DERIVATION OF STANDARD MODEL GAUGE COUPLINGS FROM SCALE-INVARIANT INFORMATION THERMODYNAMICS

**Objective:** To derive the relationship between the Standard Model’s gauge couplings and the Kappa information field ($\kappa(x)$) using a self-contained, category-theoretic approach based on the principle of scale-invariant information thermodynamics. This derivation establishes that effective gauge couplings are proportional to $\kappa(x)$, leading to spatial and energy-scale dependence of fundamental constants like the fine-structure constant ($\alpha \propto \kappa^2$).