{
  "abstract": "An exact zero of a generated harmonic needs two real cancellations; a damped oscillator's leading fundamental-source balance supplies one. Absorber loss leaves a phase deficit of fixed sign, amplitude independent at leading order, closed instead by the orbit's own $5Ω$ motion returning to $3Ω$ at weight $|Δ_1|^4$. Closure is therefore unreachable at weak amplitude: the channel supplying it ranks at $O(F^7)$, not at the leading $O(F^3)$. The fifth harmonic is $1.8\\times10^{-3}$ of the relative-coordinate fundamental, yet a balance homotopy weighting it below $0.48$ annihilates the tracked pair in a saddle-node.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01508",
  "author_total": 1,
  "authors": [
    {
      "name": "Kanchan Sarkar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/373qaq8ryx72b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01508",
  "fulltext_url": null,
  "id": "373qaq8ryx72b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01508",
  "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",
      "nlin.CD"
    ],
    [
      "openalex",
      "1705|Nonlinear Dynamics and Pattern Formation"
    ]
  ],
  "openalex": "W7206199708",
  "pdf_url": "https://arxiv.org/pdf/2609.01508",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/373qaq8ryx72b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:00Z",
      "native_id": "2609.01508",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01508"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:nlin.CD",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Fifth-Harmonic Feedback Controls the Existence of a Third-Harmonic Zero",
  "title_text": "Fifth-Harmonic Feedback Controls the Existence of a Third-Harmonic Zero",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:00Z",
  "url": "https://research.draconitic.com/paper/373qaq8ryx72b",
  "venue": "arXiv",
  "versions": []
}