---
title: "Strong cosmic censorship near two-ended Kerr data"
authors:
  - "OpenAI (internal model)"
year: 2026
venue: "openai/math manuscript collection (GitHub), result family 264; unreviewed"
arxiv: null
doi: null
source: "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"
topics:
  - "openai-math"
  - "ai-generated-math"
  - "mathematical-physics"
  - "unformalized"
seed_rank: 2119
seed_batch: "openai-math-2026-10-07"
reviewed: "2026-10-07"
pool: "maths-foundations"
relevance_score: 7
lineage: ai-mathematical-reasoning
cites:
  - title: "Generic Future Inextendibility with Square-Integrable Connection Near a Fixed Kerr Spacetime"
    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"
    year: 2026
    arxiv: null
    doi: null
  - title: "Generic C1 Future Inextendibility Near Rotating Subextremal Kerr Spacetimes"
    url: "https://github.com/openai/math/blob/main/preprints/Generic-C1-Future-Inextendibility-Near-Rotating-Subextremal-Kerr-Spacetimes-September-23-2026/paper.pdf"
    year: 2026
    arxiv: null
    doi: null
  - title: "Quantitative Near-Kerr Evolution and Generic C2 Future Inextendibility"
    url: "https://github.com/openai/math/blob/main/preprints/Quantitative-Near-Kerr-Evolution-and-Generic-C2-Future-Inextendibility-September-23-2026/paper.pdf"
    year: 2026
    arxiv: null
    doi: null
---

# Strong cosmic censorship near two-ended Kerr data

## One-sentence takeaway

OpenAI's result family 264 (Mathematical physics) claims: Proves local strong cosmic censorship near each fixed rotating subextremal Kerr bridge.

## Why it matters here

Mathematical physics results sit behind the physical models that rendering and simulation borrow. More broadly, every card in this batch is evidence for the `ai-mathematical-reasoning` thread: per the repo README, an unreleased internal OpenAI model produced it, using about three hours of ChatGPT Pro thinking compute per result on average, across roughly 4,000 posed problems.

## Key ideas

- Family summary (repo): A dense Gδ subset of a weighted smooth neighborhood of smooth complete two-ended asymptotically flat vacuum data has full maximal globally hyperbolic developments with no future continuous nondegenerate extension whose weak connection is locally square-integrable. No symmetry is imposed; extensions need not satisfy the vacuum equations.
- *Generic Future Inextendibility with Square-Integrable Connection Near a Fixed Kerr Spacetime*: For each fixed rotating subextremal Kerr background with mass M > 0 and rotation $0\lt |\mathfrak a|\lt M$, we prove that the smooth vacuum data near its complete two-ended bridge whose full maximal globally hyperbolic development admits a future $C^0\cap W^{1,2}_{\mathrm{loc}}$ extension form a meagre set in the weighted smooth topology. The extension metric is continuous and nondegenerate, and its weak connection is locally square-integrable. The neighborhood requires smallness of only the tenth weighted seminorm, while the topology tests every finite order.
- *Generic C1 Future Inextendibility Near Rotating Subextremal Kerr Spacetimes*: For each fixed Kerr spacetime with mass M > 0 and rotation $0\lt \mathfrak a\lt M$, we prove that a dense Gδ set of nearby smooth, complete two-ended vacuum data has a maximal globally hyperbolic development with no future C1 extension. The neighborhood and genericity are defined in a weighted smooth topology, and ambient extensions may be nonvacuum.
- *Quantitative Near-Kerr Evolution and Generic C2 Future Inextendibility*: For every fixed rotating subextremal Kerr bridge, we prove that smooth vacuum data admitting a C2 future extension of their full maximal globally hyperbolic development form a meagre set in a neighborhood defined by one finite-order seminorm. The topology allows arbitrary symbol-bounded asymptotically flat tails and imposes no symmetry.

## Caveats

- Unreviewed: these are AI-generated manuscripts posted to GitHub with no peer review or arXiv deposit. The repo README says results are "at different stages of verification" and that "some of the unformalized results could have issues."
- This card restates the repo's family summary, manuscript abstracts and Lean scope notes. It is not an independent check of the proofs, and the scope of each theorem is exactly as stated there.
- Lean: not formalized. The repo has no Lean development for this family, so the claim rests on the prose manuscript(s) alone.

## Links

- Manuscript: [Generic Future Inextendibility with Square-Integrable Connection Near a Fixed Kerr Spacetime](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)
- Manuscript: [Generic C1 Future Inextendibility Near Rotating Subextremal Kerr Spacetimes](https://github.com/openai/math/blob/main/preprints/Generic-C1-Future-Inextendibility-Near-Rotating-Subextremal-Kerr-Spacetimes-September-23-2026/paper.pdf)
- Manuscript: [Quantitative Near-Kerr Evolution and Generic C2 Future Inextendibility](https://github.com/openai/math/blob/main/preprints/Quantitative-Near-Kerr-Evolution-and-Generic-C2-Future-Inextendibility-September-23-2026/paper.pdf)
- Family entry: https://github.com/openai/math/blob/main/CONTENTS.md
- Overview PDF: https://github.com/openai/math/blob/main/overview.pdf
- Repo: https://github.com/openai/math