Special Relativity in Toroidal Scale Dynamics: Geometric Mass and the Conservation of Scale

Standard Special Relativity (SR) rests on the postulate of the invariance of c but lacks a structural origin for this limit. We propose that relativistic phenomena are geometric consequences of motion on a 5-dimensional toroidal manifold. In the Toroidal Scale Dynamics (TSD) framework, physical acceleration is reinterpreted as an angular rotation of the velocity vector from the temporal axis into a compact scalar dimension (w). We derive the Lorentz factor geometrically as the secant of this rotation angle, identifying c as the asymptotic limit where the velocity vector becomes orthogonal to the temporal coordinate. Furthermore, we resolve the paradox of isotropic scalar contraction vs. non-vanishing interaction cross-sections via a topological conservation law: as the geometric core of a particle contracts, its field envelope expands. This "Geometric See-Saw" mechanism recovers standard relativistic phenomenology while offering a clear falsifiable prediction: the distinction between the contracting baryonic knot and the expanding interaction field at ultra-relativistic energies.