A Two-Dimensional Gravitational-Wave Discriminant for Curvature-Controlled Extra-Dimensional Gravity: Echo Delay and Radion-Induced Frequency Sidebands as a Falsifiable Signature of the CCEGA Framework

We identify a two-dimensional gravitational-wave (GW) discriminant that constitutes the primary falsifiable prediction of the Curvature-Controlled Extra-Dimensional Gravity and Emergent Unification (CCEGA) framework. The discriminant consists of (i) a post-merger echo delay τₑcho ≈ 14 ms for 30 M☉ binary-black-hole events, set by the geometry of the CCEGA warp factor W (ρ) ; and (ii) radion-induced frequency sidebands separated from the main echo by Δfᵣad ∈ 24, 2400 Hz for a radion mass m_φ ∈ 10⁻¹³, 10⁻¹¹ eV. We show that the simultaneous presence of both features, together with the functional correlation between τₑcho and Δfᵣad imposed by CCEGA geometry, is not reproduced generically by competing models: classical exotic compact objects (ECOs) predict echoes without sidebands, while extra-dimensional models lacking a dynamical modulus predict neither sidebands nor the specific (τₑcho, Δfᵣad) correlation derived here. The combined signature lies within the projected sensitivity of the Einstein Telescope (~2035), providing a decisive observational test of the framework.