Carlson's Associated-Prime Depth Conjecture
Is the depth of the mod- cohomology ring of every finite group realized as the dimension of one of its associated primes? For over the ring has depth while every associated-prime quotient has dimension at least .
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Construction
- Field
- Group cohomology
- Posed by
- Jon F. Carlson
- Year posed
- 1995
- Years open
- 31y
- Solved
- 2026-07-26
- Model
- TARS agent system
- Vendor
- —
- Collaborators
- Xinan Dai, Wenhao Deng, Yingdong Shi, Tailin Wu, Yuchen Yang
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The candidate group was found by the TARS agent system (foundation model not disclosed); the counterexample is certified by exact GAP/Singular computations audited by the human authors.
Verification
Exact computational certificate (verifier and certificates ship with the paper, checkable with the Python standard library alone) plus a human proof audit. Not yet peer-reviewed.
Source
arXiv:2607.23732 - An exact counterexample to Carlson's associated-prime depth conjecture