This paper establishes a multi-layer classification system for biological systems based on evolutionary principles, genetic information flow, cellular organization, metabolic networks, and ecological interactions. The system takes as successive refinement criteria the hierarchical level of biological organization, evolutionary lineage and phylogenetic relationships, cellular and tissue architecture, physiological and metabolic types, ecological roles and life-history strategies, genetic and molecular parameters, and concrete species or ecosystems, forming an arbitrarily extensible classification tree. Each layer is equipped with corresponding axiom systems and fundamental theorems, so that any biological system (from molecular complexes to entire biospheres, from metabolic pathways to population dynamics) can be uniquely placed into a specific node of the tree. Conversely, any parameter combination of a node can mechanically generate an axiom system and predict as-yet-unstudied biological structures, life forms, or ecological networks. The system possesses unity, completeness, and extensibility, analogous to the periodic table of chemical elements, and can be used to systematically discover and construct new branches of biology. The paper provides formal definitions, construction methods, fundamental theorems, and multiple examples, and shows how classical branches of biology (molecular biology, cell biology, genetics, evolution, physiology, ecology, systematics) are embedded into the system, as well as how to build axiom systems and fundamental theorems for vacant parameter combinations. All theorems are given rigorous proofs (general theorems at least 4 steps, important theorems at least 8 steps), and all predictions are equipped with complete axiom systems and existence constructions, transforming the development of biology from random discovery to fill-in-the-blank construction.
shifa liu (Wed,) studied this question.