This paper investigates regimes in which first-order variational description is structurally inadmissible, while second-order variational structure remains well defined and sufficient for coherent formulation. The breakdown of first-order language is shown to arise not from analytical difficulty but from the absence of the grammatical conditions required to define states, trajectories, or extremality. In contrast, second-order relations based on comparison, equivalence, and boundary consistency persist and provide a closed descriptive framework. We develop a systematic classification of such regimes, including boundary-dominated, critical, scaling-limit, equivalence-fixed, and interface-controlled settings. These regimes are contrasted with fully admissible variational frameworks in which first- and second-order structures coexist hierarchically. Representative examples from mathematics, physics, and cosmology demonstrate that second-order admissible regimes are generic rather than exceptional. The analysis clarifies the logical function of variational language and delineates the precise limits of admissible description once first-order structure fails.
Anonymous (Thu,) studied this question.