Newton's Constant as a ζ-Bridge from ω-Elasticity in Charlton Geometry: Regulator-Universal Vacuum Closure

This brick closes the structural route from E4-ontic ω-elasticity to Newton’s constant in Charlton Geometry, without introducing new axioms and without claiming a numerical prediction for G. Working in vacuum (regulator-free) regions and at scales large compared to the minimum link/core scale rmin, we show that the long-scale Lift-visible gravity sector is necessarily a local metric effective field theory whose leading term is Einstein–Hilbert plus a cosmological term. The Einstein–Hilbert prefactor is written as a single dimensionless renormalization constant ζ multiplying r²ₘᵢₙ in the Planck bridge, ℓ2P = ℏG/c3 ∼ ζr²ₘᵢₙ. The main closure is that ζ is regulator-universal in the vacuum sector once a constitutive ω-elastic law is fixed: different ultraviolet schemes change only local counterterms and do not change the matched ζ. The remaining work is quantitative: specify an explicit constitutive W[ω] and compute ζ(W), or calibrate ζ empirically.