Unified Tripartite Framework for the Origin of Life: Integrating Nonlinear Chemical Diversity, Network Topology, and Non-equilibrium Kinetics

The origin of life represents a fundamental phase transition from a lifeless chemical soup to an autonomous, information-preserving dissipative structure. Historically, theoretical approaches to this transition have been bifurcated: graph-theoretical models focus on the topological emergence of autocatalytic sets, while kinetic models emphasize the ther- modynamic conditions required for physical survival. This paper proposes three explicit mathematical conditions as a conceptual hypothesis to synthesize these two approaches: (1)Diversity Explosion (Chemical Potential), (2) Information Network Emergence (Topology), and (3) Physical Survival of Dissipative Structures (Kinetics). By defining the intersection of these three conditions, we present a working hypothesis that the emergence of a chemical ecosystem—the precursor to the Last Universal Common Ancestor (LUCA)—is not a singular miraculous event, but a statistical consequence when nonlinear chemical combination intersects with highly localized, non-equilibrium thermodynamic conditions. This framework provides a theoretical basis for mathematically coupling topology and kinetics, which have largely been treated as semi-independent paradigms.