What was already known
Petty conjectured the ellipsoid minimum for n≥3; the manuscript describes a separate three-dimensional result and addresses the dimensions n≥4.
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
Completes the higher-dimensional part of Petty’s projection-volume conjecture.
Limitations
The selected claim is the projection-volume inequality for n≥4. Other projection-body inequalities and the separate simplex-maximization counterexample are not included.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note establishes the sharp normalized projection-body inequality and ellipsoid equality case in every dimension at least four.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- For every convex body K in Rⁿ with n≥4, its normalized projection-body volume is at least the ellipsoid value, with equality exactly for ellipsoids.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
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, prior-work, and scoped checking review for non-notifying local inclusion.
Read this published revision