This paper develops the second step of the Structural Admissibility Regimes (SAR) framework by introducing admissible ordering of refinements within the finite-capacity algebraic structure established in Structural Admissibility Regimes (SAR): Finite-Capacity Constraints on Algebraic Decompositions (SAR I). While SAR I established admissibility as a purely algebraic constraint on subsystem decompositions, the present work studies how admissible refinements can be consistently ordered under finite structural capacity. Using an ordered refinement algebra and ordered commutator calculus, we analyze how admissibility, ordering, and commutativity interact. Two ordered regimes arise: a geometric regime, corresponding to maximal commuting ordered refinement families, and a temporal regime, arising when admissible ordering exists but commuting structure cannot be maintained. Non-commuting, non-invertible refinements produce directional refinement chains with finite depth due to capacity constraints. The analysis establishes algebraic conditions for the emergence, stability, and breakdown of ordered regimes under finite structural capacity. Geometry and temporal order therefore arise as capacity-limited regimes of admissible ordered organization within the SAR framework, without invoking geometric, dynamical, or probabilistic assumptions. Part of the Structural Admissibility Regimes (SAR) foundational series and building directly on Structural Admissibility (SAR I).
Ravikumar Rajappa (Wed,) studied this question.