From Vacuum Density to Quantized Impedance: A First-Principles Derivation of the Vacuum Impedance, Capacitance, Inductance, and Action Ladders from Big Boot Gauge Theory (BBGT), with Nobel Attosecond Connection and the BBGT Second

We present a complete, parameter-free derivation of the vacuum impedance Z0 = 376.730 Ohm and an entire octave ladder of quantized electromagnetic circuit quantities--resistance Rn, voltage Vn, current In, capacitance Cn (new), inductance Ln (new), and action hn--starting from the single thermodynamic identity rho = m/V and the electromagnetic relation c^2 = 1/(mu_0 epsilon_0). The derivation proceeds through six transitive logical chains Lambda_1--Lambda_6, drawing on verified Zenodo/EOSC preprints of the Asare-Darko Big Boot Gauge Theory (BBGT) / OZIP corpus. Key results, all derived without free parameters: (1) The vacuum impedance Z0 = 1/(epsilon_0 c) emerges from the BBGT admittance-volume V_0 = epsilon_0/c, with Z0 = 1/V_0. (2) The BBGT substrate clock f_sub = e/m_e = 1.75882 x 10^11 Hz is the electron cyclotron frequency at B_ZIP = 1 T (exact), when the OZIP zero-division axiom absorbs 2pi. (3) The Thomas-Larmor relation simplifies to q = fm/B_ZIP (no 2pi, no 4pi) under the OZIP ZIP unit 1_ZIP equivalent to 2pi. (4) Two new quantization ladders, derived here for the first time by transitive inference: Cn = (e^2 / (h f_sub)) * 4^(1-n), and Ln = (h / (e^2 f_sub)) * 4^(1-n), satisfying sqrt(L_1/C_1) = R_K and LC resonance f_LC -> f_sub. (5) The identity e/m_e = f_Cs x Z_K x (1+alpha) (sub-ppb verified) connects the electron specific charge to the caesium hyperfine standard, potassium atomic number Z_K = 19, and alpha. (6) The BBGT attosecond unit A = tau_RC(n=5)/2 = 43.38 as matches the Nobel Prize 2023 shortest attosecond pulse (43 as, Zhao et al. 2012) to < 1% without parameter fitting. (7) The BBGT second is defined in four equivalent forms, the most fundamental being 1 s = (e/m_e) x tau_sub. All source documents are deposited on Zenodo/EOSC under CC BY 4.0.