{
  "abstract": "Let $r \\ge 2$ and $t \\ge 1$. It is shown that if $T$ is an $r$-uniform tight tree with $t$ edges and $H$ is a $T$-free $r$-uniform hypergraph, then $|E(H)|\\le (t-1)|\\sh H|/r$, where $\\sh H$ is the $(r-1)$-shadow of $H$. \\iffalse Equality holds only for $(n,t + r - 2,r)$-designs.\\fi The bound is tight infinitely often, and establishes Kalai's Conjecture, whose $r=2$ case is the Erd\\H os-Sós Conjecture. The proof was found by GPT-6 Astra, extending its method of proof for the Erd\\H os-Sós conjecture to the hypergraph setting. It is noteworthy that previous proofs of special cases of the Erd\\H os-Sós conjecture do not extend to give tights bounds in the hypergraph setting. A strengthening of the Erd\\H os-Sós conjecture due to the authors about tight lower bounds on the number of copies of a tree in a graph with average degree $d \\ge t-1\\ge 0$ remains open.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08012",
  "author_total": 2,
  "authors": [
    {
      "name": "Dhruv Mubayi"
    },
    {
      "name": "Jacques Verstraete"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6z1dqsqfpjasq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08012",
  "fulltext_url": null,
  "id": "6z1dqsqfpjasq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08012",
  "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"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7212081833",
  "pdf_url": "https://arxiv.org/pdf/2609.08012",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6z1dqsqfpjasq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08012",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08012"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Kalai's Conjecture for Tight Trees",
  "title_text": "Kalai's Conjecture for Tight Trees",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/6z1dqsqfpjasq",
  "venue": "arXiv",
  "versions": []
}