The computational genesis of a self: Representational time and self-modeling in living systems.

The transition from inanimate physicochemical dynamics to autonomous agency represents a fundamental challenge across theoretical biology and cognitive science. While traditional accounts have approached this transition through descriptive frameworks of autopoiesis, anticipatory systems, or the free energy principle, a formal deductive derivation linking computational irreducibility to functional agency has remained elusive. Here, a deductive framework demonstrates that core attributes of biological agency, specifically representational time, forward predictive processing, and self-modeling, emerge as operational necessities for an autonomous agent persisting within a computationally irreducible environment under a defined operational regime of delayed hazards and counterfactual pre-commitment. Grounded in organizational closure and viability theory, this framework establishes three principal deductive results. First, it is demonstrated that purely reactive behavioral strategies fail under observationally aliased environmental states requiring mutually incompatible viability-preserving actions; persisting under delayed viability hazards without lethal trial-and-error mandates the internal synthesis of a tripartite representational time. Second, this representational time is shown to share the operational organization of counterfactual forward prediction. Third, drawing upon closed-loop regulator theory, the Conant-Ashby theorem, and the internal model principle, it is established that evaluating candidate interventions over extended horizons (H > 1) in a coupled system requires internalizing the agent's own generative action dynamics, yielding a functional self-model distinct from simple state-dependent regulation. These formal derivations are subsequently grounded in concrete molecular and cellular phenomena, including cyanobacterial KaiABC timekeeping, synthetic protocellular clocks, microbial adaptive regulation, and bacterial chemotaxis, explicitly demarcating experimentally demonstrated substrates from theoretical extrapolations. Finally, the framework develops a theoretical bridge connecting computational irreducibility to the semiotic hypothesis of organic codes as physical adaptors bridging decoupled biological domains, incorporating the code-mediator-artifact distinction. The analysis concludes that within the specified operational regime, functional self-representation emerges as an inevitable computational consequence of autonomous persistence.