What was already known
Höring proved a compatible product when one summand is integrable and conjectured automatic integrability. Earlier Fano and low-rank cases needed extra assumptions.
AI involvement
OpenAI is credited as author, and its release identifies these manuscripts as internal-model outputs. The result-specific degree of human direction is undisclosed, supporting AI-led rather than autonomous involvement.
The manuscript is OpenAI-authored model output, with no contrary human-origin account for its tangent-box construction.
Importance
Removes the integrability premise in Höring’s rationally connected projective setting.
Limitations
The Lean scope covers automatic integrability; the product corollary uses Höring’s earlier theorem. A distinct compact-Kähler universal-cover result has different assumptions.
Technical verification
The family scope note identifies a Lean formalization of automatic integrability for both summands, and the named solution theorem has a proof body. It excludes the product corollary and the different universal-cover theorem. This is source-reported; no local build was performed.
Formal checking
Lean solution theorem SplitTangent.integrability_main in RationalVariation.lean, compared with the scoped statement
- Checker
- Lean proof checker, as reported by OpenAI's formalization scope note
- Scope
- Integrability of both positive-rank summands on a rationally connected projective manifold
- 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. The manuscript's tangent-box and bracket-tensor explanation is model-authored; no identified human explains the central proof. This is a missing-evidence default.
Correction and publication history
Removes the integrability premise in Höring’s rationally connected projective setting.
Read this published revision