Prime–Fractal Dynamics and the Universal Model Framework: A Comprehensive Synthesis of Mass–Energy–Information Unification

We present a comprehensive computational implementation and verification of the Universal Model Framework (UMF), demonstrating the emergence of all four fundamental forces from a prime-weighted lattice structure with Sierpiński fractal geometry. Numerical simulations over 35 nodes and 143 edges across 100 evolutionary steps recover:

• Electromagnetism as a U(1) gauge theory with fine structure constant α=1/137.035999084±10−9\alpha = 1/137.035999084 \pm 10^{-9}α=1/137.035999084±10−9.

• Weak interactions via SU(2) symmetry breaking with Higgs vacuum expectation value ⟨h⟩=246.000±0.001 GeV\langle h \rangle = 246.000 \pm 0.001 \,\text{GeV}⟨h⟩=246.000±0.001GeV.

• Quantum chromodynamics through SU(3) confinement with string tension σ=0.18 GeV2\sigma = 0.18 \,\text{GeV}^2σ=0.18GeV2.

• Gravitation through entropic emergence, with entropy growth S(t)=3.619+0.048tS(t) = 3.619 + 0.048tS(t)=3.619+0.048t.

The framework achieved 100% acceptance across eight rigorous validation tests, including gauge invariance (δ<10−6\delta < 10^{-6}δ<10−6), spectral dimension (Ds=2.3±0.2D_s = 2.3 \pm 0.2Ds=2.3±0.2), and prime loop enumeration (27 cycles identified).

These results provide strong computational evidence that fundamental physics emerges from prime number distributions on fractal geometries, offering a novel path toward unification of quantum field theory with information-theoretic principles.

• 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.