{
  "abstract": "On a compact connected section ${\\cal S}$ of a supersymmetric $M$-horizon the Killing-spinor bilinears give a pointwise identity relating the warp factor $Δ$, the rotation one-form $h$ and the two spinor norms, with nothing assumed about the norm of the Killing spinor. We derive three consequences of that unreduced identity. First, a single-point rigidity theorem: if $Δ$ and $h$ vanish at one point of the section, then the flux vanishes identically, ${\\cal S}$ is Ricci-flat and the horizon is $\\mathbb{R}^{1,1}\\times{\\cal S}$. A single point replaces the usual global spinorial hypothesis. Second, the ${\\rm Spin}(7)$ decomposition of the flux fixes $h$ algebraically and exhibits the invariant flux content of the scalar square $Δ=4Φ^2$ known in an adapted gauge, $Δ=\\frac{1}{108}\\|w_{\\bf 7}\\pmσ({\\cal Y}_{\\bf 7})\\|^2$. Only the two ${\\bf 7}$-summands $w_{\\bf 7}$, ${\\cal Y}_{\\bf 7}$ reach the warp factor, and the square is degenerate rather than definite: it vanishes on the linear subspace $w_{\\bf 7}=\\mpσ({\\cal Y}_{\\bf 7})$ rather than at the origin, so positivity of $Δ$ yields no case list. Third, the two combine into a pointwise budget: the single constant of supersymmetry is shared between the deviation from staticity and the ${\\rm Spin}(7)$ mismatch of the flux, each bounded by that constant. The same identities characterise the constancy hypothesis, equivalent to $V=-fh$ for the bilinear one-form $V$, which fails on the static branch of known warped $AdS_2$ solutions; they fix a weighted integral of the warp factor; and they reduce the Komar angular momentum of the horizon to a positive bilinear integral. Two no-go statements, for hidden symmetries built from the Killing spinor and for a second isometry from its bilinears, are stated with their hypotheses.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29879",
  "author_total": 1,
  "authors": [
    {
      "name": "Usman Kayani"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e9chhka55z3dr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29879",
  "fulltext_url": null,
  "id": "e9chhka55z3dr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29879",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "gr-qc"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7204952883",
  "pdf_url": "https://arxiv.org/pdf/2608.29879",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e9chhka55z3dr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2608.29879",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29879"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "The warp factor of supersymmetric $D=11$ near-horizon geometries: single-point rigidity, the $Spin(7)$ perfect square, and global constraints",
  "title_text": "The warp factor of supersymmetric D=11 near-horizon geometries: single-point rigidity, the Spin(7) perfect square, and global constraints",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:41Z",
  "url": "https://research.draconitic.com/paper/e9chhka55z3dr",
  "venue": "arXiv",
  "versions": []
}