{
  "abstract": "We study strict ground-level gaps for autonomous nonlinear Dirac equations on noncompact metric graphs. The relevant level at infinity is the autonomous full-line level \\(d_λ^\\infty=d_{λ,\\mathbb R}\\), since a concentrating sequence escaping along a half-line sees the real line after recentering far from all vertices. We prove that, uniformly for \\(λ\\) in a compact subinterval \\(I\\Subset(-mc^2,mc^2)\\), the presence of a sufficiently long pendant path in the essential reduction of the graph implies \\[ d_λ(\\mathcal G)<d_λ^\\infty. \\] The proof uses a half-line restriction of a symmetric full-line ground state, uniform exponential decay, resolvent localization for massive Dirac-Kirchhoff spectral projections, and a compactness argument for generalized Nehari fibres. We also identify elementary graph classes for which no such gap can hold: pure transmission graphs whose essential reduction is isometric to the full line satisfy \\(d_λ(\\mathcal G)=d_λ^\\infty\\).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Adv. Nonlinear Anal. 15 (2026), no. 1, Paper No. 20250201",
  "arxiv": "2609.24618",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhipeng Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ex0vmym6ktk8x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24618",
  "fulltext_url": null,
  "id": "ex0vmym6ktk8x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24618",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7214040472",
  "pdf_url": "https://arxiv.org/pdf/2609.24618",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ex0vmym6ktk8x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.24618",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24618"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Strict ground-level gaps on long-pendant generalized star graphs for nonlinear Dirac equations",
  "title_text": "Strict ground-level gaps on long-pendant generalized star graphs for nonlinear Dirac equations",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/ex0vmym6ktk8x",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1515/anona-2025-0201",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}