Vertical Relativity and Dual Matryoshka Scaling: Topological Zero-Crossings, Local Speed Limits, and Scale-Invariant Space-Time Response in Universal Physics

Abstract Classical and modern physics predominantly describe relativistic phenomena within a fixed space-time scale. This paper introduces Vertical Relativity, a theoretical framework developed within Universal Physics (UP), in which recurring topological structures connect microscopic, macroscopic, and cosmological scales. The proposed framework employs Dual Matryoshka Scaling, represented by the extended navigation vector P = (x, y, z, τ, n, N), together with scale-dependent local limiting velocities, topological zero-crossings, and proper-time chirality reversal. The First and Second Wolf Transformations provide the mathematical bridge between electromagnetic wave propagation and the proposed formation of bound, mass-bearing structures. A complete derivation of the First Wolf Transformation is presented using the relativistic energy-momentum invariant, the Planck-Einstein relation, and the de Broglie momentum relation. The resulting Lorentz-invariant wave representation of rest mass is distinguished from its proposed topological interpretation. The framework is subsequently applied to three phenomena spanning different physical scales: quantum entanglement, the anomalous magnetic moment of the muon (g−2), and gravitational lensing associated with dark matter in the Bullet Cluster. These applications illustrate the proposed role of topological phase coupling, electromagnetic confinement, and scale-invariant space-time response. Vertical Relativity is presented as a deterministic, geometrically motivated approach to connecting quantum mechanics, quantum field theory, general relativity, and cosmology within a common topological framework.