What was already known
Hanebaly’s 2019 paper had already proposed a proof of the same original-norm assertion and later announced another; Nourouzi subsequently described the general question as unresolved. Earlier established cases include uniformly convex spaces, normal-structure domains, reflexive subspaces of L¹, and certain other structured spaces (manuscript introduction, pp. 1–2).
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
Supplies a different proof mechanism for the general original-norm theorem amid the unresolved status reported in later literature.
Limitations
The result concerns real reflexive Banach spaces and nonexpansive selfmaps of nonempty closed bounded convex sets. Priority for the theorem itself is qualified by Hanebaly’s earlier proof claims; the assessed contribution is OpenAI’s distinct argument.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
Pinned OpenAI Lean solution module contains a proved matching headline theorem. This is source-reported code inspection; local build and imported-module audit were not performed.
- Checker
- OpenAI-reported Lean 4
- Scope
- Every nonexpansive selfmap on a nonempty closed bounded convex subset of a real reflexive Banach space has a fixed point in the original norm.
- 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 verification-scope review for non-notifying local inclusion.
Read this published revision