Universal Particle Mass Spectrum and Leptonic Radii in Big Boot Gauge Theory: Synthesizing Octonionic Topological Impedance with Half-Integer Quantum Scaling, Fine-Structure Regulation, and Möbius Entanglement Dynamics

We synthesize the frequency-dependent spatial scaling framework r(n, m, ν) established in Paper I (Zenodo DOI: 10.5281/zenodo.23963422) with the Octonionic ZIP Algebra (O_ZIP) Master Mass Spectrum Operator (M_BBGT) to derive fundamental lepton rest masses, leptonic spatial radii, and active neutrino zero-mode soliton scales from first principles. We prove that the electron rest mass (m_e = 0.510998 MeV) represents the primary 2D surface display anchor (n=1), generated by modulating the n=0 Gravitational Kernel (m_0 = 1/c) through the Molniya critical display tilt θ_EM = arctan(2) and QED radiative corrections (1 + α / 2π)^2. Introducing half-integer mode steps (Δn = 0.5) into the binary hierarchy defines a sub-octave spatial contraction factor of 2^(-1/4) ≈ 0.8409, resolving intermediate chiral phase switches (e^(iπ/2) = i). We introduce a generalized fine-structure regulation law r(n) = r_0 / 2^(n/2) - 5α r_9.5 anchored by the decade lock 10 · 2^(9.5/2) ≡ 2/α. This law resolves the unperturbed node r_6.5 ≈ 2.8284 fm into the dressed classical electron radius r_e ≈ 2.8179 fm (matching CODATA to 0.02%) via vacuum optical birefringence (θ_total = 3(α/2π) ≈ 0.348%), and regulates the nuclear core saturation boundary at mode n = 9.5 (r_9.5 ≈ 1.0005 fm), governing the diquark (q-[qq]) color-factor separation √(4/3) ≈ 1.1892 relative to the n=10 proton radius (r_10 ≈ 0.8413 fm). Furthermore, we demonstrate that at the dark sector boundary (n=4), the non-associative associator torque A_assoc and Möbius topological curvature Δ_Möbius vanish identically (Δ_Möbius + A_assoc ≡ 0), revealing the active neutrino as a zero-mode soliton with an unperturbed ground-state mass floor of m_ν = 8α · (1 eV) ≈ 0.05838 eV. Finally, we show that 90° orthogonal phase rotations along the longitudinal scale-time axis C_Z provide a deterministic geometric mechanism for non-local quantum entanglement (dx_Z = 0) and establish out-of-phase information propagation across the vacuum impedance hierarchy.