Strong cosmic censorship near two-ended Kerr data

What OpenAI claims

Proves local strong cosmic censorship near each fixed rotating subextremal Kerr bridge. 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.

Papers (3)

1. Generic Future Inextendibility with Square-Integrable Connection Near a Fixed Kerr Spacetime

   23 September 2026 · Preprint, not peer reviewed · PDF

   OpenAI's abstract 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. 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.

2. Generic C1 Future Inextendibility Near Rotating Subextremal Kerr Spacetimes

   23 September 2026 · Preprint, not peer reviewed · PDF

   OpenAI's abstract For each fixed Kerr spacetime with mass M > 0 and rotation 0 < 𝔞 < 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.

3. Quantitative Near-Kerr Evolution and Generic C2 Future Inextendibility

   23 September 2026 · Preprint, not peer reviewed · PDF

   OpenAI's abstract 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.

Status

Preprint. The papers have 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.