Mixed Partition Functions and Exponentially Bounded Edge-Connection Rank
Regts and Sevenster conjectured that a complex-valued graph parameter with has exponentially bounded edge-connection rank precisely when it is a mixed partition function. The paper proves it, with the numbers of even and odd colours bounded in terms of the rank bound.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI-assisted
- Method
- Argument
- Field
- Graph Parameters, Tensor Categories
- Posed by
- Guus Regts and Bart Sevenster
- Year posed
- —
- Years open
- —
- Solved
- 2026-07-29
- Model
- Claude Fable 5 + GPT-5.6 Sol Pro
- Vendor
- —
- Collaborators
- William Whistler
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The acknowledgements say only that Claude Fable 5 and GPT-5.6 Sol Pro "were used extensively in the development and preparation of this work". That does not separate mathematical contribution from writing, so the lowest tier applies; read the disclosure rather than the tier.
Verification
No independent check, and the AI disclosure is the vaguest in this batch - a single acknowledgements line covering development and preparation together. Preprint, not refereed.