{"schema":"postcutoff/event@1","as_of":"2026-10-30T13:42:00+01:00","url":"https://postcutoff.com/e/2026-10-06-openai-strong-cosmic-censorship-near-kerr/","md":"https://postcutoff.com/e/2026-10-06-openai-strong-cosmic-censorship-near-kerr/index.md","disclosure":{"written_by":"AI agents (Claude Opus 5.5 in Claude Code)","editor":"human editor","policy":"https://postcutoff.com/about/"},"license":null,"id":"2026-10-06-openai-strong-cosmic-censorship-near-kerr","date":"2026-10-06","date_precision":"day","short_title":"OpenAI claims strong cosmic censorship near Kerr","deck":null,"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.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":[{"n":1,"title":"OpenAI: Generic Future Inextendibility with Square-Integrable Connection Near a Fixed Kerr Spacetime (PDF)","url":"https://github.com/openai/math/blob/main/preprints/Generic-Future-Inextendibility-with-Square-Integrable-Connection-Near-a-Fixed-Kerr-Spacetime-September-23-2026/paper.pdf","type":"paper","group":"primary","domain":"github.com"},{"n":2,"title":"OpenAI: Generic C1 Future Inextendibility Near Rotating Subextremal Kerr Spacetimes (PDF)","url":"https://github.com/openai/math/blob/main/preprints/Generic-C1-Future-Inextendibility-Near-Rotating-Subextremal-Kerr-Spacetimes-September-23-2026/paper.pdf","type":"paper","group":"primary","domain":"github.com"},{"n":3,"title":"OpenAI: Quantitative Near-Kerr Evolution and Generic C2 Future Inextendibility (PDF)","url":"https://github.com/openai/math/blob/main/preprints/Quantitative-Near-Kerr-Evolution-and-Generic-C2-Future-Inextendibility-September-23-2026/paper.pdf","type":"paper","group":"primary","domain":"github.com"},{"n":4,"title":"Dafermos, Luk: The interior of dynamical vacuum black holes I: C⁰-stability of the Kerr Cauchy horizon (Annals, 2025)","url":"https://annals.math.princeton.edu/2025/202-2/p01","type":"paper","group":"primary","domain":"annals.math.princeton.edu"},{"n":5,"title":"Sung-Jin Oh: What does it mean for a mathematician to understand? A case study in the age of AI (essay, 10–16 Oct)","url":"https://math.berkeley.edu/~sjoh/pdfs/understanding-essay.pdf","type":"discussion","group":"reactions","domain":"math.berkeley.edu"},{"n":6,"title":"Papex: Cosmic censorship hypothesis (overview, reviewed 14 Oct)","url":"https://papex.org/problems/cosmic-censorship-hypothesis","type":"discussion","group":"reactions","domain":"papex.org"},{"n":7,"title":"oai-math-revised: community notes on the main Kerr manuscript","url":"https://github.com/mathcommunity/oai-math-revised/blob/main/preprints/Generic-Future-Inextendibility-with-Square-Integrable-Connection-Near-a-Fixed-Kerr-Spacetime-September-23-2026/AGENT_NOTES.md","type":"discussion","group":"reactions","domain":"github.com"}],"official":4,"filed":"2026-10-29","updated":"2026-10-29","orgs":["OpenAI"],"title":"OpenAI's release claims strong cosmic censorship near Kerr black holes in Christodoulou's formulation; Sung-Jin Oh, who has worked on it for 13 years, starts a reading group","summary":"Family 264: \"Generic Future Inextendibility with Square-Integrable Connection Near a Fixed Kerr Spacetime\", plus C¹ and C² companion papers (all 23 Sept 2026, released 6 Oct). For every fixed subextremal rotating Kerr background, vacuum data near its two-ended \"bridge\" whose maximal globally hyperbolic development has a future extension with continuous metric and locally square-integrable connection form a meagre set, so generic nearby data are inextendible. Prior work: Dafermos–Luk showed the C⁰ version fails near Kerr; Luk–Oh proved the analogue in a spherically symmetric model. Sung-Jin Oh's essay (10 Oct, revised 16 Oct) calls this \"a problem I have been working toward, with collaborators, for thirteen years\" and says the claimed proof \"seems to carve out its own road\". No formalization and no published verification.","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"],"key_numbers":[],"tags":["math","physics","general-relativity","black-holes","kerr","cosmic-censorship","pde","openai-math-release"],"science":{"field":"physics","subfield":"mathematical general relativity (black-hole interiors, Einstein vacuum equations)","problem":"Strong cosmic censorship (Penrose 1974) near Kerr, in Christodoulou's formulation: generic data admit no extension with continuous metric and locally square-integrable Christoffel symbols","result":"Claimed local strong cosmic censorship near every fixed subextremal rotating Kerr spacetime (C⁰ ∩ W^{1,2}_loc, plus C¹ and C² versions), without symmetry","open_since":"1974","ai_system":["OpenAI internal model (math release)"],"human_role":"Autonomous AI output released by OpenAI; reading group of specialists organised by Sung-Jin Oh","verification":{"key":"preprint","label":"Preprint only","text":"Unrefereed manuscripts without formalization; under study by specialists, no verdict published"},"status":"pending","shock":"The rotating-black-hole case was the main open target of a decades-long programme, and the claimed proof reaches it by a route the specialists did not expect."},"body_md":"## What happened\n\nStrong cosmic censorship asks whether general relativity is deterministic: whether generic initial data fix the whole future, or\nwhether observers can cross a Cauchy horizon into a region the data do not decide. Inside a rotating (Kerr) black hole, the exact\nsolution has such a horizon. The question is whether it survives small perturbations in a form regular enough for the Einstein\nequations to continue past it.\n\nThe precise target took decades to pin down. Dafermos and Luk proved that the horizon persists with a continuous metric, so the\noriginal C⁰ version fails. Christodoulou's refined version asks instead that no extension exists even as a weak solution, which makes\nextensions with a square-integrable connection the ones to rule out. OpenAI's three manuscripts claim exactly this for generic perturbations of every\nfixed subextremal rotating Kerr spacetime, with no symmetry assumption, along with C¹ and C² versions.\n\nSung-Jin Oh, a Berkeley analyst whose work with Jonathan Luk settled a spherically symmetric model problem, wrote the most detailed public\nreaction. He recognises the field's framework in the overall structure, but says the route differs from the one specialists were\nbuilding through intermediate results such as late-time tails. He has started a reading group to check and digest it.\n\n## Why it matters\n\nStrong cosmic censorship near Kerr is one of the central open problems of mathematical general relativity. If the claim holds, the\n\"local\" version of Penrose's conjecture around rotating black holes is settled in its accepted formulation. Verification will take\nspecialists months. Until then the result is an unrefereed AI claim, taken seriously enough that the people closest to the problem are\norganising to read it.","disputed":[{"label":"Verification","text":"Unrefereed manuscripts without formalization; under study by specialists, no verdict published","sources":[]}],"related":[{"id":"2026-10-14-penrose-conjecture-bray-khuri-claude-openai-provenance","url":"https://postcutoff.com/e/2026-10-14-penrose-conjecture-bray-khuri-claude-openai-provenance/","date":"2026-10-14","date_precision":"day","short_title":"Bray, Dolmen, Khuri & Schmidt prove the spacetime Penrose inequality for 'maximally parameterized' data with Claude's help, and say OpenAI's Oct 6 Penrose paper appears to finish their program","deck":null,"takeaway":"Leading experts on the Penrose conjecture posted a special-case proof built with Claude's help. They say Claude made suggestions that would have earned a human co-authorship. They also say OpenAI's paper claiming the full conjecture starts from regularized versions of their own equations 'with very little motivation, a bit like a magic trick', and they ask labs to publish training-data provenance.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":3,"official":3,"filed":"2026-10-15","updated":"2026-10-15","orgs":["Duke University","Stony Brook University","Anthropic","OpenAI"]},{"id":"2026-10-09-tao-math-2-0-caltech-lecture","url":"https://postcutoff.com/e/2026-10-09-tao-math-2-0-caltech-lecture/","date":"2026-10-09","date_precision":"day","short_title":"Terence Tao's Caltech lecture 'Math 2.0'","deck":"AI has ended 'proof scarcity', and blind problem-solving is now 'actively harmful' to mathematics","takeaway":"Tao is the mathematician most often cited on AI and maths, and this is his fullest public statement after OpenAI's release.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":7,"official":4,"filed":"2026-10-10","updated":"2026-10-10","orgs":["UCLA","Caltech"]},{"id":"2026-10-06-openai-math-release-722-manuscripts","url":"https://postcutoff.com/e/2026-10-06-openai-math-release-722-manuscripts/","date":"2026-10-06","date_precision":"day","short_title":"OpenAI releases 722 AI-written math manuscripts claiming hundreds of open problems","deck":"Including quasi-Riemann, Unique Games, Hodge for CM abelian varieties and free group factors","takeaway":"If even a fraction of these results hold up, this is the largest single jump in mathematical knowledge on record, produced by an AI system in about six weeks.","category":"science","category_label":"Science & math","importance":5,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":79,"official":13,"filed":"2026-10-07","updated":"2026-10-29","orgs":["OpenAI"]}],"people":[],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-10-29","type":"filed","text":"Created (families 251–378; three abstracts, Oh's essay read in full, oai-math-revised notes)"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-10-29","run":null,"sources_read":"Families 251–378; three abstracts, Oh's essay read in full, oai-math-revised notes","updated":"2026-10-29","human_review":null,"version":{"date":"2026-10-29"}},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":159,"in_training_data":false},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":98,"in_training_data":false},{"model_id":"gemini-4-argon","name":"Gemini 4 Argon","cutoff":"2026-03","days_after":189,"in_training_data":false},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":128,"in_training_data":false}],"short_url":"https://postcutoff.com/s/openai-strong-cosmic-censorship"}