Toroidal Scale Dynamics: Metric Saturation and the Geometric Unification of Forces
Abstract
We present Toroidal Scale Dynamics (TSD), a geometric unification of Quantum Mechanics and General Relativity that resolves the hierarchy problem through topological constraints rather than fine-tuning. By redefining the scalar dimension (w) as a compact, complex coordinate on a 5-dimensional toroidal manifold, we demonstrate that the Strong Nuclear Force is not a distinct interaction, but the localized magnitude of the gravitational coupling G(w) required to maintain the Schwarzschild condition at the hadronic radius. We derive the Metric Saturation Limit (B_sat), a fundamental density constraint that identifies the proton not as a point particle, but as a stable Spindle Torus black hole (alpha < 1), and the observable universe as its topological dual. Furthermore, TSD reinterprets the Dark Sector not as hidden mass-energy, but as the geometric consequence of flux saturation in a toroidal topology: Dark Matter arises from the transition between spherical and cylindrical flux propagation, while Dark Energy represents the relaxation of scalar curvature at the manifold's outer rim. Finally, we resolve the Hubble Tension as a scalar parallax effect resulting from the observer's phase position on the toroidal loop. By adopting a projective geometry where zero and infinity are topologically identified, the Hadronic Limit (Inner Rim) and the Vacuum Limit (Outer Rim) become antipodal transition points on a continuous toroidal loop. We conclude by proposing specific falsifiable experiments to distinguish TSD from the standard Lambda-CDM model.
Fields of Study & Subjects
Relativity and Gravitational Theory
Advanced Mathematical Theories and Applications
Cosmology and Gravitation Theories
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 19 January 2026
- Document type
- Preprint