Informational Architectonics of Space: Six Models of Dimensional Reduction.

We present a formal taxonomy of six internally distinct mechanism classes, derived from three ontological modalities of the substrate–space relationship, for the reduction of spatial dimensionality (3D → 2D → 1D → 0D). The six models are alternative, not complementary, ontological commitments — mutually exclusive at the level of substrate interpretation, though individual mathematical tools may be shared across them. The terminal state 0D is formally defined not as a geometric point but as a codified information structure, devoid of metric and topological realization, preserving a representation sufficient for re-instantiation under stated reconstruction assumptions. 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, is shown to lack modality-invariant applicability, necessitating a typologized family of operators. The taxonomy renders explicit the ontological obligations entailed by any operational definition of dimensional reduction, enabling rigorous discrimination between competing models. We demonstrate computationally, via six numerical protocols (§7), that the six models are operationally distinguishable and yield determinate, non-degenerate consequences: capacity-limited moment hierarchies, monotonic entropy increase under compression, formal reversibility of metric retraction, substrate invariance under index deactivation (shown to require substrate isotropy), and persistence of the predicted distinctions in a real-data benchmark (MNIST). A further protocol shows an ontological fingerprint vector for hybrid algorithms is directly computable (a β-VAE case), and a negative-control check finds no forced classification: candidates unrelated to any of the six operators return a null result in the tested setting. These protocols demonstrate non-degeneracy for the tested observables, not general uniqueness theorems, and not empirical confirmation of the underlying ontology — which is not directly testable by physical experiment. The framework is foundational and taxonomic, not algorithmic; predictions are validated via consistency checks, not benchmark competition against existing dimensionality-reduction methods.