Topology·OpenAI Math·Result 311
The Hovey–Strickland and Chai conjectures
One of the 372 results in OpenAI's public mathematics catalogue, filed under topology: 1 preprint, the latest dated 24 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and embeds the animation.
In one line: OpenAI reports a proof of the Hovey–Strickland and Chai conjectures (topology) in a preprint dated 24 September 2026. It has not been peer reviewed. The channel's animation, Every OpenAI Math Result, Part 3 of 4: Operator Paving, Naimark's Problem and 82 More, is on YouTube.
Chapter 17 of 84 in Every OpenAI Math Result, Part 3 of 4: Operator Paving, Naimark's Problem and 82 More · starts at 5:36 · watch from there on YouTube →
What OpenAI claims
Proves Chai's invariant-ideal conjecture for Lubin–Tate deformation rings over finite residue fields, at every prime and positive height n. Through the implication of Barthel–Heard–Naumann, this proves the Hovey–Strickland conjecture: dualizable K(n)-local spectra have exactly n+2 thick tensor ideals, and their Balmer spectrum is a chain of n+1 points.
Paper
Stabilizer orbits and thick tensor ideals of dualizable K(n)-local spectra
OpenAI's abstract We classify the prime and radical ideals of the Lubin–Tate deformation ring invariant under an open Morava stabilizer subgroup, at every prime and positive height. This proves Chai's invariant-ideal conjecture in the standard finite-residue-field formulation. It also proves the Hovey–Strickland conjecture: the dualizable K(n)-local category has exactly n+2 thick tensor ideals, and its Balmer spectrum is a chain of n+1 points.
Status
Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.
Quick answers
- Is it proven?
- Not independently yet. OpenAI posted a preprint on 24 September 2026; it has not been peer reviewed, so treat the result as OpenAI's claim until other mathematicians have checked it.
- What exactly does OpenAI claim?
- Proves Chai's invariant-ideal conjecture for Lubin–Tate deformation rings over finite residue fields, at every prime and positive height n. Through the implication of Barthel–Heard–Naumann, this proves the Hovey–Strickland conjecture: dualizable K(n)-local spectra have exactly n+2 thick tensor ideals, and their Balmer spectrum is a chain of n+1 points.
- Where is the proof?
- In the paper, Stabilizer orbits and thick tensor ideals of dualizable K(n)-local spectra (PDF).
- Is there a video?
- Yes, on YouTube (29:20, chapter 17).
Also in
- Chapter 6 of 10 in Kervaire Invariant Problem at Prime 3, The Grothendieck Homotopy Hypothesis and 8 More · starts at 1:45 · watch from there on YouTube →
The video
Every OpenAI Math Result, Part 3 of 4: Operator Paving, Naimark's Problem and 82 More · Compilation · 29:20 · chapter 17 from 5:36 · description, sources and chapters →
