What was already known
Meridional, same-sign and many opposite-slope cases had been ruled out through classical and Floer-theoretic obstructions. The remaining opposite-slope cases kept the purely cosmetic surgery conjecture open.
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Resolves the purely cosmetic surgery conjecture for knots in the three-sphere.
Limitations
The homeomorphism may be arbitrary; it need not preserve the surgery core. Orientation-reversing coincidences are outside the claim.
Technical verification
Reported is the default when evidence for a higher level is insufficient. The OpenAI-authored manuscript reports and argues the result, but the reviewed sources do not document a completed check of the full assessed claim.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, and prior-work review for non-notifying local inclusion; technical verification remains Reported.
Read this published revision