Fractal Entropic Geometrodynamics: Emergent Gravity and Standard Model Synthesis via Discrete Topological Constraints

Title: Fractal Entropic Geometrodynamics: Emergent Gravity and Standard Model Synthesis via Discrete Topological Constraints Description: Abstract: We propose Fractal Entropic Geometrodynamics (FEG), a strictly discrete causal set framework synthesizing General Relativity and the Standard Model without invoking a continuous background manifold. We establish two foundational axioms: spacetime as a Poisson-sprinkled causal set, and geometry as an emergent property of the Petz-Chentsov quantum information metric. To formalize dynamics, we introduce the Kuratowski Calculus, substituting continuous differential operators with exact combinatorial counterparts. By treating causal histories as states on a non-commutative algebra, we demonstrate that the Strong Force is not a fundamental gauge field, but a strict topological obstruction preventing non-planar ($K_5$) topological minors in the ultraviolet (UV). This discrete, non-commutative architecture uniquely derives the transitional coupling constant $\alpha_{\text{trans}} \approx 0.31$, and provides a rigorous mathematical foundation for dissolving major anomalies, including the Hubble Tension, the Hierarchy Problem, and the Singularity. --- Computational Note: The topological transition can be executed using pure integer logic. An ensemble of $M=10$ independent realizations at $N=50,000$ events computes in approximately 5 minutes on standard consumer hardware. (T480 Thinkpad) source code, and reproducible Monte Carlo simulations supporting this framework, please refer to the associated GitHub repository at: https://github.com/ertwro/fractal_entropic_geometrodynamics