Bogoliubov Coefficients, Correlated Hawking Radiation, and the Page Curve in the CCEGA Framework: The Echo Delay as the Carrier of Quantum Information

We compute the Bogoliubov coefficients for a massless scalar field in the regular black hole background of the Curvature-Controlled Extra-Dimensional Gravity and Emergent Unification (CCEGA) framework. The regular core at r=0 imposes a Dirichlet boundary condition u(0)=0 for all Regge-Wheeler modes, producing perfect reflection and introducing off-diagonal Bogoliubov coefficients Δβ_ωω' that are absent in the Schwarzschild case. These off-diagonal terms encode correlations between Hawking quanta emitted at times separated by the echo delay τ_echo, providing an explicit geometric mechanism for information release. The correlation rate is Γ_corr = 1/τ_echo ≈ 6×10⁻⁶ c³/GM, a factor ~10⁻⁴ smaller than the thermal emission rate. The Page time occurs at t_Page ≈ 0.02 t_evap, identical numerically to Schwarzschild, but the mechanism of information release differs fundamentally: in CCEGA it is explicit and geometric, mediated by correlated pairs of Hawking quanta separated by exactly τ_echo. This establishes a direct connection between the classically observable gravitational-wave echo delay and the quantum information content of the Hawking spectrum, unifying the observational and theoretical sectors of the CCEGA programme.