The ΛVSC One-Parameter Cosmological Model: A Unified Analysis of the Cosmological Constant, Singularities, Ultraviolet Divergence, and Hubble Tension with Lean 4 Verification

We present the Lambda Vacuum Spectrum-Coupled (LVSC) universe model as a one-parameter framework addressing four problems: the cosmological constant, spacetime singularities, perturbative quantum-gravity ultraviolet divergence, and the Hubble tension. With the vacuum ground-state energy density rho0 as the only core parameter, and starting from five axioms plus the least-action principle, we derive the vacuum-field dynamics, a natural Planck-scale ultraviolet cutoff, strong-energy-condition violation, and bounded curvature. Using CODATA 2022 alpha with effective QED renormalization-group matching, we obtain a closed alpha -> N -> Lambda chain with N = 1.037111 x 10^13, Delta_RG(N*) = 9.187251, Lambda_th = 1.10560 x 10^-52 m^-2, and H0_th = 67.6600 km s^-1 Mpc^-1. We interpret the Hubble tension as the combined effect of weak effective dark-energy evolution and local void structure, and we cross-audit key results with Lean 4, Python, and Maxima.