Space as Separation: A Relational Account of Extension and Dimensionality develops a relation‑first framework in which spatial structure is not a primitive container but the stabilized expression of persistent non‑coincidence within a generative relational field. The paper identifies separation as the fundamental operator underlying space and shows how extension, dimensionality, and geometry emerge from the system’s generative bandwidth rather than from an assumed manifold. The radius of the relational hypersphere represents the system’s active capacity to sustain stable differences, and spatial growth is interpreted as the stabilization of newly generated relational degrees of freedom. This account dissolves the container model, reframes spatial extension as an internal relational process, and grounds the geometry of space in the structural dynamics of generativity, boundary, and expression.
Denis Bailey (Sat,) studied this question.