Structural Conditions for the Persistence of Time

This paper presents a structural, eliminative analysis of the conditions required for the persistence of temporal ordering in closed domains. Treating temporal ordering as an operationally primitive feature, it derives necessary constraints on global reconciliation structure without appeal to dynamics, geometry, spacetime, or specific physical laws. The central result shows that in any closed system capable of sustaining temporal ordering, completion must be structurally forbidden: finite configuration spaces admitting intrinsic reconciliation symmetry cannot admit finite exhaustion under intrinsically admissible procedures. The analysis is conditional and non-constructive, intended to classify time-bearing universes rather than model physical realization. Questions of physical admissibility, legitimacy of intrinsic structure, and connections to established physical frameworks are explicitly deferred to subsequent work in the series.