Experimental Validation of Field Dynamic Number Equation: R′-Space Group Mapping and Symmetry Oscillation in the Mg-Si Binary System

The Field Dynamic Number Equation (FDNE) introduces a dimensionless parameter R′ = |E_above_hull| / (|E_formation| + ε), derived from convex hull thermodynamics, to quantify the phase transition readiness of crystalline polymorphs. This study presents the first systematic experimental validation of the FDNE theory through the Mg-Si binary system, leveraging the OQMD database (1,407,395 materials) cross-validated with the AFLOW database. Key findings: (1) R′ ≈ 16 maps to space group P6₃/mmc (#194), matching the experimental Mg₂Si high-pressure endpoint at ~21.3 GPa; (2) a non-monotonic symmetry oscillation pattern is discovered; (3) three target space groups (Cmcm #63, P4/mmm #123, Imma #74) are validated as exclusive high-pressure indicators. This is the English version of the paper, which also exists in Chinese (DOI: 10.5281/zenodo.21483316).