Informational Architectonics of Space: Six Models of Dimensional Reduction

Abstract

We present a formal taxonomy of six mutually exclusive mechanisms for the reduction of spatial dimensionality (3D → 2D → 1D → 0D), grounded in three distinct ontological modalities of the substrate–space relationship. The six models constitute alternative, not complementary, ontological commitments: the substrate of an object cannot simultaneously function as a three-dimensional information repository and as a non-dimensional invariant. The terminal state 0D is rigorously defined not as a geometric point, but as a codified information structure devoid of metric and topological realization, preserving the complete informational content requisite for potential re-instantiation. Each model is characterized by its reduction operator, substrate modality, and the functional role of the spatial frame. The access operator A(d), initially hypothesised as a unified descriptor of reduction, is shown to lack modality-invariant applicability; Protocol 4 demonstrates its restriction to index-based models, necessitating a typologized family of operators. The primary function of this taxonomy is to render explicit the ontological obligations entailed by any operational definition of dimensional reduction, and thereby to enable rigorous discrimination between competing models. We demonstrate computationally, via four numerical protocols (§7), that the six models are operationally distinguishable and that the formalism yields determinate, non-degenerate numerical consequences: (I) the capacity-limited moment hierarchy, (II) monotonic entropy increase in compression cascades, (III) perfect reversibility of metric retraction, and (IV) substrate invariance under index deactivation. These simulations establish internal consistency and discriminability of the models, not an empirical confirmation of the underlying ontology, which is not directly testable by physical experiment.

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