{
  "abstract": "Finite-$N$ trace relations can produce $Q$-cohomology classes with no stable large-$N$ ancestor. The brane-fused construction at $SU(3)$ suggests that such states can retain an $SU(2)$ nonabelian core accompanied by scalar hair. We develop this idea into a general construction for every $SU(N)$, $N\\geq3$. Starting from the $SU(2)$ threshold operator $O_{24}$, we select pairs of eigenvalues of one scalar and construct corrected two-colour letters whose $Q$-transformations obey the $SU(2)$ rules exactly. Substitution into $O_{24}$ gives a closed rational operator for each pair. Multiplying by eigenvalue-separation factors removes the denominators, and summing over all pairs produces a gauge-invariant polynomial. An exact block-restriction identity recovers a nonzero multiple of $O_{24}$. The restriction maps every stable class to a stable $SU(2)$ class, proving that the resulting operator is non-exact and fortuitous, even when non-Coulombic stable classes are included. This proves the existence of fortuitous BMN cohomology at every $N\\geq3$. The construction is an exact algebraic realization of a nonabelian core with scalar dressing.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21592",
  "author_total": 3,
  "authors": [
    {
      "name": "Robert de Mello Koch"
    },
    {
      "name": "Minkyoo Kim"
    },
    {
      "name": "Sinong Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2ngaqg6kf5vj2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21592",
  "fulltext_url": null,
  "id": "2ngaqg6kf5vj2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21592",
  "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"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7222752436",
  "pdf_url": "https://arxiv.org/pdf/2610.21592",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2ngaqg6kf5vj2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:18Z",
      "native_id": "2610.21592",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21592"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Fortuitous BMN Cohomology at Every $N$",
  "title_text": "Fortuitous BMN Cohomology at Every N",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:18Z",
  "url": "https://research.draconitic.com/paper/2ngaqg6kf5vj2",
  "venue": "arXiv",
  "versions": []
}