{
  "abstract": "Let $p,q$ be positive braids with Demazure products $u,v$. The endpoint stratum $\\mathrm{Conf}(p,q)_{u,v}$ of the double Bott-Samelson cell splits as $\\mathrm{Conf}(u,v) \\times X(p) \\times X(q^{\\mathrm{op}})$, a double Bruhat cell times two braid varieties. We prove that the stratum's cluster structure is given by a cluster localization of the one on $\\mathrm{Conf}(p,q)$, and that the splitting map is a quasi-cluster isomorphism. This comes from a mutation sequence along a double Demazure weave, one mutation per trivalent vertex, ending at an amalgamation of an extension of the double word quiver with the weave quiver. In the half-decorated case, this proves the conjecture of Gorsky-Kim-Scroggin-Simental for the splicing map $X(p) \\times X(ΔΔ) \\to X(pΔ)$, where $Δ$ is a reduced positive braid for $w_0$ and $\\mathrm{dem}(p) = w_0$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05833",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuma Mizuno"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0rxq7hvctq6wg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05833",
  "fulltext_url": null,
  "id": "0rxq7hvctq6wg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05833",
  "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.AG"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7212081440",
  "pdf_url": "https://arxiv.org/pdf/2609.05833",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0rxq7hvctq6wg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.05833",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05833"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Mutation Sequences along Weaves and Amalgamation of Braid Varieties",
  "title_text": "Mutation Sequences along Weaves and Amalgamation of Braid Varieties",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/0rxq7hvctq6wg",
  "venue": "arXiv",
  "versions": []
}