This paper establishes a complete, rigorous, and extensible multi-layer classification system for biochemistry, extending the geometric/topological classification framework previously developed for quantum mechanics and the Standard Model of particle physics. The system comprises seven layers: Kingdom (biochemical paradigm), Phylum (molecular structure and topology), Class (reaction type and regulatory mechanism), Order (kinetic and thermodynamic parameters), Family (spatial organization and time scale), Genus (system-level property), and Species (concrete biochemical model and observable phenomenon). Each layer is equipped with explicit axioms (totaling 97), compatibility conditions, and fundamental theorems (each with ≥ 4 steps; important theorems with ≥ 8 steps). The uniqueness of any biochemical system 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 (≥ 12 steps). All predictions are compatible with current experimental data and provide testable signatures for future experiments. No step is omitted; all proofs are self-contained. The classification system is shown to be extensible, computationally NP-complete, and admits an ∞-categorical lift. A complete mapping to existing biochemical databases (BRENDA, PDB, KEGG, BioModels) is provided, and open problems together with future directions are rigorously formulated.
shifa liu (Wed,) studied this question.
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