Kalton-Peck Space and its Hyperplanes

Precise statement

Whether the real Kalton-Peck space $Z_2$ is isomorphic to its hyperplanes. It is not: no hyperplane of $Z_2$ is isomorphic to $Z_2$, proved through a rank parity theorem for symplectic spaces applied to the Kalton-Swanson symplectic structure.

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

GPT-5.5 Pro-Extended

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.

Provider: OpenAI · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

arXiv preprint, not yet peer-reviewed. The paper reports a Lean formalization alongside; the site has not checked it.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-08-03

   arXiv:2608.02126 - Kalton-Peck space is not isomorphic to its hyperplanes

   VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

argument (source-reported)

Source-reported tools: argument.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.