What was already known
The two-sphere case was classical, and generic or strongly bumpy higher-dimensional metrics had infinitude results. Arbitrary degenerate metrics on higher-dimensional spheres remained outside those arguments.
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 sphere case of the closed-geodesic infinitude problem for all smooth metrics.
Limitations
Geodesics are counted by image, so iterates or reversed parametrizations do not create new examples. The separate three-manifold consequence is outside this selected 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