Complete Parameter Derivation from the Vacuum Condensate Poisson Ratio: Gauge Couplings, Boson Masses, Planck Scale, Dark Matter, and the Cosmological Constant

Building on the vacuum condensate framework (Paper I, DOI 10. 5281/zenodo. 19143779) and the fermion mass formula (Paper II, DOI 10. 5281/zenodo. 19143896), we derive over thirty additional observables from the single condensate parameter nu = 0. 4555. The strong coupling constant is obtained as alphaₛ (MZ) = (mu/kappa) x 9/7 = 0. 1179, matching the measured value to 0. 06%. The Higgs boson mass follows from the quartic coupling lambda = sqrt (2) x mu/kappa, giving mH = 125. 3 GeV (0. 04%). The Planck mass is MP = v x R^ (16 + mu/kappa), accurate to 0. 02%, resolving the hierarchy problem as a material property of the condensate raised to a power fixed by the Pati-Salam gauge structure. The dark matter to baryonic matter density ratio is derived as kappa/ (2 mu) = 5. 45, matching the observed 5. 36 to 1. 7%, identifying dark matter with longitudinal condensate modes. The cosmological constant is obtained within a factor of two via a double see-saw suppression of the condensate self-energy. We prove three structural results from the Frobenius theorem and quaternion algebra: exactly three fermion generations, 3+1 spacetime dimensions, and thetaQCD = 0 exactly from quaternionic conjugation symmetry -- the last implying no QCD axion exists. The CKM mixing angles are derived using gammaU = 0. 824 as a universal dynamical exponent acting on down-type mass ratios. The NLO mass correction coefficients are shown to be ratios of three integers: b₀ = 11 (QCD beta function), Nc = 3 (colors), and NPS = 4 (Pati-Salam colors), consistent with one-loop self-energy structure. In total, the three-paper series addresses 41 quantitative observables, proves 4 structural theorems, and makes 2 falsifiable predictions, with zero free parameters beyond nu and v = 246 GeV, and zero failures against experiment.