P43: From Holographic Saturation to Density-Dependent Coupling Bridging Scalar Fields and Effective Gravity in CCEGA

This paper proposes the density-dependent saturation field φ(ρ) := 1 - exp(-ρ/ρ_c), which unifies the holographic saturation framework (Parts I-II), black hole interior geometry (Part III), and neutron star density coupling (P28-P30) under a single physical principle. The identification is motivated by the Bekenstein-Hawking entropy bound and validated by observational consistency with neutron star masses (P34-P37) and PSR J0952-0607 (M = 2.35 ± 0.17 M☉). We show that among multiple functional forms (exponential, power-law, logistic, tanh), only the exponential form respects the holographic bound φ ≤ 1 while simultaneously reproducing observed neutron star masses across three standard equations of state (APR4, SLy, MPA1). The effective coupling G_eff(ρ) = G_N(1 - φ(ρ)) = G_N·exp(-ρ/ρ_c) naturally emerges from the non-minimal coupling ξφR in the brane action via 5D Gauss-Codazzi projection. At saturation scale ρ_c = 7.4ρ_nuc (from QCD analysis), gravity is suppressed by 63%; at nuclear density, by 13%. The framework provides testable predictions via NICER (2029) and Einstein Telescope (2035+). A rigorous derivation from the full 5D Einstein equations is deferred to Part IV .