Carlson's Associated-Prime Depth Conjecture
Is the depth of the mod-$p$ cohomology ring of every finite group realized as the dimension of one of its associated primes? For $G = \operatorname{SmallGroup}(128, 859)$ over $\overline{\mathbb{F}}_2$ the ring has depth $2$ while every associated-prime quotient has dimension at least $3$.
Exact FrontierDelta
Scope and record
Occurred: Jul 26, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-discovered. Imported under CC BY 4.0.
Canonical aliases: Carlson's Associated-Prime Depth Conjecture · Carlson depth
Confidence: Not scored
Registry verification: unreviewed · preprint · resolved
Attribution
VibeMathed
registry · event recorded by
TARS agent system
model · ai model contributor
Xinan Dai
human · human collaborator
Wenhao Deng
human · human collaborator
Yingdong Shi
human · human collaborator
Tailin Wu
human · human collaborator
Yuchen Yang
human · human collaborator
Lineage and corrections
This event attributed to Xinan Dai
This event attributed to Wenhao Deng
This event attributed to Yingdong Shi
This event attributed to Tailin Wu
This event attributed to Yuchen Yang
This event attributed to TARS agent system