Advanced Geometric Unification of Strong and Weak Interactions: A Hyper-Geometric Framework for Subatomic Force Synthesis

The unification of the four fundamental interactions remains the pinnacle challenge of modern theoretical physics. While General Relativity provides a geometric description of gravity through space-time curvature, the Standard Model of particle physics relies on internal gauge symmetries for strong, weak, and electromagnetic interactions. This research explores a novel framework for unifying the strong and weak nuclear forces under a “Hyper-Geometric” system. By interpreting subatomic interactions as local deformations of quantum space-time geometry rather than mere particle exchanges, we propose a synthesis based on Tangent Bundle Geometry and Hypergeometric functions. This approach leverages engineering-based geometric intuition—specifically the principles of stress-strain relations in continuum mechanics—to model the subatomic “fabric” of space. We derive advanced mathematical formulations that suggest the strong and weak forces are manifestations of specific metric tensor perturbations in higher-dimensional manifolds, effectively resolving the “mystery of matter” through geometric synthesis.