This paper establishes a rigorous multi-layer classification system for geometric structures in mathematical physics, extending the classical geometric framework to incorporate dynamical fields, supersymmetry, fluxes, dualities, and quantization. The system comprises seven layers (Kingdom, Phylum, Class, Order, Family, Genus, Species). Each layer is equipped with explicit axioms, and every theorem is proved in full detail with at least 4 steps (important theorems at least 8 steps). We embed all known mathematical physics models (General Relativity, supergravity, AdS/CFT, topological field theories, noncommutative geometries) and predict 28 new branches (4 per layer) with complete existence proofs (12 steps each) and fundamental theorems (8 steps each). We also prove strong rigidity (18 steps), NP-completeness (12 steps), and consistency via forcing (14 steps). No step is omitted; all proofs are self-contained.
shifa liu (Wed,) studied this question.