Structural Dimension and Consistency Conditions A Pre-Theoretical Framework for Relating Observational Regimes

This work introduces the concept of structural dimension as a pre-theoretical framework for organizing and relating physical quantities defined across distinct observational regimes. Dimension is not treated as a count of spatial or temporal coordinates, nor as a dynamical or observable entity. Instead, it is defined as a structural attribute specifying the conditions under which physical quantities are meaningfully definable, comparable, and relatable. Within this framework, apparent discrepancies between observations are not interpreted as failures of dynamics or modeling accuracy. Rather, they are understood as consequences of comparing quantities defined in different structural dimensions. Consistency is therefore formulated not as pointwise agreement of predictions, but as the existence of admissible relations (dimensional mappings) between such dimensions. The main text presents a minimal, self-contained formulation of this framework.The appendices serve distinct and non-overlapping roles: * **Appendix A** makes explicit the formal assumptions and logical structure implicitly used in the main text.* **Appendix B** delineates the scope and limitations of the framework, preventing common misinterpretations.* **Appendix D** collects structural implications that follow from the framework, without extending or modifying it. This paper does not propose a new physical theory, modify existing dynamics, or derive novel predictions. Its purpose is to clarify how structural dimension can function as an organizing principle for theory comparison and observational interpretation, prior to detailed model construction or empirical analysis.