Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 004-01. Hilbert’s tenth problem over the rational numbers
Manuscript map · lines 2515–2524
OpenAI@2026-10-07#rem:oai-p-004-01
Authors: OpenAI. Family 004.
Title: Hilbert’s tenth problem over the rational numbers.
Abstract: We give a negative answer to Hilbert's tenth problem over the rational numbers: no algorithm decides whether a polynomial with integer coefficients has a rational zero. The number of variables is part of the input.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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