Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: Family 004. Hilbert's tenth problem over Q
Family claims › Number theory · lines 211–216
OpenAI@2026-10-07#rem:oai-004
Proves that no algorithm decides whether an integer-coefficient polynomial in an arbitrary number of variables has a rational zero, resolving Hilbert's tenth problem over negatively.
The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.
Nearby in this section
- remark: Remark: Family 001. Milne's rationality conjecture
- remark: Remark: Family 002. The full Birch–Swinnerton-Dyer formula in Selmer coranks zero and one
- remark: Remark: Family 003. The quasi-Riemann hypothesis
- remark: Remark: Family 005. Irrationality of Catalan's constant
- remark: Remark: Family 006. Goldfeld's conjecture
- remark: Remark: Family 007. Two-point Chowla and the corrected binary Elliott conjecture
- remark: Remark: Family 008. The Deligne–Drinfeld conjecture
- remark: Remark: Family 009. Bogomolov–Pop and Milnor K -theoretic reconstruction