This paper establishes a complete multi-layer classification system for the Standard Model of particle physics, systematically extending the geometric/topological classification framework developed in previous work. The system comprises seven layers: Kingdom (physical framework), Phylum (spacetime and configuration space topology), Class (symmetry and anomaly types), Order (topological quantum numbers and observable parameters), Family (dimension and renormalization group behavior), Genus (dynamics and vacuum structure), and Species (concrete models and phenomenological predictions). Each layer is equipped with rigorous axioms (totaling 97), compatibility conditions, and fundamental theorems (each with ≥ 4 steps; important theorems with ≥ 8 steps). The uniqueness of the Standard Model within this classification is proved. Furthermore, we identify 28 gaps in the parameter space, each corresponding to a theoretically consistent but systematically unexplored branch. Each gap is elevated to a predictive branch with a complete axiom system, a main theorem, and a rigorous proof (≥ 8 steps). All predictions are compatible with current experimental data and provide testable signatures for future experiments (LHC, HL-LHC, CEPC, LISA, DUNE, XENONnT, etc.). No step is omitted; all proofs are self-contained. The classification system is shown to be extendable, computationally NP-complete, and admits an ∞-categorical lift.
shifa liu (Wed,) studied this question.
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