Prime-Fractal Dynamics in the Universal Model Framework

The Universal Model Framework (UMF) posits that prime-indexed fractals at the Planck scale encode spacetime, forces, and information. Here a consolidated synthesis of fifteen UMF modules is presented. Key outcomes include: (i) an information mass mbit = kBT ln 2/c2 consistent with Vopson’s mass–energy–information equivalence; (ii) a prime cross of form 6n±1 generating a Sierpi´nski lattice with fractal dimension Dq ≃ 1.63; (iii) an entropy–area law S = −κMA/ℏc predicting gravity as an entropic force; (iv) a prime-modulated Higgs excitation yielding test resonances at 541 and 809 GeV; (v) proton–neutron Monte Carlo on a 30 × 30 Planck lattice producing a robust 83:17 neutron excess under prime-resonant binding. Blind anti-confirmation tests demonstrate that prime alignment of CMB peaks (ℓ = 223, 541, 809) and of LIGO strain resonances at 541 Hz and 809 Hz is reproduced in randomised controls with probability p < 0.002. The study integrates SEAT quantum-gravity thermodynamics and Neukart’s GID prime search, framing all fundamental interactions as emergent expressions of an arithmetical Logos. Testable predictions for Euclid void radii, NV-centre coherence, and high-field LHC scans are outlined. 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.