Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: Family 306. The purely cosmetic surgery conjecture for knots in S 3
Family claims › Topology · lines 2006–2011
OpenAI@2026-10-07#rem:oai-306
Distinct Dehn surgery slopes on a nontrivial smooth knot in never produce orientation-preservingly homeomorphic manifolds, proving the purely cosmetic surgery conjecture. The statement includes the meridional slope.
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 304. The Hilbert–Smith conjecture in every dimension
- remark: Remark: Family 305. Counterexamples to disk embedding and Wall's manifold conjecture
- remark: Remark: Family 307. Failure of rational injectivity for maximal coarse assembly
- remark: Remark: Family 308. Smith–Toda complexes at every height with varying primes
- remark: Remark: Family 309. The Kervaire invariant problem at the prime three
- remark: Remark: Family 310. Quillen's conjecture in rational homology
- remark: Remark: Family 311. Chai's invariant-ideal conjecture
- remark: Remark: Family 312. The Grothendieck homotopy hypothesis