A Unified Digital Physics Framework: Deriving the Cosmic Refresh Rate, Relativistic Latency, and Quantum Superposition from Geometric Information Optimization

This paper introduces a comprehensive mathematical framework within the domain of digital physics, conceptualizing the universe as a discrete, relational computational system. By enforcing an information-theoretic optimization constraint based on the asymmetric properties of the golden ratio (φ), we derive the precise fundamental processing interval of spacetime, termed the base Server Tick (ℵc), calculated to be exactly ℵc ≈ 8.72282 × 10⁻¹⁹ seconds. Multiplying this temporal baseline by the speed of light (c) yields an explicit spatial batch-processing resolution of D ≈ 0.2615 nm, aligning precisely with the empirical characteristic scale of stable atomic structures. We formulate a Unified Rendering Equation () that integrates global cosmological expansion and localized general relativistic phenomena (via Schwarzschild metrics) as algorithmic latencies within the execution loop, successfully deriving the macroscopic friction-adjusted clock rate of 8.71109 × 10⁻¹⁹ seconds. Finally, we provide two explicit, falsifiable empirical predictions designed to distinguish this model from continuous frameworks: (1) a distinct background spectral anomaly concentrated at 4.741 keV within the Cosmic X-ray Background (CXB) in deep-space environments, and (2) the rigid temporal quantization of electronic state transitions constrained to integer blocks of 0.87228 attoseconds.