This paper establishes a rigorous, multi-layer classification system for the entire field of genetics, extending the axiomatic methodology previously developed for geometric and topological structures in mathematical physics. The system comprises seven hierarchical layers (Kingdom, Phylum, Class, Order, Family, Genus, Species). Each layer is endowed with explicit parameter sets, compatibility conditions, and fundamental theorems proved in full detail. All essential features of genetics—genetic information storage (DNA/RNA), the central dogma, mutation, recombination, natural selection, genetic drift, population equilibrium, epigenetic inheritance, and genotype–phenotype mapping—are built into the classification. We embed every major branch of genetics (Mendelian, molecular, population, quantitative, evolutionary, developmental, epigenetic, medical, forensic, and synthetic genetics) into the system. Based on a rigorous gap analysis we predict 34 new branches, each accompanied by a complete seven-layer axiom system, a main theorem, and a fully detailed proof. We also prove a strong rigidity theorem, NP-completeness and QMA-completeness theorems, and the existence of non-standard genetic vacua via forcing. All conjectures and open problems from earlier treatments are resolved and promoted to theorems. The classification is shown to be arbitrarily extensible, admits an ∞-categorical lift, and is logically consistent. The 34 predictions are experimentally testable, and specific protocols are provided.
shifa liu (Wed,) studied this question.