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Complex coordinates forced by finite orthogonality hypergraphs in dimension three — arXiv:2609.20205

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.20205
License (as archived): CC0-1.0
Archived: 2026-10-10T04:47:09.946Z
SHA-256 of the archived text: ac73c0839ec62aea9bc750565c85176055fcb8c373266ab7f953bfc7e275213d
Stable URL of this page: https://metraipolis.com/documento/dc_656df7b2d5fe

How to cite

Complex coordinates forced by finite orthogonality hypergraphs in dimension three — arXiv:2609.20205 — arXiv (en), https://arxiv.org/abs/2609.20205 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_656df7b2d5fe (Metraipolis archive dc_656df7b2d5fe, sha256 ac73c0839ec62aea9bc750565c85176055fcb8c373266ab7f953bfc7e275213d)

BibTeX

@misc{dc656df7b2d5fe,
  title = {Complex coordinates forced by finite orthogonality hypergraphs in dimension three — arXiv:2609.20205},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.20205},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_656df7b2d5fe; sha256 ac73c0839ec62aea9bc750565c85176055fcb8c373266ab7f953bfc7e275213d},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.20205. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-18 in math.CO).
Categorie arXiv: Combinatorics (math.CO) ; Quantum Physics (quant-ph).
Pagina del lavoro: https://arxiv.org/abs/2609.20205 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-10T04:15:33.140Z dalla pagina https://arxiv.org/catchup/math.CO/2026-09-18?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).