Classical TCM Formula Four-Qi (Si Qi) Geometric Atlas: TPSA x logP x Q_LTE x GII Analysis of 12 Canonical Formulas — From Coptis Antitoxin (Yin-Cold) to Four Gentlemen (Yang-Warm)

Building on Paper 5 (DOI: 10.5281/zenodo.20161037), which established TPSA as the primary single-herb Four-Qi descriptor, this paper (Paper 6 of Genesis Series) extends the analysis to 12 classical TCM formulas (66 herb-compound pairs). Key findings: (1) Formula mean TPSA inversely correlates with thermal Nature Score (rho=-0.55, p=0.065, trend). (2) Three thermal classes emerge: Yin-Cold formulas (Huang Lian Jie Du, Long Dan Xie Gan) at TPSA>140; Yang-Warm (Si Jun Zi, Ma Huang, Bu Zhong Yi Qi); Neutral/Complex (Xiao Chai Hu, Gui Zhi Fu Ling, Xue Fu Zhu Yu) near NS=0. (3) Xiao Chai Hu Tang achieves NS=0.00 exactly — geometric confirmation of the classical Harmonize Shaoyang principle, where cold herbs (Huang Qin, Chai Hu, sum -3) precisely cancel warm herbs (Ban Xia, Ren Shen, Sheng Jiang, sum +3). (4) Formula modification (jia jian) is geometrically measurable: Liu Wei -> Zhi Bai Di Huang NS shift = -0.45, quantifying the added fire-draining component. A computational prescribing algorithm is proposed: measure patient pulse lambda2, compute required NS delta, select formula from the geometric atlas. Part of Genesis Geometric Medicine Framework v4.