What was already known
The generalized star-height problem asked whether one finite bound works for every regular language. This manuscript improves earlier bounds of thirteen and four from the same research series.
AI involvement
OpenAI credits an internal model with the manuscript and proof artifacts. No separate human construction or item-specific autonomous session is documented.
OpenAI credits an internal model with producing the manuscripts and proof artifacts; the record does not establish little or no human mathematical input for this particular result.
- Supporting source (raw.githubusercontent.com) — Model provenance and verification caveat
- Supporting source (github.com) — Result 134 and linked bound-three manuscript
Importance
A universal bound of three would settle the uniform-boundedness question.
Limitations
The theorem bounds nesting depth, not expression size or construction time. It does not determine whether height one suffices or the exact maximum.
Technical verification
The public Lean main theorem proves HasHeightAtMost L 3 for every regular language over a finite alphabet. The scope note identifies same-alphabet expressions and same-free-monoid complements; the comparator file contains a placeholder challenge and is not itself the completed proof. The completed Lean theorem supports the Formal rating.
Formal checking
Lean proof term for the selected statement, with source-reported formalization
- Checker
- OpenAI Lean formalization
- Scope
- Every regular language over a finite alphabet has generalized 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
The available release provides no named human explanation of the central construction. Few is the evidence default.
Correction and publication history
A universal bound of three would settle the uniform-boundedness question.
Read this published revision