The ΛVSC One-Parameter Cosmological Model: A First-Principles Interpretation of the W-Boson Mass 7σ Anomaly, Z-Boson Compatibility Check, and Lean 4 Verification

In 2022, CDF II reported m_W = 80433.5 +/- 9.4 MeV, about 7 sigma above representative SM electroweak-fit benchmarks. This paper studies that anomaly within the one-parameter Lambda Vacuum Spectrum-Coupled (LambdaVSC) cosmological model, whose only free parameter is the vacuum ground-state characteristic energy density rho0. Using the primordial cycle count N = 1.037111 x 10^13 from the companion LambdaVSC framework, we derive the dominant low-energy weak-coupling correction and obtain the leading prediction m_W^(LambdaVSC,lead) = 80433.4 +/- 6 MeV, consistent with CDF II within 1 sigma. The direct Planck-suppressed higher-dimensional contribution remains of order 10^-29 MeV. We also derive controlled electroweak-precision compatibility bounds: |delta m_Z| <~ 0.082 MeV, |delta m_Z|/sigma_Z^PDG <~ 0.039, |delta sin^2 theta_W^eff(m_Z)| <~ 2.09 x 10^-7, and the corresponding ratio to the current experimental uncertainty <~ 1.6 x 10^-3, with retained-order shifts of G_F and alpha equal to (0,0). Finally, the model yields a parameter-free prediction for the total W-boson decay width and predicts per-mille-level universal normalization shifts in electroweak differential observables. Key relations are cross-audited with Lean 4, Python, and Maxima.