The origin of temporal ordering and irreversible structure remains a central problem in foundational physics. While several modern approaches eliminate time as a primitive parameter, most retain an ordering relation over configurations, states, or events. The temporal structure is then reconstructed from this pre-existing order. Consequently, time may be removed while ordering itself remains unexplained. This paper investigates whether ordering can be constructed without assuming temporal parameters, causal relations, dynamical evolution, or globally available ordering structures. We formulate the problem as one of ordering circularity: explanatory frameworks often derive temporal behavior from ordering while treating ordering itself as primitive. To address this issue, we introduce the Local Monotonic Constraint Relation (LMCR), a framework in which ordering emerges from the conjunction of locality-restricted comparability and monotonic constraint structure. Configurational ordering is not postulated but constructed from locality-constrained monotonic comparability. We prove that LMCR induces a directed acyclic accessibility structure whose directional asymmetry arises intrinsically from admissible constraint relations rather than from temporal evolution. A central result concerns the role of locality. We argue that locality constitutes a weaker primitive than temporal or causal order because locality contains neither orientation, succession, duration, nor directional asymmetry. Ordering emerges only through the interaction between locality and constraint monotonicity. We further show that the induced ordering relation constitutes a non-invertible projection of a richer locality-constrained structure, implying that the underlying locality architecture cannot in general be uniquely reconstructed from ordering information alone. To establish physical relevance, we introduce a thermodynamic toy realization in which configurations correspond to particle microstates, locality corresponds to elementary admissible rearrangements, and the constraint functional corresponds to entropy-like structure. Within this realization, directional accessibility and entropy-compatible asymmetry emerge from the same underlying ordering topology. The framework therefore reverses the conventional explanatory hierarchy. Rather than deriving ordering from temporal asymmetry, temporal asymmetry becomes representable because admissible ordering structure already exists. The resulting construction provides a non-circular foundation for ordering and a structural route toward irreversibility without assuming time as a primitive ingredient.
Aruna Reddy Katanguri (Wed,) studied this question.