{
  "abstract": "OpenAI’s disproof of the Erdős unit distance conjecture marks a milestone in AI for mathematical research. However, the result relied on an internal model with undisclosed test-time compute, hindering independent reproduction and analysis by the community. Here we present a simple autonomous agent built on the publicly available GPT-5.5 Pro. The agent uses a problem-agnostic three-stage prompting pipeline: brainstorm, execute, and review. We ran eight independent trials with web search disabled. In each trial, the agent produced a correct or essentially correct disproof of the conjecture. The resulting proofs are diverse and do not merely reproduce earlier AI-generated proofs. Since GPT-5.5 Pro was released nearly a month before OpenAI published its disproof, our evaluation is free from data contamination. The system operates efficiently, using an average of 106.7 k reasoning tokens per trial. We release our code and all outputs, providing a publicly accessible AI agent to resolve this conjecture autonomously.",
  "abstract_shown": true,
  "affiliations": [
    "Santa Clarita, CA 91350"
  ],
  "article_type": "brief report",
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Yichen Huang",
      "orcid": "0000-0002-8496-9251"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1ke84qexv5xpb.bib",
  "cited_by": 0,
  "doi": "10.1073/pnas.2621541123",
  "fulltext_url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC13732072/",
  "id": "1ke84qexv5xpb",
  "issns": [
    "0027-8424",
    "1091-6490"
  ],
  "landing_url": "https://doi.org/10.1073/pnas.2621541123",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "heading",
      "411"
    ],
    [
      "heading",
      "524"
    ],
    [
      "heading",
      "Computer Sciences"
    ],
    [
      "heading",
      "Physical Sciences"
    ],
    [
      "openalex",
      "1702|Artificial Intelligence Applications"
    ]
  ],
  "openalex": "W7165797887",
  "pdf_url": null,
  "pmcid": "PMC13732072",
  "pmid": "42932656",
  "published": "2026-10-26",
  "publisher": "National Academy of Sciences",
  "ris": "https://research.draconitic.com/paper/1ke84qexv5xpb.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T12:22:07Z",
      "native_id": "PMC13732072",
      "source": "pmc",
      "url": "https://doi.org/10.1073/pnas.2621541123"
    }
  ],
  "subjects": [
    {
      "field": "biochemistry",
      "origin": "journal-openalex:1312|Genomics and Chromatin Dynamics",
      "subfield": "molecular-biology"
    }
  ],
  "title": "Autonomous disproofs of the Erdős unit distance conjecture with GPT-5.5 Pro",
  "title_text": "Autonomous disproofs of the Erdős unit distance conjecture with GPT-5.5 Pro",
  "type": "peer-reviewed",
  "updated_at": "2026-11-08T12:22:07Z",
  "url": "https://research.draconitic.com/paper/1ke84qexv5xpb",
  "venue": "Proceedings of the National Academy of Sciences of the United States of America",
  "versions": []
}