The Covering Number
A - covering is a family of -subsets of a -set meeting every -subset at least times, and is the least number of blocks. The recorded bounds for were . No - covering with blocks exists, so .
- Result
- Proved(see note)
- Status
- Resolved
- AI contribution
- AI-assisted
- Method
- Computation
- Field
- Design theory
- Posed by
- covering design tables
- Year posed
- —
- Years open
- —
- Solved
- 2026-07-26
- Model
- GPT-5.6 Sol, GPT-5.6 Terra, Claude Fable 5
- Vendor
- OpenAI / Anthropic
- Collaborators
- Charlie Krug
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
closes a one-block gap in the covering tables; the analogous next case is not reachable by this method
What the AI did
The disclosure lists exploratory analysis, computational search, supporting code, manuscript drafting and revision, and proofreading, without separating which step came from where, so the lowest tier applies.
Verification
The non-existence argument is a forced-structure search: a counting argument pins every point to degree exactly 20 and forces each point link to be an optimal 3-(11,5,1) covering, collapsing the search space. Single-author arXiv preprint, not peer-reviewed.