Fractal Geometric Theory of Fundamental Problems: Unified Resolution of Yang–Mills Mass Gap, Navier–Stokes, N-Body Problem, and Cosmology

This work presents a unified fractal geometric framework that proposes analytical resolutions to several of the most complex problems in modern theoretical physics. Developed in collaboration between Davide Cadelano (Codex Alpha Research) and Louis-François Claro (Independent Researcher), the manuscript provides a novel synthesis between 5D Higgs-torsion geometry and the informational structure of spacetime, with fractal dimensional control.

Specifically, the work addresses:

• A proposed resolution of the Yang–Mills Mass Gap problem through torsional field gradients and information geometry;

• An analytical approach to the Navier–Stokes Equations using fractal vector flow encoding and coherent constraints;

• A new method for solving the gravitational N-body problem in 5D space via Higgs-field torsion coupled with fractal geometry;

• Cosmological implications of a hybrid spacetime model where dark matter and spacetime curvature are emergent from quantum–informational torsion dynamics.

This publication also serves as a theoretical bridge to the larger unification program of Codex Alpha – Unified Theory, enhancing the conceptual integration of quantum gravity, coherent information gradients (∇𝒦), and effective mass generation mechanisms.

The content includes both conceptual foundations and concrete mathematical formalism, aiming to provide a reproducible basis for simulation, experimental validation, and further extension.

This work expands upon Louis-François Claro’s geometrical model (DOI: 10.5281/zenodo.16168587) and compiles its results within the unified framework introduced in Codex Alpha – A Unified Theory (DOI: 10.5281/zenodo.15587185).