{
  "abstract": "For positive integers \\(m,n\\), let \\[ A_{m,n}=(\\{1,\\ldots,m\\}\\times\\Z_n)\\cup\\{0\\} \\] have flat addition and multiplication truncated at degree \\(m\\). We prove that \\(A_{m,n}\\) is finitely based exactly when \\(m\\le 2\\) or \\((m,n)=(3,1)\\). Explicit finite bases are supplied throughout this region. Outside it, high-girth hypergraphs with a constant-sum rigidity property yield finite countermodels to every bounded-variable fragment of the equational theory. The proof places no divisibility or coprimality restriction on the parameters.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26451",
  "author_total": 2,
  "authors": [
    {
      "name": "Qirui Ma"
    },
    {
      "name": "Zidong Gao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cmjhbgf1v88wb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26451",
  "fulltext_url": null,
  "id": "cmjhbgf1v88wb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26451",
  "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.GR"
    ],
    [
      "openalex",
      "1703|semigroups and automata theory"
    ]
  ],
  "openalex": "W7214073407",
  "pdf_url": "https://arxiv.org/pdf/2609.26451",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cmjhbgf1v88wb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.26451",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26451"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Finite Bases for Truncated Cyclic Group Flat Semirings with Two Independent Parameters",
  "title_text": "Finite Bases for Truncated Cyclic Group Flat Semirings with Two Independent Parameters",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/cmjhbgf1v88wb",
  "venue": "arXiv",
  "versions": []
}