Time as an Indexing Structure of Trace Updates: An Operational Framework for Recurrence, Slip, and Projection in Finite-Boundary Systems

This paper presents an operational framework for systems where motion is conserved but trace carriers are finite. It defines recurrence as repeated state visitation within a bounded space and introduces "slip" (S) as the necessary geometric mismatch resulting from finite capacity. Time is treated not as a primitive variable but as a post-hoc index structure generated by irreversible trace updates. The framework explains how accumulated slip projects as observable rotational patterns or results in system collapse.