Year: 2026
Type: preprint
Abstract: We exhibit two finite orthogonality hypergraphs that admit faithful orthogonal representations by rays in complex three-dimensional space but admit none in real three-dimensional space. Thus, although each orthogonality diagram is unchanged, its coordinatizability in dimension three depends on whether the scalar field is complex or real. The first hypergraph has 20 vertices and 12 contexts. The second hypergraph adds one vertex and two contexts. Phase-adjusted realification also gives explicit faithful orthogonal representations of both hypergraphs in real six-dimensional space.
Source: arXiv (Cornell University)
Authors: Navara, Mirko, Svozil, Karl
Institutions: Czech Technical University in Prague, TU Wien
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213595840