An AI system claims that in every dimension three and up, infinity-harmonic functions have Hölder continuous gradients, so they are continuously differentiable.
What does that even mean, and has anyone checked? Each episode takes one claim like this, builds the intuition with animation, and keeps a running record of how far the proof has been verified.
Episode 377: Continuous gradients in every dimension?, about 4 minutes.
Where this claim stands
- Posted as a preprint
- OpenAI, October 4, 2026
- Peer reviewed
- Not yet
- Checked in Lean
- Not yet
Last checked October 19, 2026. The claim has not been withdrawn. One preprint (46 pages); no Lean proof, catalogued or uncatalogued. Dimension three and up only; the exponent is not explicit. Not yet peer reviewed.
Recent episodes
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Episode 377 · 3:52
Continuous gradients in every dimension?
An AI preprint claims interior C¹,α estimates for infinity-harmonic functions in three and more dimensions
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Episode 376 · 4:26
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Episode 375 · 4:12
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Episode 374 · 3:40
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Episode 373 · 3:55
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Episode 372 · 3:56
Feel the inside from the surface?
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Episode 371 · 4:29
Stable blowup for waves that spread?
An AI preprint claims an open set of finite-time blowups for a defocusing Schrödinger equation on the 12-dimensional torus
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Episode 370 · 4:18
No solutions below the curve?
An AI preprint claims the subcritical Lane–Emden conjecture and its weighted Hénon extension in every dimension
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Progress
- Explained
- 372 of 372 results (719 papers in all)
- Lean proof published by OpenAI
- 242 of 372 results: 177 of the main theorem, 65 of part of the claim
- Peer reviewed
- 0 as of October 19, 2026
OpenAI’s 719 papers are grouped into 372 results. A result is one main claim plus any companion papers, such as alternative proofs, supporting results or consequences, and each episode explains one whole result, all of its papers included.
How to read the record
Every claim gets the same three steps. A filled gold box means a step has happened; an empty box means it hasn’t yet.
- Posted as a preprint
- The proof is public
- Peer reviewed
- Refereed by mathematicians
- Checked in Lean
- Verified step by step by computer
Posted as a preprint means the lab has released a written proof anyone can read. That’s where a claim starts, not where it ends. Peer reviewed means independent mathematicians have refereed it, usually for a journal. Checked in Lean means the main result has been verified by Lean, a computer program that accepts a proof only when every step is justified.
When OpenAI’s published Lean proof covers only part of a claim, the box stays empty and the record says so. In lists, a half-filled box marks these.
If a claim is withdrawn, its box turns red and the episode stays up, clearly marked. Mistakes are part of the story.