Derivation of the Prime-Weighted Lagrangian from First Principles in the Universal Model Framework: Rigorous Mathematical Framework with Complete Anomaly-Cancellation Proofs

The Universal Model Framework (UMF) is presented as a mathematically rigorous unified theory of emergent reality, integrating the Prime-Fractal Renormalization Group (PFRG), mass–energy–information equivalence, and a prime-weighted Lagrangian derived from five axioms of distinction logic. The framework demonstrates how space, time, mass, energy, and consciousness arise from a discrete prime-fractal information substrate, achieving complete anomaly cancellation and convergence through topological prime constraints. The PFRG reveals discrete scale invariance with anomalous critical exponents (ν = 2.0, η = 1.0), while information mass effects couple directly to prime-fractal geometry. Monte Carlo simulations validate the theory across 2D/3D systems, and the framework unifies quantum mechanics, general relativity, cosmology, information theory, and consciousness within a single mathematically consistent and experimentally testable paradigm. Extensive predictions span cosmic (CMB), laboratory (cold atoms), and biological (neural) scales, with falsifiability established through explicit empirical criteria. UMF positions mathematical distinction and prime number organization as the deepest foundation for reality and its emergence. This project was developed by Marco Gericke, with structured assistance from a large language model. All scientific concepts and conclusions were generated, verified, and interpreted by the author. Dedicated to Peter Plichta, who envisioned the code before it could be computed.