Near-Extremal Kerr QNM Damping as a Surface-Gravity Scaling Classifier: A Reproducible Exponent Diagnostic for Zero-Damping and Damped Modes

This technical appendix presents a toy constrained-optimization demonstration showing why binary partition intuition should not be automatically transferred to ternary or higher-channel systems. In a conserved binary partition a+b=1, additive balance and maximum multiplicative coupling coincide: by AM–GM, the pair coupling ab is maximized at a=b=1/2. In a ternary simplex a+b+c=1, however, the additive balance point remains fixed at the centroid (1/3,1/3,1/3), while the maximum of a chosen coupli