OpenAI claims strong cosmic censorship near Kerr
Awaiting review
Importance: historic (5 of 5)The takeaway
Three manuscripts in OpenAI’s 6 Oct 2026 math release (family 264, dated 23 Sept) claim local strong cosmic censorship for rotating Kerr black holes, with no symmetry assumption. For generic small perturbations of two-ended Kerr data, the spacetime cannot be extended past its maximal development with a continuous metric and square-integrable connection. That is the weak-solution formulation Christodoulou proposed in 2009. Berkeley’s Sung-Jin Oh, who has worked toward this problem for thirteen years, wrote that the proof takes a route different from the field’s and organised a reading group. No Lean proof; no expert verdict yet.
Status
- Claim
Awaiting review
- Our reporting
- Medium confidence
- Verification
- Preprint only
- Importance
- Historic (5 of 5)
- Last verified
- 29 October 2026
Your AI and this story
- GPT-6 Astra159 days after its cutoff
- Claude Opus 5.598 days after its cutoff
- Gemini 4 Argon189 days after its cutoff
- Grok 4.7128 days after its cutoff
None of these four assistants can know about it. The closest, Claude Opus 5.5, stops 98 days before it.
Key facts
- Main claim (abstract, verbatim): ‘For each fixed rotating subextremal Kerr background with mass M > 0 and rotation 0 < |𝔞| < M, we prove that the smooth vacuum data near its complete two-ended bridge whose full maximal globally hyperbolic development admits a future C⁰ ∩ W^{1,2}_loc extension form a meagre set in the weighted smooth topology.’
- Companions (verbatim): ‘a dense G_δ set of nearby smooth, complete two-ended vacuum data has a maximal globally hyperbolic development with no future C¹ extension’; and C² inextendibility with a neighbourhood ‘defined by one finite-order seminorm’. Extensions need not satisfy the vacuum equations; no symmetry is imposed
- Formulation history (Oh’s essay): Penrose proposed the conjecture in 1974; Christodoulou (1999) stated it with continuous metrics; Dafermos showed that C⁰ version fails in spherically symmetric models; Christodoulou (2009) asked for no extension even as a weak solution, which makes W^{1,2}_loc the natural target; Dafermos and Luk proved the C⁰ version fails for perturbations of Kerr without symmetry. ‘The W^{1,2}_loc formulation is the one the claimed proof takes.’
- Sung-Jin Oh (UC Berkeley), essay ‘What does it mean for a mathematician to understand? A case study in the age of AI’: the claimed proof ‘does not go through these intermediate results, and it develops its own version of some of the ingredients instead of drawing on existing work’; the comparison of routes ‘is not a judgment of the proof’s correctness’; ‘I have started organizing a reading group to digest the claim.’ The essay’s AI disclosure says it was developed in conversation with Claude
- What it is not: a global proof for all initial data. The result is local (near each fixed Kerr bridge), for vacuum data in a weighted smooth topology; the full conjecture concerns generic asymptotically flat data
- Status: no Lean scope note for family 264; no withdrawal or revision in history.md; Papex’s overview (reviewed 14 Oct) and Latent Seminar’s exposition (7 Oct) both separate the claim from independent verification
What happened
Strong cosmic censorship asks whether general relativity is deterministic: whether generic initial data fix the whole future, or whether observers can cross a Cauchy horizon into a region the data do not decide. Inside a rotating (Kerr) black hole, the exact solution has such a horizon. The question is whether it survives small perturbations in a form regular enough for the Einstein equations to continue past it.
The precise target took decades to pin down. Dafermos and Luk proved that the horizon persists with a continuous metric, so the original C⁰ version fails. Christodoulou’s refined version asks instead that no extension exists even as a weak solution, which makes extensions with a square-integrable connection the ones to rule out. OpenAI’s three manuscripts claim exactly this for generic perturbations of every fixed subextremal rotating Kerr spacetime, with no symmetry assumption, along with C¹ and C² versions.
Sung-Jin Oh, a Berkeley analyst whose work with Jonathan Luk settled a spherically symmetric model problem, wrote the most detailed public reaction. He recognises the field’s framework in the overall structure, but says the route differs from the one specialists were building through intermediate results such as late-time tails. He has started a reading group to check and digest it.
Why it matters
Strong cosmic censorship near Kerr is one of the central open problems of mathematical general relativity. If the claim holds, the “local” version of Penrose’s conjecture around rotating black holes is settled in its accepted formulation. Verification will take specialists months. Until then the result is an unrefereed AI claim, taken seriously enough that the people closest to the problem are organising to read it.
What is disputed or not yet verified
| Verification | Unrefereed manuscripts without formalization; under study by specialists, no verdict published |
|---|
Sources
7 sources from 4 sites. Numbers match the chips in the text.
7 sources: 4 primary, 3 reactions
Primary
- OpenAI: Generic Future Inextendibility with Square-Integrable Connection Near a Fixed Kerr Spacetime (PDF)github.com, paper
- OpenAI: Generic C1 Future Inextendibility Near Rotating Subextremal Kerr Spacetimes (PDF)github.com, paper
- OpenAI: Quantitative Near-Kerr Evolution and Generic C2 Future Inextendibility (PDF)github.com, paper
- Dafermos, Luk: The interior of dynamical vacuum black holes I: C⁰-stability of the Kerr Cauchy horizon (Annals, 2025)annals.math.princeton.edu, paper
Reactions
- Sung-Jin Oh: What does it mean for a mathematician to understand? A case study in the age of AI (essay, 10–16 Oct)math.berkeley.edu, discussion
- Papex: Cosmic censorship hypothesis (overview, reviewed 14 Oct)papex.org, discussion
- oai-math-revised: community notes on the main Kerr manuscriptgithub.com, discussion
Changes
- Filed (families 251–378; three abstracts, Oh’s essay read in full, oai-math-revised notes)