Renormalizable EBIKK-β Model: Unifying Ricci-Perona-Malik Flows, Holography and Quantum Gravity

We present a renormalizable Entropic-Born-Infeld-Kaluza-Klein (EBIKK) model with β-regularization, establishing connections between geometric flows, Noether symmetries, and holographic duality. The framework demonstrates:• Ricci-Perona-Malik flow equations emerging from entropic gradients• Enhanced conservation laws• Smooth classical limits• Observational advantages over pure Born-Infeld or Kaluza-Klein theories• A novel AdS5/CFT4 correspondence• Viable quantization prospects• Testable predictions including regularized black holes and modified early universe dynamicsThe model resolves UV divergences while preserving predictive power across energy scales.