Operational Extraction of the Fine-Structure Constant and Acceleration Scales from a Compact U(1) Substrate in Lorentzian Randers Geometry

We present an operational framework modeling fundamental field dynamics via an anisotropic Randers-Finsler spacetime metric F(x, y) = \alpha(x, y) + \beta(x, y), defined over a compact U(1) topological substrate. By enforcing the strict Lorentzian Randers admissibility condition \|A\|_g < 1 for the perturbation vector field A_\mu, the metric tensor g_{\mu\nu}(x, y) maintains positive-definiteness and preserves signature continuity across the manifold, eliminating singular metric determinants and unphysical light-cone deformations. Under this geometric constraint, localized topological phase-slips across the substrate yield analytic derivations matching empirical values for both the electromagnetic fine-structure constant (\alpha^{-1} \approx 137.036) and the modified Newtonian dynamics (MOND) critical acceleration threshold a_0. This revised draft formalizes the mathematical boundary conditions connecting local drift vectors to cosmological field limits while maintaining strict thermodynamic and sub-luminal stability.