What was already known
Earlier nonisomorphic examples concerned weaker uniform equivalence or special settings. Positive rigidity results for c₀ and other classes left the global separable bi-Lipschitz question open.
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Answers the separable Banach-space Lipschitz-isomorphism problem negatively.
Limitations
The formalized bijection has lower and upper Lipschitz bounds 4/21 and 76/25. The obstruction is c₀(ℓ₂), not ordinary c₀.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note constructs the stated separable real spaces, explicit bi-Lipschitz bijection and c₀(ℓ₂) linear obstruction.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- There are separable real Banach spaces X and Y with a global bi-Lipschitz bijection but no bounded linear isomorphism between them; X contains an isometric copy of c₀(ℓ₂), while Y contains no bounded linear copy of that space.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.
Read this published revision