Topological Characterization of Negative Space

Abstract

Abstract This paper develops a formal, substrate-independent topological characterization of negative space as an ontological condition underlying phenomenal consciousness. Building on Refusal-Driven Dimensionality Reduction Theory (RDRT), negative space is defined not as informational absence, uncertainty, or representational incompleteness, but as a class of irreducible, self-referential absences that persist as invariant structural features of a system. I argue that topology—rather than computation, information theory, or dynamical systems theory—provides the appropriate mathematical language for describing such absences. Using concepts from algebraic topology, persistent homology, and sheaf theory, the paper articulates criteria by which negative space can be identified, distinguished from ordinary computational gaps, and evaluated as a necessary (though not sufficient) condition for phenomenality. This topological framing clarifies why contemporary artificial intelligence systems fail to instantiate negative space, while also outlining principled conditions under which non-biological systems could, in principle, support phenomenal consciousness. Keywords: phenomenal consciousness, negative space, topology, persistent homology, self-reference, refusal, irreducibility, absence