Time, Records, and Irreversibility: Operational Foundations Without Temporal Primitives

We establish two foundational results concerning time and irreversibility within an operational framework where physical measurements correspond to distinguishable, persistent record states. First, we prove that no physical clock can ground time as a fundamental parameter: any clock-induced ordering necessarily reduces to a preorder defined by reachability among record states via admissible transformations. Second, we prove that bounded recording capacity forces accessible irreversibility: any system capable of recording more distinct events than its accessible register capacity must exhibit non-invertible operations at the accessible level. These results are derived without assuming time, entropy, or thermodynamic principles as primitives. Together, they establish that temporal structure and irreversibility are not independent physical laws but emerge from operational constraints on physical memory and distinguishability. The framework is compatible with globally unitary microscopic dynamics while explaining effective irreversibility for bounded observers. We conclude that time is a representational index for record structure rather than an ontological primitive , establishing the necessary foundation for the failure of deterministic prediction addressed in companion work [3]