{
  "abstract": "Compactified spectral discretisations may yield stable negative-imaginary-axis (NIA) eigenvalue ladders, but finite-matrix convergence does not establish quasinormal poles. For axial Schwarzschild perturbations, ingoing--outgoing factorisation leaves an unwanted horizon solution behaving as $t^{4α}$ at $Ω=-iα$, and a $C^\\infty$-flat unwanted infinity solution. Thus endpoint $C^k$ regularity is nonselective for $4α>k$, so the $C^2$ continuum problem cannot have a discrete NIA spectrum over $α\\simeq15$--32. Exact Chebyshev-grid formulas give roots-grid maximum radius $O(n^{2p})$ for $x\\sim C(1-y)^{-p}$, explaining C1, $x=2/(1-y)$, versus C2, $x=4/(1-y)^2$. Arbitrary-precision pencils nevertheless reveal a reproducible 68-point C1 ladder, while C2 reorganises it. Both physical lateral Jost determinants remain stably nonzero at every C1 frequency. A 0.05-spaced on-cut scan finds no zero, and refined argument-principle calculations give zero winding in both continuation strips. This rejects all 68 candidates, although the mesh and strip evidence is not interval-certified. Same-damping controls recover Schwarzschild QNMs $n=60,100,130$, with $|\\widehat{\\mathcal D}|=10^{-48}$--$10^{-56}$. The ladder has surface-gravity quarter spacing, follows the parameter-free Casals--Ottewill branch-cut-strength phase, and pairs with damping projections of QNMs $n=62,\\ldots,129$. At its first member, a finite-frequency calculation finds a branch-strength zero at $α_q=15.07832396512359$, between the asymptotic prediction and the C1 root, supporting, but not proving, sequence-wide cut-phase locking. Thus accurate finite-pencil eigenvalues can fail the invariant Jost/Evans pole criterion. Whether representation-dependent nodes with Keldysh weights converge collectively to the Schwarzschild cut response and Price tail remains open.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29095",
  "author_total": 3,
  "authors": [
    {
      "name": "Davide Batic"
    },
    {
      "name": "Denys Dutykh"
    },
    {
      "name": "Mark Essa Sukaiti"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6hcpndjnkhfzn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29095",
  "fulltext_url": null,
  "id": "6hcpndjnkhfzn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29095",
  "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"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7204892551",
  "pdf_url": "https://arxiv.org/pdf/2608.29095",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6hcpndjnkhfzn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2608.29095",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29095"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Schwarzschild spectral ladders on the negative imaginary axis: Endpoint nonselection, branch-cut phase, and Jost classification",
  "title_text": "Schwarzschild spectral ladders on the negative imaginary axis: Endpoint nonselection, branch-cut phase, and Jost classification",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:41Z",
  "url": "https://research.draconitic.com/paper/6hcpndjnkhfzn",
  "venue": "arXiv",
  "versions": []
}