Kalton-Peck Space and its Hyperplanes
Whether the real Kalton-Peck space is isomorphic to its hyperplanes. It is not: no hyperplane of is isomorphic to , proved through a rank parity theorem for symplectic spaces applied to the Kalton-Swanson symplectic structure.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Argument
- Field
- Banach space theory
- Posed by
- W. B. Johnson, Joram Lindenstrauss, Gideon Schechtman
- Year posed
- 1980
- Years open
- 46y
- Solved
- 2026-08-03
- Model
- GPT-5.5 Pro-Extended
- Vendor
- OpenAI
- Collaborators
- A. Das, V. Ferenczi, Ch. Rosendal
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 25 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The AI use and Lean formalization section states that the principal result was first obtained through an extended interaction with ChatGPT using GPT-5.5 with Pro-Extended reasoning, which supplied an ingredient of the argument.
Verification
arXiv preprint, not yet peer-reviewed. The paper reports a Lean formalization alongside; the site has not checked it.