An Axiomatic Theory of Life Systems Based on Organizational Principles

Living systems contain immense molecular, structural, and hierarchical complexity, yet complexity alone does not explain why heterogeneous components constitute a determinate living whole. This paper develops an axiomatic theory in which the Life Organizational Structure O(L) is the sole primitive object, and every other theoretical object is derived through a non-circular dependency relation. The framework establishes the formal sequence O(L) => R => C => M => Ω => FO => Σ => Ψ => T, where R denotes organizational relations, C organizational constraints, M organizational boundary, Ω the Organizational Regulatory Domain, FO Fixed Order, Σ an admissible organizational realization, Ψ the complete Life Organizational State, and T organizational transformation. This architecture separates admissibility, order, transformation, irreversibility, and uniqueness. At hierarchical level h, a collection satisfying a common organizational condition becomes a higher-level unit through a boundary, C_h ->[M_h] U_{h+1}, providing a recursive mechanism by which internal complexity becomes higher-level organizational simplicity. For DNA-based life, the four-base alphabet B={A,T,C,G} admits an exact quaternary representation, but alphabet cardinality alone does not imply a quaternary biological law. The stronger biological hypothesis concerns ordered organizational realization under a DNA-specific Regulatory Domain and Fixed Order. The theory distinguishes organizational growth, completion, division, inheritance, development, maturity, lifecycle persistence, aging, and pathology as logically separate processes. A complete Life Organizational State is represented as Ψ_L=(X,R,E,V), where E and V denote Explicit and Implicit Organization. An empirical interface connects theoretical organization to measurable prediction, and a biological specialization is experimentally falsifiable only when its predicted measurement set is a proper subset of the possible measurement space. The resulting theory provides a formal path from primitive life organization to restrictive and experimentally testable biological predictions.