OpenAI · 258-01 · 2026-09-25 · Group theory
Baumslag-Solitar-free one-relator groups are hyperbolic
preprints/Baumslag-Solitar-free-one-relator-groups-are-hyperbolic-September-25-2026
Family 258. Gersten's conjecture for one-relator groups.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Proves Gersten's conjecture: every finitely generated one-relator group containing no Baumslag–Solitar subgroup , with , is word-hyperbolic. It also proves that every word-hyperbolic one-relator group is virtually compact special.
We prove Gersten's conjecture: every finitely generated one-relator group containing no subgroup isomorphic to a Baumslag–Solitar group , for nonzero integers m, n, is word-hyperbolic.
Preprint source and Lean scope
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No Lean scope note is in the repository for this family. The preprint source below is still the full manuscript, not only the abstract. No compilation is asserted.