Twenty-Four Mountain Celestial Compass as a Multi-Scale Geometric Descriptor of Protein Topological Order: From Allosteric Classification to Oncogenic Mutation Detection -- A Four-Layer Investigation with Robustness Analysis

We report a geometric isomorphism between the classical Chinese Twenty-Four Mountain (Er-Shi-Si Shan) geomantic compass and the Fiedler eigenvector phase space of protein contact networks, validated across four complementary experimental layers with full robustness analysis. Layer 1 (Population, n=569 AlloBench): Allosteric proteins show significant Golden sector enrichment (p=0. 0018) and Danger sector depletion (p=0. 0003) ; non-allosteric proteins show no deviation from uniform. Layer 2 (Geometric theorem): Six Danger sectors form an exact centrosymmetric nodal set (offset std=0. 000 deg, vector sum=0. 00000000). Danger = nodal lines; Golden = antinodal regions of Fiedler vibrational mode. Layer 3 (Kan-Li classification, n=336): Kan-type proteins (low lambda2 + low fracᵣigid) show allosteric rate 85. 7% vs. 57. 1% for Li-type; Fisher exact OR=4. 50, p0) =100%. All four methods p<0. 01. Related: Genesis v8 doi: 10. 5281/zenodo. 20252223; Paper N v2 doi: 10. 5281/zenodo. 20252637.