What was already known
The Auslander–Reiten conjecture predicted projectivity from these Ext vanishings. Earlier proofs covered classes such as complete intersections, some normal domains, and rings satisfying Auslander’s condition.
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
Disproves the unrestricted Auslander–Reiten conjecture for Artin algebras and its Gorenstein-projective variant.
Limitations
The selected construction is over the stated characteristic-two rational-function field. A separate companion addresses Tachikawa’s conjecture.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned OpenAI Lean scope note identifies this selected claim.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- A finite-dimensional algebra over F₂(q,H₁,H₂) has a finite-dimensional nonprojective Gorenstein-projective module Z with Extⁱ(Z,Z)=Extⁱ(Z,Λ)=0 for every i>0.
- 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 scoped checking review for non-notifying local inclusion.
Read this published revision