{
  "abstract": "This note develops three multiplication-closed families of stochastic matrices for consensus under arbitrary switching. The first is a support-dominance enlargement of an earlier power-generated construction, in which exact support-pattern matching is relaxed to a dominance-type condition without losing closure under multiplication. The second is a fixed-core class with an exact uniform scrambling horizon and corresponding convergence-rate guarantees for switching products. The third and main contribution is the almost Sarymsakov class, obtained by allowing variable mixing-core dimensions under suitable structural conditions. This new semigroup class properly contains the classical Sarymsakov class and admits a dimension-only scrambling-horizon bound. Examples illustrate the necessity of the proposed structural assumptions and clarify the sharpness or limitations of the derived bounds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05050",
  "author_total": 1,
  "authors": [
    {
      "name": "Shun-Pin Hsu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9603hb8s6dbja.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05050",
  "fulltext_url": null,
  "id": "9603hb8s6dbja",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05050",
  "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.DS"
    ],
    [
      "openalex",
      "1705|Distributed Control Multi-Agent Systems"
    ]
  ],
  "openalex": "W7211879005",
  "pdf_url": "https://arxiv.org/pdf/2609.05050",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9603hb8s6dbja.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.05050",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05050"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Sarymsakov-Type Semigroups With Support Dominance and Nested Mixing Cores",
  "title_text": "Sarymsakov-Type Semigroups With Support Dominance and Nested Mixing Cores",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/9603hb8s6dbja",
  "venue": "arXiv",
  "versions": []
}