A Geometric Pharmacology Framework for TCM Four-Qi Classification: From Single-Herb TPSA Validation to 50-Formula Categorical Mapping and Application to NRICM101 (Qing Guan Yi Hao)

Unified paper integrating Papers 5-7 of the Genesis Geometric Medicine Series. Three-scale validation of TCM Four-Qi classification. Study 1 (n=15 clean molecules): TPSA separates Hot/Warm from Cold/Cool herbs (Mann-Whitney p=0.045*, Cohen d=-1.03, Spearman rho=-0.514*). Berberine anomaly defines two-mechanism rule (target-override ~25% of herbs). Study 2 (n=50 formulas, 12 categories): Therapeutic category predicts formula Nature Score with perfect rank correlation (Spearman rho=1.000, p<0.001; Kruskal-Wallis H=30.6, p=0.0013**). Formula-level TPSA non-significant (rho=-0.09) — explained by saponin macro-molecule dilution (orthogonality of scales). Xiao Chai Hu Tang NS=0.00: geometric proof of Harmonize Shaoyang principle. Study 3: NRICM101 (Taiwan COVID-19 formula) NS=-0.44 Yin-Cool. Three-layer architecture: Layer 1 TPSA/molecular, Layer 2 category/NS, Layer 3 lambda2/Windkessel/pulse. Genesis Geometric Medicine Framework v4.