What was already known
The hyperplane-isomorphism question for Z₂ had remained open since the space’s introduction. Earlier symplectic and Fredholm results are used in the proof.
AI involvement
The authors credit ChatGPT GPT-5.5 Pro-Extended with the principal result and an initial proof. A. Das, V. Ferenczi and Ch. Rosendal checked and rewrote the proof.
The first-person declaration assigns the principal theorem and initial proof to ChatGPT, followed by substantial human checking and rewriting.
Importance
The result settles a long-standing question about this Banach-space example.
Limitations
The authors report a complete human check and Lean formalization. The precise prompts in the original model interaction are unavailable.
Technical verification
The authors report independently checking all statements and proofs, and a complete Lean 4 formalization of the parity and hyperplane results.
Independent checking
Complete Lean/mathlib formalization with top-level theorem statements in KaltonPeck.lean
- Checker
- Lean 4 kernel, reported by the authors' KaltonPeck project
- Scope
- rankParityGeneral, rankParityZ2 and noHyperplaneComplexStructure for the real Kalton–Peck space
- Basis
- Reported by the linked checker
Independent checking
Detailed independent examination and rewriting of the model's initial proof
- Checker
- A. Das, V. Ferenczi and Ch. Rosendal
- Scope
- All statements and proofs in the submitted hyperplane manuscript
- Basis
- Reported by the linked checker
Human understanding
The human authors explain the symplectic rank-parity obstruction and its application to hyperplanes of Z_2 after rewriting the argument.
Correction and publication history
The result settles a long-standing question about this Banach-space example.
Read this published revision