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

Abstract: This paper proposes the density-dependent saturation field φ (ρ): = 1 - exp (-ρ/ρc), 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 Gₑff (ρ) = GN (1 - φ (ρ) ) = GN·exp (-ρ/ρc) naturally emerges from the non-minimal coupling ξφR in the brane action via 5D Gauss-Codazzi projection. At saturation scale ρc = 7. 4ρₙuc (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.