What Zeno Required: Stable Systems, Observational Closure, and a Unified Continuous-Discrete Spacetime

Around 450 BCE, Zeno of Elea posed a paradox that has haunted Western thought for two and a half millennia: an arrow in flight must occupy a definite position at each instant, yet at any such instant it is motionless. The standard mathematical response — that calculus resolves the paradox by summing infinitely many intervals — is formally correct, yet it leaves the deeper physical question untouched. Can a durationless instant ever function as a real existence event for an embedded observer? Within the framework of Subsystem Epistemics — the study of what knowledge embedded subsystems can acquire under finite resources — the answer is no. An event exists physically only if it admits observational closure by at least one embedded subsystem. Since closure requires finite registration, comparison, and distinction, a zero-duration instant cannot itself be a closed existence event. The arrow's motion is therefore not a sequence of static instantaneous positions, but an ordered succession of discrete closure events — what we call xent — anchored within a minimal stepped structure. This paper develops the Information-Spacetime Stepping Framework (ISSF): a structure discrete at the ontic level of closure events and continuous at the observational level of interval relations. Continuity is not rejected; it is relocated. Discreteness belongs to the closure events that make existence registerable; continuity belongs to the measurement relations that embedded observers recover from those events. The framework therefore returns to Zeno with a different answer. Zeno's paradox does not merely call for calculus. It calls for a theory of observational closure. The ISSF supplies precisely that: a unified continuous-discrete spacetime in which existence occurs through discrete xent events, while embedded observers reconstruct continuous relations through intervals between them. What appeared as an ancient paradox thereby becomes the structural condition for any stable system capable of supporting knowledge from within.