Transformation-Stable Structures and Emergent Compression

Abstract

This work proposes a conceptual framework in which observable form, representation, and meaning emerge through transformations across different representational scales. An underlying system may contain a high-dimensional relational structure whose complete state is not directly accessible to a lower-dimensional observer. As this structure undergoes transformations, projections, and dynamic slicing, different subsets of its relations become distinguishable at different scales. Most microscopic distinctions may disappear from the resulting representation, while some relations remain sufficiently stable to persist across transformations. The central proposal is that these transformation-stable relations can become progressively compressed and eventually function as reusable structures within subsequent transformations. Form, therefore, is not assumed to be a primitive property already contained in the underlying state. Rather, it may emerge when a relational configuration remains stable under a particular class of transformations and scales. This perspective provides a possible interpretation of phenomena such as shape and color. Such properties need not correspond directly to primitive microscopic variables. Instead, they may represent stable relational structures produced when high-dimensional information is transformed into a lower-dimensional observable representation. The same principle may extend to symbolic and linguistic representations. A symbol can be understood as a highly compressed representation of a relation that has already achieved sufficient stability to become reusable. Meaning would then not necessarily reside intrinsically within the symbol itself. It may emerge from the preservation of a relational structure across transformations between different representational systems. This shifts the fundamental question from what a representation means to what structure remains invariant enough during transformation to allow the representation to emerge. High-dimensional structure→Transformation→Slicing→Stabilization→Compression→Representation The proposed framework does not assume that different observers, artificial systems, biological systems, or hypothetical civilizations must share the same symbols or representations. Instead, it considers the possibility that different systems may independently develop structurally analogous forms of compression because similar transformation constraints can produce similar stable relational structures. The potentially universal object is therefore not the symbol but the process through which relations become distinguishable, stable, compressible, and reusable.