Geometry and topology · Oct 6, 2026
Kakeya maximal/set assertions
Resolves the Kakeya maximal conjecture in three dimensions and the Hausdorff-dimension conjecture in four. In three dimensions, the radius-δ tube maximal operator maps to with norm for every ε > 0. In four dimensions, every set containing a unit segment in every direction has Hausdorff dimension four.
Scope and what remains
These are distinct claims; three-dimensional set progress from earlier human work is not a new 2026 AI resolution of the same statement.
Contributors
OpenAI source publisher and an unnamed unreleased internal model. Exact paper-level human roles are not disclosed by the family summary.
AI systems: Unreleased OpenAI model