{
  "abstract": "For the mirror word $\\mathbf{m}_n=a_1\\cdots a_na_n\\cdots a_1$, let $\\mathcal{V}_n=\\mathrm{V}(S(\\mathbf{m}_n))$ and $\\mathcal{W}_n=\\mathrm{V}(S(\\mathbf{m}_n)^0)$. We show that $[\\mathcal{W}_n,\\mathcal{W}_{n+1}]$ ($n\\geq 1$) and $[\\mathcal{V}_n,\\mathcal{W}_n]$ ($n\\geq 2$) have cardinality $2^{\\aleph_0}$. Every variety in $[\\mathcal{W}_2,\\mathcal{W}_\\infty]$ has infinite axiomatic rank. The unique limit subvariety of $\\mathcal{W}_1$ is $\\mathrm{V}(SR_6)$. For $n\\geq 2$, we construct a distinct directed-path limit variety contained in $\\mathcal{W}_n$ but not in $\\mathcal{V}_n$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23478",
  "author_total": 2,
  "authors": [
    {
      "name": "Ruijing Wang"
    },
    {
      "name": "Mengya Yue"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f1smy3syqnh8m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23478",
  "fulltext_url": null,
  "id": "f1smy3syqnh8m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23478",
  "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"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "1703|semigroups and automata theory"
    ]
  ],
  "openalex": "W7222939689",
  "pdf_url": "https://arxiv.org/pdf/2610.23478",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f1smy3syqnh8m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23478",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23478"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Subvariety intervals and limit varieties of zero extensions of mirror-word semirings",
  "title_text": "Subvariety intervals and limit varieties of zero extensions of mirror-word semirings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/f1smy3syqnh8m",
  "venue": "arXiv",
  "versions": []
}