{
  "abstract": "We study the low transverse-traceless spectrum of positive Einstein manifolds and its effect on the Morse index of Ricci-flat cones. Free quaternionic quotients of four equal round spheres have exactly determined first scalar and tensor eigenvalues. For four round two-spheres, the quotient cone is nine-dimensional, is stable and has restricted holonomy $SO(9)$, whereas its eightfold cover has infinite negative index. For a general Einstein link, its invariant eigenspaces below the Hardy threshold determine the exact index on cone annuli and the leading logarithmic accumulation of negative eigenvalues on complete Ricci-flat manifolds with weighted $C^2$ convergence to the cone. No convergence rate is required for the leading term. At the threshold, an error of order $o((\\log r)^{-2})$ makes cone stability equivalent to finite index. A pointwise comparison for canonically conformally Kähler Einstein four-manifolds gives, for the Chen–LeBrun–Weber metric at Einstein constant $3$, the inequality $207/100<\\sup D_k(s^2)<21/10$, where $g=s^{-2}k$, $s=\\operatorname{Scal}_k>0$ and $D_k=\\operatorname{div}_k\\nabla$. This proves the Hall–Haslhofer–Siepmann derivative inequality and improves the low tensor eigenvalue bound. Applications include an explicit leading coefficient for the complete Ricci-flat Böhm metrics, an index formula on long Einstein necks, and Euclidean rigidity for finite-index five-dimensional fillings under a uniform half-Weyl eigenvalue inequality.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Anass Nifa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8pr7vmrpbb6ex.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.22914003",
  "fulltext_url": null,
  "id": "8pr7vmrpbb6ex",
  "issns": [],
  "landing_url": "https://hal.science/hal-05769876v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-dg"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05769876/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8pr7vmrpbb6ex.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:43Z",
      "native_id": "hal-05769876",
      "source": "hal",
      "url": "https://hal.science/hal-05769876v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-dg",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Einstein link spectra and the Morse index of Ricci-flat cones",
  "title_text": "Einstein link spectra and the Morse index of Ricci-flat cones",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:43Z",
  "url": "https://research.draconitic.com/paper/8pr7vmrpbb6ex",
  "venue": "HAL",
  "versions": []
}