Gravity as the Singular Manifestation of Manifold Tension: Fractal Isomorphism of Mass and Energy Bases

Overview: This preprint presents a fundamental paradigm shift in theoretical physics, challenging the Standard Model's reliance on empirical constants and the artificial segregation of the four fundamental forces. By introducing Arc-Closure Geometry within a 2+1 sub-Riemannian tension manifold, this work establishes that the universe possesses only one singular outward manifestation of force: Gravity. Abstract: The persistent reliance on empirical constants and phenomenological coupling parameters (e. g. , G, ²W) presents a fundamental barrier to a unified ontology of physics. Building upon the framework of Arc-Closure Geometry within a 2+1 tension manifold, we demonstrate that the universe does not possess four independent fundamental forces. Instead, Gravity is the singular outward manifestation of geometric tension. The Light and Magnetic Energy Arcs serve as the primordial progenitors of all physical entities, gestating the foundational Electric Arc Helix—the absolute mainspring of all gravitational interactions. We establish that gravity bifurcates into an Energy Base (microscopic) and a Mass Base (macroscopic), both of which share identical, co-existing fractal topologies: symmetric (strong/inertial), asymmetric (weak/electrostatic), and mutual (electromagnetic/chemical bond). By analyzing the asymmetric intersection of the temporal coupling axis, we derive the exact topological baseline for the weak mixing angle as ²W = 1/4. Finally, we resolve the ultimate macroscopic inter-sector tension by formulating the Big G Formula, proving that gravity is the geometric tension modulus required to compensate for the fundamental 16/15 spatiotemporal divergence across the Law of Spontaneous Doubling (LSD) network. Key Analytical Breakthroughs Detailed in the Appendices: The Topological Weinberg Angle: A pure geometric proof utilizing the Calculus of Variations to demonstrate that the temporal coupling axis must undergo an absolute 1: 3 asymmetric cleavage (minimizing Elastica Energy), firmly locking the weak mixing angle at exactly ²W = 0. 25 without invoking spontaneous symmetry breaking. The Big G Operator Formulation: Stripping the density matrix () and Trace operator (Tr) of their statistical probabilities, and mathematically proving the necessity of the natural logarithm () as the algebraic inverse to extract topological fold layers from the macroscopic LSD network. Geometric Confinement and Mass Emergence: Resolving the isomorphism between electromagnetic waves and chemical bonds by applying Dirichlet boundary conditions (the co-intersection chord) to the intrinsic Arc action functional, mathematically precipitating "rest mass" as a pure geometric consequence of spatial confinement.