Time as a Bookkeeping Structure: Emergent Ordering from Irreversible Records

The macroscopic arrow of time is commonly attributed to irreversibility, yet many theoretical treatments implicitly assume time as a primitive parameter even when discussing emergent temporal behavior. In this work, we study a minimal framework in which time is not presupposed but arises operationally from irreversible record formation. We show that the existence of persistent, non-erasing records is sufficient to induce a monotone, reparameterization-invariant ordering of events, independent of microscopic dynamics or background time parametrization. Using a minimal concrete realization, we explicitly demonstrate monotonicity, reparameterization invariance, and the breakdown of temporal ordering when irreversibility is relaxed. We do not address relativistic or quantum time directly; rather, we isolate the minimal structural requirements for temporal ordering to exist at all. Taken together with companion work on coherence stabilization, these results support a modular view of emergent classicality in which time and coherence arise from distinct physical mechanisms. Keywords: emergent time, irreversibility, records, relational time, arrow of time, foundations of physics