{
  "abstract": "Let $g$ be a complete Ricci-flat Böhm metric on $\\mathbb{R}^{p+1}\\times S^q$, where $p, q\\ge2$ and $p+q\\le8$. We classify the geometric Dirichlet kernel on every compact truncation and prove that the reduced Morse index counts the preceding umbilic orbits. Every negative $L^2$ Lichnerowicz eigentensor is $O(p+1)\\times O(q+1)$-invariant, and the quadratic form is coercive in homogeneous energy on the complementary subspace. These results imply symmetry of sufficiently small ancient Ricci–DeTurck solutions whose non-invariant component is bounded in $L^2$, without an assumption of backward convergence. They also give stationary rigidity in a fixed background gauge. Each degeneracy of the smooth induced-metric map is a fold. Arbitrarily large finite collections of pairwise nonisometric Ricci-flat fillings, with arbitrarily large reduced index, persist under nonsymmetric boundary perturbations. The reduced negative spectrum converges to the complete negative spectrum; a transverse Dirichlet-to-Neumann form has a positive-measure representation. All scalar coefficient identities are given explicitly, with their exact integer data.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Anass Nifa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1fh08smxkqdvr.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.22810800",
  "fulltext_url": null,
  "id": "1fh08smxkqdvr",
  "issns": [],
  "landing_url": "https://hal.science/hal-05770000v1",
  "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-05770000/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-06-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1fh08smxkqdvr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:43Z",
      "native_id": "hal-05770000",
      "source": "hal",
      "url": "https://hal.science/hal-05770000v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-dg",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Dirichlet deformations, Morse index, and nonlinear symmetry of Ricci-flat Böhm metrics",
  "title_text": "Dirichlet deformations, Morse index, and nonlinear symmetry of Ricci-flat Böhm metrics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:43Z",
  "url": "https://research.draconitic.com/paper/1fh08smxkqdvr",
  "venue": "HAL",
  "versions": []
}