Analytic Derivation of the Dense Matter Equation of State and Maximum Neutron Star Mass via QCD Vacuum Condensate Phase Transitions

Current models of the dense matter Equation of State (EOS) rely heavily on phenomenological parametrizations, utilizing multiple free parameters fitted a posteriori to astrophysical observables. We present the Null-Vector Gravity (NVG) Vacuum Mass Fraction (VMF) model, an analytic framework that derives the dense matter EOS strictly from the non-perturbative QCD mass gap M_{Δ,0} = 859 MeV without any empirical parameter tuning. By treating the nucleon structural mass as an effective coupling to a macroscopic QCD vacuum condensate, we show that increasing baryon density triggers a predictable melting of this structural mass. This continuous phase transition naturally stiffens the EOS while strictly respecting causality (c²_s ≤ 0.33). The model analytically predicts a maximum neutron star mass of M_max = 2.25 M☉, a canonical radius of R_{1.4} = 12.0 km, a tidal deformability of Λ_{1.4} = 470, and a post-merger peak gravitational wave frequency of f_peak = 2730 Hz for a 1.35-1.35 M☉ binary. These zero-parameter predictions fall precisely within the stringent observational constraints established by GW170817, PSR J0030+0451, and PSR J0740+6620, providing a rigid, falsifiable benchmark for future high-precision multi-messenger astronomy.