The Emergent Geometry of the Vacuum: Impedance Modulation Z0, Proper Time Restriction (∆τ = 0), and Median Logic in Local Warp Metrics

We present a unified formulation where the geometry of spacetime and the effective propagationspeed of signals emerge from the electrodynamic properties of the quantum vacuum, rather thanconstituting primitive postulates of the four-dimensional manifold. We demonstrate that the constant c0 represents the asymptotic phase velocity in an undisturbed vacuum with a characteristicimpedance Z0 ≈ 377 Ω. By imposing the null proper time condition (∆τ = 0) on gauge bosonsand applying a Median Logic (M) algebra to resolve the phase transition at curvature boundaries,we establish a dynamical mechanism for the creation and stabilization of negative energy densities(ρvac < 0). This formalism resolves the cosmological constant catastrophe via infrared/ultraviolet (UV /IR) coupling, provides an algebraic solution for boundary instabilities in Alcubierre-typesolutions, and establishes causal dispersion limits for interplanetary data transmission.