Define Life: The Response–Persistence Operator.

This paper introduces a universal, mechanistic definition of life based on a single operator: response–persistence. A system is living when it registers conditions in its environment and the effects of that registration persist long enough to shape its future states. This operator dissolves the traditional boundary between living and non‑living systems, reframes abiogenesis as the closure of a continuity loop rather than a threshold event, and reveals evolution as a reciprocal living process between organisms and environments. Meaning, cognition, agency, and large‑scale systems emerge as higher‑resolution implementations of the same mechanism. The paper unifies origin‑of‑life research, evolutionary theory, cognitive science, artificial intelligence, and cosmology under one scale‑invariant definition: wherever response‑persistence closes, life appears.