The da Silva Machado-Seade Conjecture
da Silva Machado and Seade conjectured that weighted homogeneous isolated hypersurface singularities are exactly those admitting a logarithmic vector field transverse to the link. True: for a reduced isolated hypersurface germ in with , or and the germ irreducible, the criterion holds.
- Result
- Proved(see note)
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Argument
- Field
- Singularity theory
- Posed by
- da Silva Machado, Jose Seade
- Year posed
- —
- Years open
- —
- Solved
- 2026-06-29
- Model
- Danus (built on Rethlas)
- Vendor
- —
- Collaborators
- Jihao Liu, Xiping Zhang
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
an independent human proof of the same conjecture appeared the same week
What the AI did
The paper states that its main result was obtained by the Danus system, a specialized agent built on Rethlas and described as substantially more capable for fundamental mathematical research. A separate paper published the same week gives a different, human proof of the same conjecture and cites this one as the agent's.
Verification
arXiv preprint; not yet peer-reviewed.