Intrinsic Dimensionality Preservation: A Framework for Distinguishing Entity Transfer from Dimensional Change

Theoretical physics contains many constructions involving spaces or descriptions of unequal dimensionality: embeddings, dimensional reduction, brane localization, bulk propagation, emergent dimensions, holographic dualities, and even dynamical transitions between string backgrounds of different dimension. These phenomena do not, however, answer a narrower question: can the same physical entity continuously enter a domain of unequal intrinsic dimension and become native to that domain while preserving its structural identity? This paper introduces a framework for separating intrinsic, ambient, effective, representational, and background dimensionality. Under an explicit Structural Identity Assumption, Brouwer's invariance of dimension yields a conditional no-go result: a continuous native transfer that preserves a nonempty local topological structure cannot connect native regions of unequal dimension. This motivates an Intrinsic Dimensionality Preservation Principle for ordinary identity-preserving propagation. Two further conjectures are proposed but kept distinct from the mathematical result. The Native Carrier Principle states that cross-dimensional re-instantiation, if physically possible, requires degrees of freedom native to the target dimensional domain. The Sequential Native-Carrier Conjecture adds that, when dimensional domains form a nested carrier hierarchy, re-instantiation between nonadjacent levels must respect that hierarchy. The framework is designed not to prohibit known dimensional phenomena. Brane-to-bulk propagation, holographic duality, effective dimensional reduction, emergent dimensions, and dimension-changing backgrounds are distinguished as changes in localization, description, effective behavior, representation, or background dimensionality rather than genuine transformations of an entity's intrinsic dimensionality. The central purpose of the framework is therefore to distinguish dimensional interaction, representation, and background change from genuine cross-dimensional entity transfer.