The Generalized Vanishing Conjecture
Zhao's Generalized Vanishing Conjecture asks whether, for a differential operator with constant coefficients, for all large forces for all large . Refuted by an explicit five-variable counterexample.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI-assisted
- Method
- Construction
- Field
- Commutative algebra; differential operators
- Posed by
- Wenhua Zhao
- Year posed
- 2007
- Years open
- 19y
- Solved
- 2026-08-07
- Model
- GPT-5.6 Sol
- Vendor
- OpenAI
- Collaborators
- Alexander Dvorsky
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
Used "as an interactive research assistant": the paper credits it with testing the homogenized five-variable construction, generating computational verification code and locating relevant literature, with all computations and references independently verified afterwards. The construction itself is the author's.
Verification
A preprint days old with no independent review. The verification is described as entirely algebraic, needing no general implication from the Mathieu conjecture, so the counterexample can be checked directly.