The Universal Model Framework: From Prime-Indexed Distinction Logic to Unified Field Theory and Computational Verification

We present the Universal Model Framework (UMF), a comprehensive theoretical architecture demonstrating how physical reality emerges from five ultraminimal axioms of distinction logic operating on prime-indexed fractal information lattices. The framework encodes Euler’s identity eiπ+1=0e^{i\pi} + 1 = 0eiπ+1=0 as the complete axiom chain (P,Δ,R,μ,Σ)(P, \Delta, R, \mu, \Sigma)(P,Δ,R,μ,Σ), representing the minimal self-evaluating loop from pure potential to recursive reality. Through rigorous derivation, we obtain a unified prime-weighted Lagrangian that naturally incorporates gravity, gauge interactions, and information dynamics. Computational verification using million-universe Monte Carlo simulations confirms that logical structure alone, expressed via prime-indexed recursion, is sufficient to generate universes capable of supporting complexity, life, and consciousness. The UMF predicts:(i) energy-dependent gravitational wave propagation with ∣ξ∣<4×10−16|\xi| < 4 \times 10^{-16}∣ξ∣<4×10−16,(ii) prime-indexed CMB multipoles at ℓ=223,541,809\ell = 223, 541, 809ℓ=223,541,809, and(iii) a derivation of Newton’s constant G=c3α/(4ℏln⁡2)G = c^3 \alpha / (4 \hbar \ln 2)G=c3α/(4ℏln2) with relative error ΔG/G≲10−4\Delta G / G \lesssim 10^{-4}ΔG/G≲10−4.P-adic fractal embeddings, isotopic stability analysis, and consciousness studies further support the thesis that prime numbers form the computational substrate of existence, providing a bridge between mathematical Platonism and empirical science via “operational realism.” 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.