{
  "abstract": "We study how the structure of the coupling matrix $\\boldsymbol A$ shapes the energy landscape $E_{\\boldsymbol A}(\\boldsymbolθ)=-\\frac12\\sum_{i,j}A_{ij}\\cos(θ_i-θ_j)$ of the Kuramoto model. We prove that, for an entrywise nonnegative coupling matrix $\\boldsymbol A$ with connected support, if $\\boldsymbol A$ has rank-width one over $\\mathbb R$, then the landscape is \"simple\", i.e., every local minimum is synchronized. The rank-width bound is sharp, and the result has many interesting implications for global synchronization. The key contribution of this work is to uncover a structural synchronization mechanism beyond the rank-one regime, which has served as a starting point for earlier analyses of global synchronization.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38670",
  "author_total": 1,
  "authors": [
    {
      "name": "Hongjin Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/arajj7k68tsth.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38670",
  "fulltext_url": null,
  "id": "arajj7k68tsth",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38670",
  "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",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38670",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/arajj7k68tsth.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38670",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38670"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Simple Cuts, Simple Landscapes: Global Synchronization and Rank-Width-One Matrices",
  "title_text": "Simple Cuts, Simple Landscapes: Global Synchronization and Rank-Width-One Matrices",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/arajj7k68tsth",
  "venue": "arXiv",
  "versions": []
}