{
  "abstract": "The Schur sector of four-dimensional $\\mathcal N=4$ super Yang$--$Mills theory contains infinitely many protected operators, while the invariant polynomials of a single adjoint scalar are organized by finitely many Casimir degrees. I prove that the small $\\mathcal N=4$ short multiplets built from these invariants strongly generate the associated chiral algebra, thereby establishing the $SU(N)$ case of the strong-generation conjecture of Beem et al. For every $N\\ge2$, all field components associated with degrees $2,\\ldots,N$ suffice, in every conformal weight and every degree of the standard relative quantum BRST cohomology. The proof brings together cyclic trace cohomology, quantum lifting, and an arbitrary-degree quartic$--$odd transport identity. Exact field relations and a finite-rank Newton obstruction exclude every additional lowest space, including non-scalar flavor representations; the required normal-ordering corrections and BRST primitives are derived explicitly. The resulting completeness theorem explains how a finite family of supersymmetric multiplets organizes an unbounded quantum spectrum. Every Schur class is a normal polynomial in their components and derivatives, even when its gauge-theory representative involves fermions and arbitrarily many derivatives. This supplies a uniform set of local inputs for meromorphic operator products, bounds protected state multiplicities before cancellations in an index, and gives an algebraic account of the finite-rank reorganization of protected trace operators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24594",
  "author_total": 1,
  "authors": [
    {
      "name": "Yifan He"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5k3ghnw77xxyv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24594",
  "fulltext_url": null,
  "id": "5k3ghnw77xxyv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24594",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7222993619",
  "pdf_url": "https://arxiv.org/pdf/2610.24594",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5k3ghnw77xxyv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.24594",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24594"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Casimir multiplets suffice: strong generation in $\\mathcal{N}=4$ $SU(N)$ SYM",
  "title_text": "Casimir multiplets suffice: strong generation in 𝒩=4 SU(N) SYM",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/5k3ghnw77xxyv",
  "venue": "arXiv",
  "versions": []
}