Cognitive Voids: First Cohomology of Typed Hypergraphs, Forced Recurrence as Topological Invariant, and Error Detection via Cohomological Inconsistency

We develop the cohomological theory of typed cognitive hypergraphs—the combinatorial structures un- derlying creative production, associative memory, and real-time generative cognition. We show that the first cohomology group H1(K(H); Z) of the clique complex of a cognitive hypergraph H classifies forced recurrences: thematic returns that are not caused by memory failure or cache exhaustion but are topologi- cally mandated by the structure of the graph. We prove that each generator of H1 corresponds to a distinct cognitive void—a region of concept-space where associations are sparse—around which typed traversals are forced to curve. We establish that erroneous edges (false associations) are detectable as cohomologi- cal inconsistencies: cycles that close when the topology says they should not, or fail to close when it says they should. We connect forced recurrence to the phason degrees of freedom of cognitive quasicrystals (Elliott 2026a), proving that the H1 generators of the hypergraph are exactly the phason modes of the corresponding aperiodic tiling. We introduce three new metrics—typed diameter, traversal centrality, and self-avoiding walk capacity—and prove their relationship to the filter density of the Rosetta Stone corre- spondence (Elliott 2026f). Keywords: cognitive hypergraph, first cohomology, forced recurrence, typed traversal, phason, cognitive void, error detection, self-avoiding walk, traversal centrality, cognitive quasicrystal