Regular Black Hole Solutions in the CCEGA Framework: Metric Reconstruction, Observational Constraints, and Linear Stability

We present the first explicit numerical construction of regular black hole solutions in the Curvature Constrained Emergent Gravity Ansatz (CCEGA). Starting from the five-dimensional geometric regulator of Part I and the holographic information field φ of Part II, we reconstruct the scalar profile φ(r) and potential V(φ) that render the metric with mass function M(r) = M(1 − exp(−r³/rc³)) a numerically consistent solution of the field equations (residual error < 10⁻⁶). Neutron-star observations constrain the critical density to ρc ≳ 10 ρnuclear (95% CL). A complete linear stability analysis (Regge–Wheeler/Zerilli) demonstrates stability for all multipoles, including the physically crucial monopole (ℓ = 0) and dipole (ℓ = 1) modes. The fundamental quasinormal mode (ℓ = 2) deviates by up to 9.8% from general relativity, a signature detectable by the Einstein Telescope and Cosmic Explorer. The cosmological background φ∞ ∼ 10⁻¹² simultaneously satisfies the GW170817 speed constraint and accounts for the observed dark-energy density without fine-tuning. Possible gravitational-wave echoes and modifications to black-hole shadows are briefly discussed.