Non-Perturbative Constraints on the Emergent Constant C_G₂ in the EGESB–G₂ Framework (Companion Technical Note to Version 7)

This technical note derives non-perturbative constraints on the emergent constant C_G₂ 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 ≤ C_G₂ ≤ 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.