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        "title": "OpenAI, Hilbert's tenth problem over the rational numbers",
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          "citation": "OpenAI, Hilbert's tenth problem over the rational numbers",
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      "statement": "# OpenAI: A claimed negative solution of Hilbert’s tenth problem over the rationals\n\nThe manuscript claims that no algorithm can decide, for an integer-coefficient polynomial whose number of variables is part of the input, whether it has a rational zero. Rational numbers permit fractions, so this is a different decision problem from the classical integer result. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.\n\n## Scientific scope\n\nIt does not assert that any given equation is unsolvable, nor that restricted classes cannot have algorithms. The already known integer undecidability theorem cannot simply be relabelled as the rational result. WRS has inspected the cited statement and source-reported formalization scope where available; it has not audited the full proof or replayed Lean.\n\n## Reading status\n\nThis is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.\n\n## People and systems\n\n\n\nOpenAI (organizational manuscript byline); individual human roles not fully disclosed\n\nOpenAI research model / OpenAI / Unreleased internal frontier model; exact identifier not disclosed: Source-reported mathematical argument generation; human preparation/editing roles retained separately where disclosed (source reported).\n\n## Original sources\n\n- [OpenAI, Hilbert's tenth problem over the rational numbers](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Hilberts-tenth-problem-over-the-rational-numbers-October-6-2026/main.pdf)\n",
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