Closed Paths Do Not Imply Temporal Reversal: A Structural Clarification of State Return and Time Ordering

This note clarifies a common misinterpretation in which returning to a prior configuration is taken as evidence of temporal reversal. Using the Paton Admissibility Framework, it is shown that identical initial and final states can arise from closed admissible trajectories that preserve transition history. The result is a minimal structural clarification: state equivalence does not imply historical equivalence, and temporal ordering is not inverted by state return.