P43 Extended: 5D to 4D Dimensional Reduction — Rigorous Derivation of G_eff(ρ)

Technical supplement to P43 providing detailed mathematical derivation of the 4D effective Newton constant from 5D brane-world geometry. Covers: warped metric, Israel junction conditions (boundary matching), extrinsic curvature, Gauss-Codazzi projection, dimensional reduction via integration over fifth dimension. Shows how φ(ρ) = 1 - exp(-ρ/ρ_c) and G_eff(ρ) = G_N·exp(-ρ/ρ_c) emerge from first principles (to leading order). Includes honest caveats: violation of strong equivalence principle in strong field (~12% at nuclear density), non-uniqueness of 5D geometry, perturbative Weyl tensor treatment, undetermined coupling parameter ξ. All identified as Part IV tasks. Clarifies that equivalence principle violation does not imply falsity—it is testable feature distinguishing CCEGA from GR.