{
  "abstract": "Let $\\mathcal{K}_n$ be the simplex of nonnegative $n \\times n$ matrices whose entries sum to $n$. For $A$ in $\\mathcal{K}_n$, with row sums $r_1,\\ldots,r_n$ and column sums $c_1,\\ldots,c_n$, define $Φ(A)=\\prod_{i=1}^n r_i+\\prod_{j=1}^n c_j-\\mathrm{per}(A)$. Dittert conjectured that $Φ$ is uniquely maximized by the uniform matrix $U_n=J_n/n$, with maximum $2-n!/n^n$. We prove the conjecture for every $n \\geq 2$. Hwang's theorem already determines every positive maximizer, so the essential problem is to exclude maximizers on the boundary of $\\mathcal{K}_n$. A reduction of Cheon and Wanless supplies two zero entries in distinct rows and columns. In order four, we classify all admissible support strata and exclude them by exact Karush-Kuhn-Tucker identities together with a Bernstein-form positivity certificate. For all $n \\geq 5$, an attained-stratum averaging argument compresses a hypothetical boundary maximizer to a seven-parameter matrix with one multiplicity $m=n-2$. A symbolic odd-variable expansion, a cofactor identity at the two missing entries, and uniform coefficient inequalities then contradict the one-sided multiplier conditions. This argument is uniform in $m$ and uses no finite enumeration. We also give independent spectral proofs in dimensions 7 through 13 and prescribed-zero proofs in dimensions 14 and 15. Every dimension-dependent calculation is certified over the rationals and recorded explicitly in the appendices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10545",
  "author_total": 5,
  "authors": [
    {
      "name": "Xinan Dai"
    },
    {
      "name": "Wenhao Deng"
    },
    {
      "name": "Yingdong Shi"
    },
    {
      "name": "Tailin Wu"
    },
    {
      "name": "Yuchen Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ad3b3cc5p8pk4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10545",
  "fulltext_url": null,
  "id": "ad3b3cc5p8pk4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10545",
  "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.RA"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7221105221",
  "pdf_url": "https://arxiv.org/pdf/2610.10545",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ad3b3cc5p8pk4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.10545",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10545"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A Proof of the Dittert Conjecture via Boundary Rigidity",
  "title_text": "A Proof of the Dittert Conjecture via Boundary Rigidity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/ad3b3cc5p8pk4",
  "venue": "arXiv",
  "versions": []
}