Non-Perturbative Constraints on the Emergent Constant CG₂ in the EGESB–G₂ Framework (Companion Technical Note to Version 7)

This technical note derives non-perturbative constraints on the emergent constant CG₂ within the EGESB–G₂ framework. Three independent approaches are combined: • Functional Renormalization Group (FRG) • Large-N saddle-point approximation• Entanglement entropy bounds The resulting interval 0. 63 ≤ CG₂ ≤ 1. 00 confirms the emergent, non-topological origin of the constant and remains fully consistent with Version 7 of the EGESB framework. This note serves as a methodological companion providing theoretical stabilization without modifying the core equations.