Twelve Common Flex Lines in a General Pencil of Cubics
Does a general pencil of plane cubics over have exactly common flex lines? Ciliberto, Miranda and Roé asked this in Remark 5.3 of their paper; the answer is yes.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Argument
- Field
- Algebraic Geometry, Plane Curves
- Posed by
- Ciro Ciliberto, Rick Miranda, Joaquim Roé
- Year posed
- 2026
- Years open
- 0y
- Solved
- 2026-07-29
- Model
- ChatGPT 5.5 Pro + Danus
- Vendor
- —
- Collaborators
- Jihao Liu, Yanze Wang
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The main result was obtained with ChatGPT 5.5 Pro and the Danus system, an agent built on Rethlas; human verification and polishing came afterwards. The authors caution that AI limitations mean related literature may have been missed.
Verification
No independent check. The authors verified and polished the AI-produced argument themselves and explicitly flag that relevant references may have been missed. Preprint, not refereed.
Source
Submitted by Curator34