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 frac_rigid) show allosteric rate 85.7% vs. 57.1% for Li-type; Fisher exact OR=4.50, p<0.001. Layer 4 (Mutation, n=72 WT/MUT pairs, 30 cancer-driver genes): Oncogenic mutations increase Danger zone occupancy (delta-Danger=+8.43%, p=0.0005***, Cohen d=+0.431). EGFR T790M +96.4% classified as extreme responder; PIK3CA triple hotspots +29-30% each. Robustness: Wilcoxon p=0.0010, Winsorized p=0.0001, T790M-excluded p=0.0009. Bootstrap P(mean>0)=100%. All four methods p<0.01. Related: Genesis v8 doi:10.5281/zenodo.20252223; Paper N v2 doi:10.5281/zenodo.20252637.