{
  "abstract": "The Okubo algebra brings together ternary gradings, integral root frames and rank-three geometry. We examine how these structures extend to the complex Exceptional Periodicity algebras. With $N=4(n+1)$, a tetracode character gives eight nonzero homogeneous components of dimension $t_n=8n+3+2^{4n}$. On a tip, a compatible grading has zero component of dimension $8n-5$ and eight nonzero components of dimension $1+2^{4n-3}$. The arithmetic behaves differently: for $n\\geq2$, the lattice $D_N^+$ has no full-rank orthogonal frame of unscaled $A_2$ lattices. We exhibit failures of the Jacobi and Jordan identities and determine the derivations and full automorphism group of the ambient algebra above level one. We also give a Clifford-module proof, with the normalization fixed by root products, of the published realization of EP tips as special Vinberg $H$-algebras. This identifies a positive real form and yields explicit formulas for its cone, cubic, Cholesky coordinates and rational dual invariant. The cone is symmetric exactly at $n=1$. Its determinant-one hypersurface belongs to the known $L(8n,1,0)$ series, whose $r$- and $c$-maps give homogeneous scalar manifolds for supergravity theories with eight real supercharges.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18643",
  "author_total": 2,
  "authors": [
    {
      "name": "Alessio Marrani"
    },
    {
      "name": "Daniele Corradetti"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3n2x1scmhe1ws.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18643",
  "fulltext_url": null,
  "id": "3n2x1scmhe1ws",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18643",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7221752691",
  "pdf_url": "https://arxiv.org/pdf/2610.18643",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3n2x1scmhe1ws.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:11Z",
      "native_id": "2610.18643",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18643"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Okubo algebras and Exceptional Periodicity: tetracode gradings, root-lattice obstructions and Clifford cones",
  "title_text": "Okubo algebras and Exceptional Periodicity: tetracode gradings, root-lattice obstructions and Clifford cones",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:20Z",
  "url": "https://research.draconitic.com/paper/3n2x1scmhe1ws",
  "venue": "arXiv",
  "versions": []
}