{
  "abstract": "A hard hadron-collider event is represented here as a single geometric object: the kinematics and object-type labels of all reconstructed final-state particles in one multivector $\\evMV$, one $\\Cl(1,3)\\otimes\\Vflav$ slot per object, whose higher grades the algebra generates from the measured four-momenta --- rather than as a list of four-momenta with label fields attached. The setting is geometric algebra, whose grade decomposition organises essentially every observable in current use: invariants at grade zero, four-momenta at grade one, decay-plane bivectors at grade two, oriented three-volumes at grade three, the CP-odd pseudoscalar at grade four. The high-level invariants, the low-level recipe and the equivariant-network inputs are recovered as projections onto specific grades. A per-grade dictionary of $32$ classical observables and an inventory of the symmetries acting on $\\evMV$ are provided. Theorem settles which Lorentz invariants the higher grades unlock: none beyond $\\{p_i\\!\\cdot\\!p_j,\\,m_i^2\\}$, the CP-odd sign of the pseudoscalar being the one genuine channel. The representation is intended as a uniform input layer for foundation models of collider physics, and the realisations demonstrated here occupy two rungs of a ladder: the higher grades are formed inside the network from the per-object slots, or selected grade-two and grade-three objects are supplied at the input layer. It is demonstrated on the resonance-topology separation of $pp\\!\\to\\!tWb$ with a Lorentz-equivariant multivector transformer of L-GATr type. An ablation over eight input representations separates what supplying algebraic content explicitly can and cannot buy: content reconstructible from the measured momenta unlocks no new invariant, by the theorem, whereas a fixed reference blade encoding the beam plane carries structure the momenta do not contain.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.15910",
  "author_total": 5,
  "authors": [
    {
      "name": "E. Abasov"
    },
    {
      "name": "L. Dudko"
    },
    {
      "name": "F. Grigoryev"
    },
    {
      "name": "P. Volkov"
    },
    {
      "name": "A. Zaborenko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/arpmzetwkz185.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.15910",
  "fulltext_url": null,
  "id": "arpmzetwkz185",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.15910",
  "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-ph"
    ],
    [
      "openalex",
      "3106|Particle physics theoretical and experimental studies"
    ]
  ],
  "openalex": "W7161551554",
  "pdf_url": "https://arxiv.org/pdf/2605.15910",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/arpmzetwkz185.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:22Z",
      "native_id": "2605.15910",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.15910"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    }
  ],
  "title": "Geometric algebra as the input language of collider foundation models",
  "title_text": "Geometric algebra as the input language of collider foundation models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:22Z",
  "url": "https://research.draconitic.com/paper/arpmzetwkz185",
  "venue": "arXiv",
  "versions": []
}