{
  "abstract": "We study multipartite hypergraphs definable in $1$-semi-equational theories and prove almost-linear Zarankiewicz bounds in every fixed arity $r\\geq2$. If $T$ is a $1$-semi-equational theory, then, for every formula $φ$ and fixed $t,r\\geq2$, there is a constant $c$ such that each $K_{t,\\ldots,t}$-free $r$-partite hypergraph defined by $φ$ on $n$ vertices has $O_{T,φ,t,r}\\!\\left( n^{r-1}(1+\\log(1+n))^c \\right) $ edges. Put $α_k=\\min\\{k-1,2\\}$. In the bipartite case, a Boolean combination of $m$ $(k,1)$-semi-equations has $ O_{k,t,m}\\!\\left( n(1+\\log(1+n))^{(m-1)α_k} \\right) $ edges whenever it is $K_{t,t}$-free. In particular, a relation defined by one $(k,1)$-semi-equation or its negation has a linear bound. The proofs combine incidence estimates for indexed set systems with low-crossing orderings of finite $k$-wise laminar families. Consequently, no $1$-semi-equational theory locally trace-defines an infinite domain.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.25464",
  "author_total": 5,
  "authors": [
    {
      "name": "Hongyi Gou"
    },
    {
      "name": "Mostafa Mirabi"
    },
    {
      "name": "Mihir Mittal"
    },
    {
      "name": "Chieu-Minh Tran"
    },
    {
      "name": "Zhenyu Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dmsfkwggc232f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.25464",
  "fulltext_url": null,
  "id": "dmsfkwggc232f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.25464",
  "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.CO"
    ],
    [
      "arxiv",
      "math.LO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7204464399",
  "pdf_url": "https://arxiv.org/pdf/2608.25464",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dmsfkwggc232f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2608.25464",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.25464"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Almost-linear Zarankiewicz bounds in $1$-semi-equational theories",
  "title_text": "Almost-linear Zarankiewicz bounds in $1$-semi-equational theories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/dmsfkwggc232f",
  "venue": "arXiv",
  "versions": []
}