What was already known
Kalton asked whether a bi-Lipschitz copy of c₀ forces a linear copy. The public companion record concerns a different pair of spaces and an obstruction involving c₀(ℓ₂), not ordinary c₀ absorption.
AI involvement
OpenAI credits an internal model with the Banach-space manuscripts and proof artifacts. The release does not document a human-origin construction for this c₀ absorption result.
OpenAI credits an internal model with producing the dated Banach-space manuscripts and Lean artifacts; no human-origin central construction is documented.
Importance
Answers Kalton’s c₀ absorption question negatively.
Limitations
The source-reported Lean result is the c₀ absorption theorem; a separate sorry-bearing comparison stub is not its proof. The Lean build and manuscript-to-formal mapping were not reproduced in the review.
Technical verification
The family 324 note maps the c0 absorption statement to OAI.C0Absorption.main_result, whose implementation constructs the space and proves the full MainConclusion without sorry. The separate ComparatorChallenges statement is a sorry-bearing comparison stub and is not the checked proof. This is a source-reported Lean check, not rerun here.
Formal checking
Formal proof in OAI/Analysis/C0Absorption/Main.lean, mapped by family 324 scope note
- Checker
- Lean 4/mathlib on OAI.C0Absorption.main_result
- Scope
- A separable real Z without linear c0 that is bi-Lipschitz equivalent to Z×c0, with the stated metric universality
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
No named human explanation of the central nonlinear absorption construction appears in the release material. Few is the evidence default, not a finding that the proof is inherently opaque.
Correction and publication history
If correct, answers Kalton’s c₀ absorption question negatively.
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