A Theory of Life: The Φ-Stable Transition in Chemical State Space

We propose that life is not the endpoint of a gradual accumulation of improbable steps, but the result of a sharp, dynamical phase transition in chemical state space. A system becomes alive only when four necessary and sufficient conditions—persistent asymmetric records, localized construction exceeding destruction, a self-produced boundary, and template-directed replication—are satisfied simultaneously. This defines a Φ-stable fixed point: a topologically protected attractor where symbolic information, energy flow, and compartmentalization co-stabilize. Crucially, this transition resolves "Zeno’s paradox" of abiogenesis: life does not require an infinite sequence of validated micro-steps; it emerges in a single basin-crossing event, much like water boiling at 100°C. Using a minimal three-variable ODE model (replicator, membrane, energy), we analytically derive the existence and stability of this living fixed point and show it appears only above a critical energy influx threshold. The theory explains why viruses, crystals, fires, and computers are not alive, predicts abrupt onset of lifelike behavior in prebiotic experiments, and offers quantitative, falsifiable criteria for the origin of life. Grounded in non-equilibrium thermodynamics and consistent with the SFIT framework’s topological irreversibility, this work reframes life not as chemistry plus magic—but as chemistry plus a phase transition.