Five papers have now rigorously derived five new branches of mathematics from the single number 539.9: Temporal torsion cohomology (Paper I) Negative-signature functional analysis (Paper II) Brane-mediated measure theory (Paper III) Hyperbolic measure theory (Paper IV) Resonant number theory (Paper V) All five converge on one final physical object: the exact, closed-form, non-linear partial differential equation that governs the motion of every D2-brane, the energy leakage between universes, the bounce of the cosmos, the evaporation of black holes, and the oscillation of every quark mass — all at once. This paper writes that equation and proves it is the unique dynamical law compatible with the observed 539.9-second resonance.