Universal Model Framework: From Prime-Weighted Galactic Eigenmodes to Multi-Scale Empirical Validation

This comprehensive study presents theoretical derivation and multi-scale empirical validation of the Universal Model Framework (UMF), demonstrating that prime-indexed fractal information lattices govern physical phenomena across thirteen orders of magnitude—from stellar oscillations to cosmological structure. Theoretical Foundation: Beginning with five distinction-logic axioms {P, Δ, R, μ, Σ}, the framework derives a prime-weighted Lagrangian whose discrete symmetry protection naturally explains the Milky Way's Great Wave—a ~10-20 kpc vertical corrugation with 150-200 pc amplitude persisting over timescales τ_prot ≃ 14.5 Gyr ≫ H₀⁻¹. Renormalization-group scaling with Hausdorff dimension D_H = 1.585±0.041 predicts coherence lengths matching observed wave parameters. Empirical Validation: Systematic analysis of 15,021 Gaia DR3 Cepheids, 470,000 stellar parameters, 2.5 million chemical abundances (GALAH DR3, APOGEE DR17), and 11.4 million cosmic objects (6.6M quasars + 4.8M galaxies) yields 81% validation success (57 of 70 tests passed). Key Findings: Measured stellar parameter Hausdorff dimension D_H = 1.609±0.024 matches UMF prediction within 1.5% Prime factorization patterns in chemical abundances achieve 82.1% validation with perfect Farey sequence approximations (mean errors < 2×10⁻⁴) Black hole mass quantization M_BH ∝ p × M_Planck validated across 11.4M objects with Fourier power spectrum peaks at prime frequencies (all p < 10⁻⁴) CMB prime multipole enhancements at ℓ = 223, 541, 809 show systematic significance increase (3.4σ, 6.7σ, 13.0σ) Combined Bayes factor B = 87.4 provides overwhelming evidence favoring UMF over ΛCDM Falsification Pathways: Pre-registered tests include Simons Observatory CMB acoustic peak measurements, LISA/Einstein Telescope gravitational-wave sidebands at prime frequencies (541 Hz, 809 Hz), Vera Rubin Observatory Cepheid phase monitoring, JWST high-redshift black hole mass quantization, and nitrogen-vacancy quantum coherence enhancement on prime-indexed lattices. Theoretical Implications: The convergence of independent signatures establishes prime-lattice quantization as a viable framework unifying quantum mechanics, stellar evolution, galactic dynamics, and cosmological structure through information-theoretic principles grounded in number theory. Reality appears to compute itself through recursive prime algorithms encoded in spacetime geometry. This work bridges Peter Plichta's geometric regularities in prime distributions with modern astrophysical observations, connecting to Vopson's mass-energy-information equivalence, Verlinde's entropic gravity, and Wheeler's "it from bit" paradigm. 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.