{
  "abstract": "The undirected multiple-unicast conjecture [LL04] asserts that network coding offers no throughput advantage over multicommodity flow. We refute this conjecture by constructing a deterministic linear network code over $\\mathbb{F}_9$ on a 182-vertex bipartite subgraph of the point-line incidence graph of $\\mathrm{PG}(2,9)$. The construction supports $157$ independent unicast sessions at common coding rate at least $1$, while every fractional multicommodity flow has common rate at most $147/157$. By the amplification theorem of~[BGS17], this yields a family of undirected multiple-unicast instances with coding gap $Ω((\\log n)^\\varepsilon)$ for some $\\varepsilon>0$. We also introduce a nondeterministic model of network coding based on locally verifiable certificates, which guides our construction and may be of independent interest. Building on the high-girth graph and error-correcting code framework of [BH25], we use GPT-6 to find a nondeterministic counterexample based on a new choice of Reed--Solomon local codes, and then convert this example into a causal code using an edge orientation and local search.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10108",
  "author_total": 2,
  "authors": [
    {
      "name": "Mark Braverman"
    },
    {
      "name": "Zhongtian He"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9pf39kn47tj43.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10108",
  "fulltext_url": null,
  "id": "9pf39kn47tj43",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10108",
  "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",
      "cs.CC"
    ],
    [
      "arxiv",
      "cs.DM"
    ],
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1703|Complexity and Algorithms in Graphs"
    ]
  ],
  "openalex": "W7220935724",
  "pdf_url": "https://arxiv.org/pdf/2610.10108",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9pf39kn47tj43.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.10108",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10108"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "The Multiple Unicast Conjecture is False",
  "title_text": "The Multiple Unicast Conjecture is False",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/9pf39kn47tj43",
  "venue": "arXiv",
  "versions": []
}