What was already known
The generalized star-height question asked whether an absolute bound exists across all regular languages and alphabets; bounds in ordinary expressions without complement do not answer it.
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
Establishes a universal finite bound on the generalized star height of regular languages.
Limitations
The linked Lean scope checks a later, stronger bound of three, which implies the selected height-thirteen statement. It does not separately formalize the original twelve-split construction; neither result establishes the optimal height.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned OpenAI Lean scope note verifies a stronger numerical bound that implies this selected statement, but not the first construction.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- Every regular language over a finite alphabet has a generalized regular expression over the same alphabet of star height at most three.
- 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 precise partial or mismatched Lean-scope review for non-notifying local inclusion.
Read this published revision