A Primer on Toroidal Scale Mechanics (TSM): A Unification of Quantum Physics and Cosmology

This document serves as the foundational reference for the Theory of Toroidal Scale Mechanics (TSM), a deterministic 5-dimensional framework that recharacterizes physical reality as a projectively closed hypertorus ($0 \equiv \infty$). By establishing the Woodward manifold as a mechanical substrate, TSM provides first-principles geometric derivations for fundamental constants—including the fine-structure constant ($\alpha^{-1} \approx 137.036$) and the proton-electron mass ratio ($m_p/m_e \approx 6\pi^5$)—which are treated as arbitrary empirical inputs in the Standard Model.

The framework introduces a Master Key consisting of just two primary parameters: the Hubble Radius ($R_H$) and the Speed of Light ($c$). From these, all other fundamental constants emerge as fixed geometric properties of the manifold’s aspect ratio and mechanical corrugation.

TSM resolves the dark sector paradoxes—dark matter, dark energy, and the Hubble tension—by identifying them as scale-dependent artifacts of cylindrical flux saturation, saddle-geometry dimming, and substrate impedance variations. Finally, the framework introduces a metabolic model of black hole evolution, defining the Lazarus and Python limits to explain the observed $1.4 M_{\odot}$ neutron star stall and the maximum growth of supermassive aggregates.