Elastic Spacetime with Scale-Dependent Coupling (ESSC) Version 9 presents a structural consistency framework based on multidimensional inequalities. The purpose of this work is not to introduce new physical laws, entities, forces, or predictive mechanisms, but to clarify the conditions under which heterogeneous observational descriptions can remain mutually coherent without forced identification or closure. ESSC v9 reformulates inequality as an admissibility condition rather than a numerical comparison or tolerance around equality. Translations between descriptions are treated as structural relations constrained simultaneously along multiple axes, including observational scale, descriptive mode (differential versus integral), boundary sharpness, and degree of self-reference. Structural consistency is defined by the existence of an admissible translation region rather than by convergence, optimization, or unification. A minimal formal representation is introduced in terms of a translation space, an admissible region, and a distinguished non-closure element. This formulation encodes two core conditions: admissible translations always exist, while complete translational closure is structurally forbidden. Equality, limits, and optimization are explicitly excluded from the framework. The paper also specifies a clear set of structural prohibitions that define what ESSC v9 is not. These prohibitions prevent the framework from collapsing into dynamical modeling, probabilistic interpretation, or explanatory closure, and serve as boundary conditions for its correct use. Applications discussed in the paper—including consciousness and the “now,” the arrow and rate of time, entropy as irreducible non-closure, and the contrasting structural roles of electromagnetism and gravity—are presented strictly as structural illustrations. No new physical mechanisms or empirical claims are introduced. ESSC v9 functions as a pre-theoretical consistency filter rather than as a physical theory. Its role is to identify which translations, limits, and identifications are structurally admissible when relating descriptions across heterogeneous observational regimes.
umimoto (2026) studied this question.