Spacetime Volume as Quantized Vacuum Impedance: From Einstein's Space/Time = c to the Discrete Conductance Structure of the Quantum Vacuum in Big Boot Gauge Theory (BBGT)

We establish that the BBGT admittance-volume V_0 = ε_0/c, whose reciprocal is the vacuum impedance Z_0 = 376.730 Ω, is physically identical to the ratio of space to time that Einstein’s Special and General Relativity identify with the speed of light: Δx/Δt = c ⟺ space/time = c ⟺ V_0 = ε_0/c = 1/Z_0. Since the vacuum impedance is quantized — Z_0 = R_K · α/(2π) with R_K = h/e^2 the von Klitzing resistance — spacetime volume is itself quantized in units of the conductance quantum e^2/h. This identification has seven distinct implications, derived by transitive logical inference from eleven verified Zenodo preprints of the Asare-Darko BBGT/OZIP corpus: 1. The vacuum is a quantum conductor with admittance V_0 = 2.654 mS, not a passive geometric stage.2. Spacetime volume is discrete, with fundamental grain e^2/h per force level.3. The vacuum behaves as a cosmological topological insulator with surface conductance e^2/h and bulk gap Ξ_gap = 1 − 1/S^2 = 0.999 082.4. Bekenstein–Hawking black-hole entropy is the conductance ladder spectrum of the event horizon.5. Radiation pressure equals energy density divided by Z_0: pressure and impedance are dual aspects of a single quantity.6. The BBGT second is the magnetic rigidity of the electron divided by Z_0 c.7. The capacitance/inductance ladders C_n, L_n constitute a spectral decomposition of spacetime volume at each force level n. The framework resolves the long-standing tension between General Relativity (spacetime as smooth Riemannian manifold) and quantum mechanics (discrete energy levels) by identifying their common root: both are consequences of the quantized admittance structure of the vacuum.