What was already known
Goette, Kerin and Shankar established nonnegative sectional curvature on every exotic seven-sphere. Earlier strictly positive constructions concerned the particular Gromoll–Meyer sphere; they did not establish the all-28-class claim.
AI involvement
The acknowledgments credit ChatGPT 6 Astra and Claude Pro with exploring some proof strategies and calculations. The authors retain responsibility for human verification and exposition. The disclosure does not identify which lemmas or calculations came from each model, quantify their contribution, or establish autonomous AI discovery.
The acknowledgment of exploring some strategies and calculations does not identify an AI-supplied retained lemma or construction; importance of the sphere theorem does not establish that role.
Importance
Settles a longstanding curvature-existence question for every smooth structure on the seven-sphere.
Limitations
Preprint; AIProofWatch reviewed the statement, baseline, AI disclosure and computational scope, not the full proof. The SageMath companion is bound to a separately supplied v12 source; complete correspondence with arXiv v1 has not been audited. It reports 80 PASS groups and seven UNVERIFIED dependency groups involving global geometry, analytic estimates, gluing and smoothing. These are computational limits, not seven demonstrated errors. No end-to-end formal proof or outside verification is established. AIProofWatch has not rerun the package. The claim concerns dimension seven and does not supply quarter-pinched metrics on exotic spheres.
Technical verification
The primary source reports the contribution, but the reviewed source passages do not document a completed full rigorous check. Proof availability, authorship and publication status are not treated as completed checking.
Human understanding
Few is the default when evidence for a higher level is insufficient. No sufficient account of a named human explaining the scoped central reasoning is established in this assessment. Missing disclosure is not evidence of little understanding.
Correction and publication history
Historical backfill after primary-statement, prior-work, AI-role and artifact-scope review on 16 October 2026. The September report was absent from the published catalog and private source queue. Initial subscriber alerts disabled under the historical-entry policy.
Read this published revision