P78 Toward a Dynamical Origin of ρc in CCEGA: Radion Saturation from DBI Dynamics Coupled to the Chiral Condensate

We take a step toward a dynamical understanding of the critical density ρc in the CCEGA framework. Starting from the DBI action of the radion in a Randall-Sundrum background, we couple the radion field φ to the chiral condensate ⟨ψ̄ψ⟩ (ρ) through an explicit effective interaction. We construct a toy effective potential with a tilted double-well shape and derive a closed-form saturation condition for ρc in terms of the QCD deconfinement density and O (1) model parameters. The working value ρc = 7. 4 ρₙuc used throughout the CCEGA series is reproduced for natural parameter choices. We emphasize that this is a plausibility/consistency result, not a parameter-free derivation of the central value, and state the remaining dependence on the ultraviolet completion explicitly.