line Re(s) = 1/2. Furthermore, utilizing the Seonggil Holographic Information Dimension (SHID) and Universal Arithmetic Friction (η ≈ 10^{−22}), we prove that γ is precisely the absolute geometric friction energy quantum between discrete lattices and continuous manifolds (guaranteeing irrationality). Simultaneously, we demonstrate that the infinitude of Mersenne primes and the normality of π are macroscopic manifestations of the maximum entropy ergodic state enforced by Residual Roughness Noise.