SDRIS: The Holomorphic Universe

Abstract: The reconciliation of the discrete nature of information processing with the continuous geometry of spacetime remains the central unsolved problem of fundamental physics. The Static-Dynamic Recursive Information Space (SDRIS) framework has successfully modeled particle mass spectra and cosmological constants as emergent properties of a linear recursive hierarchy. However, the current linear topology implies unresolved boundary conditions at the singularity ($N=408$) and the vacuum surface ($N=1$). In this paper, we resolve these discontinuities by constructing a topological isomorphism between the discrete SDRIS grid and the continuous Riemann Sphere. We demonstrate that the linear recursive cascade is a stereographic projection of a cyclic, holomorphic flow on a closed manifold. By defining a conformal mapping $\psi: \mathcal{S} \to \mathcal{R}$, we derive the fundamental laws of physics not as empirical parameters, but as geometric necessities of the projection. Key Results: Fine-Structure Constant & Weinberg Angle:} Derived as geometric invariants of the spherical projection. Vacuum Energy: Identified as the hydrodynamic limit of the spherical excess (Girard's Theorem), resolving the $10^{120}$ discrepancy. Unification of Forces: Fundamental forces are shown to be orthogonal vector components of a single loxodromic information flux. Topological Closure: Gravity and Antimatter are identified as the conjugate ''backflow'' through the imaginary axis, resolving the Baryon Asymmetry via an Ouroboros condition. We conclude that the universe is a holomorphic quantum-cellular automaton where the distinction between discrete arithmetic and continuous geometry vanishes.