CP² Instanton Spectrum and Holographic Discretization of the Renormalization Group: A Companion Paper to the Geometric Entropy Principle

This paper develops the microscopic foundation of the Geometric Entropy Principle by analyzing the CP² nonlinear sigma model. It derives the sigma-model coupling constant from thermodynamic equilibrium between the instanton gas and the de Sitter horizon, showing that the finite holographic capacity of the universe fixes the coupling without free parameters. The same result is confirmed independently by a maximum entropy argument. The paper shows how the renormalization group flow of the sigma model, discretized by the holographic constraint, produces the GEP energy ladder. It provides an independent derivation of the cosmological constant from the instanton vacuum energy, identifies the ladder index as discretized RG time, and discusses structural connections between CP² geometry and the colour sector of QCD.