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 comparing physical observables and theories.Dimension is redefined not as a count of spatial or temporal coordinates, but as a structural attribute characterized by effective degrees of freedom, boundary conditions, and finite transition widths. Within this framework, discrepancies between observations and theoretical expectations are not treated as errors or failures of dynamics.Instead, they are interpreted as consequences of projecting quantities defined in **different structural dimensions**.Consistency is therefore formulated as the existence of admissible mappings between dimensions, rather than as pointwise agreement of predictions. Galactic rotation curves and weak gravitational lensing are used as illustrative examples of structurally distinct observables.They are not assumed to directly probe the same dynamical regime, but are treated as imposing complementary constraints on dimensional mappings between local and global descriptions. This paper does not propose a new physical theory, introduce new dynamics, or derive novel predictions.Elastic Spacetime with Scale-Dependent Coupling (ESSC) is discussed solely as a minimal illustrative case, demonstrating how structural-dimensional considerations can be made explicit without privileging any specific model. The purpose of this work 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 fitting.