A Graph-Theoretic Characterization of Biology in GD: Twelve Necessary and Sufficient Conditions under Structural Determination Theory

This paper develops a graph-theoretic characterization of what it is to be a biological organism, derived within Structural Determination Theory (SDT), a single-axiom meta-structural ontology. Working in SDT's determination dependency graph G_D, it identifies twelve structural conditions — bounded persistent identity, material throughflow, regulatory feedback, differentiation, information-processing integration, multi-scale organization, reproduction, and operationally-reused memory — and argues that their conjunction, together with a local-maximum principle under which an organism's boundary emerges rather than being stipulated, is both necessary and sufficient for organism-hood. Each condition is derived from an ontological prior on biology, shown independent by explicit counter-model, and jointly sufficient by structural-space analysis; the characterization is verified on a constructed representation of Escherichia coli and distinguished from vortices, crystals, viruses, and self-replicating machines. The account is meta-structural: it fixes the forced structural form of life while consigning all rates, mechanisms, and thresholds to entity-theory, and it is medium-independent, specifying a pattern rather than a substance. The static characterization is extended to the temporal life cycle — creation, dissolution (including natural death as the finite-fidelity shortfall of metabolic self-maintenance), heredity, growth, and four structural-dynamical laws for the life processes — and yields an explicit definition of life whose distinguishing core is self-maintenance rather than self-replication. The result is situated against autopoiesis, Integrated Information Theory, Constructor Theory, Rosen's relational biology, and the definitions-of-life tradition (the NASA definition, Koshland's seven pillars, Gánti's chemoton, Assembly Theory), to which it stands not as a rival but as a unifying meta-structural skeleton whose value is conceptual rather than predictive.