What was already known
The two-cycle claim was open for unrestricted classical quintic Liénard systems. Earlier proofs covered odd quintics, a slow-fast nondegenerate setting or the unrestricted quartic case.
AI involvement
OpenAI is the named author of this model-produced manuscript. No individual human proof check or human explanation is documented.
OpenAI is the named author of the specific September 24 manuscript, and the release describes model-produced manuscripts.
Importance
Settles the classical unrestricted quintic case with a sharp bound.
Limitations
This does not cover arbitrary quintic planar vector fields or the broader degree-dependent uniform-bound claim. The proof-bearing Lean endpoint addresses this scoped two-cycle theorem; the comparator file is only a statement.
Technical verification
The repository presents a Lean 4 proof of the same unrestricted degree-at-most-five statement, including existence of a two-cycle example. The comparator file is a statement stub with `sorry`; the proof-bearing endpoint is OAI.Analysis.LienardCycles.Main and its imported development. This is a source-reported formalization of the selected statement; this review did not run Lean or Comparator.
Formal checking
Proof-bearing Lean declaration paired with the separate ComparatorChallenges/QuinticLienard statement
- Checker
- Lean 4 in the OpenAI formalization release
- Scope
- OAI.QuinticLienard.main: every real F of degree at most five has at most two isolated periodic-orbit images, and some F has exactly two
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The manuscript explains its midpoint-function and quadratic-fit mechanism, but the release does not attribute a central explanation to a person. Few is the evidence default, not a claim that humans cannot understand it.
Correction and publication history
If correct, settles the classical unrestricted quintic case with a sharp bound.
Read this published revision