What is recorded here?
The 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.
Source-linked catalogue note. A detailed explanatory guide has not yet been prepared for this entry.
Scientific scope
It 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.
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People and systems
OpenAI (organizational manuscript byline); individual human roles not fully disclosed The recorded author list is incomplete.
OpenAI 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 attribution; provider attestation is unavailable.
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English catalogue narrative
OpenAI: A claimed negative solution of Hilbert’s tenth problem over the rationals
The 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.
Scientific scope
It 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.
Reading status
This 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.
People and systems
OpenAI (organizational manuscript byline); individual human roles not fully disclosed
OpenAI 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).