We construct Dan's Photocity Master Equation (DPME), a covariant nonlinear field equation for the photocity field ρ(xμ)—the local energy density of space—derived rigorously from the four ontological postulates of the Ultimate Relativity (UR) framework: the Space Postulate, the Pair Postulate, the Time Postulate, and the Measurement Postulate. The Quantex mechanism—the identity exchange between a particle and its shadow near the perception boundary v→c—acts as a geometric regulator, replacing classical curvature singularities with a smooth Planck-density core, and rendering the theory singularity-free by construction. In the weak-field slow-motion limit the DPME reduces exactly to Einstein's field equations with a derived cosmological constant; in the non-relativistic limit it reproduces the Newtonian Poisson equation. Charge relativity (q = q₀/√(1−v²/c²)), mirroring the relativistic mass formula, emerges as a first-order consequence of the photocity gradient, naturally explaining Hubble's law and flat galactic rotation curves without dark energy or dark matter. We derive a world-class falsifiable prediction—the photocity-gradient redshift—an energy-independent additional fractional frequency shift δz₂ = ½(ρ/ρₚ)² beyond the standard gravitational redshift, whose energy-independence distinguishes it phenomenologically from all existing quantum-gravity dispersion proposals.
Bimal Chandra Dan (Mon,) studied this question.