Theoretical Framework and Emergence of the Agegraphic Term

Recent works on agegraphic dark energy in anti–de Sitter (AdS) backgrounds introducean effective coupling parameter b2≃0.30 to account for the entropy–correctedinteraction between matter and vacuum. Here we demonstrate that this coefficient andthe entire dynamical structure of the agegraphic term naturally emerge from the closedand self–referential Universal Ψ Lagrangian, without any external parameter or ad–hocentropy correction. The informational constraint (Ψ†Ψ−1)2 provides the physical originof the agegraphic scaling, and the mean field energy density reproduces the observedHubble constant H0 = 67.7kms−1 Mpc−1 reported by Huang et al. (2025).