New Bounds for Double Covers of the Discrete Box
For , write for the fewest proper sub-boxes covering every point exactly twice. Leader, Miličević and Tan asked whether for all , as Question 4.1 of the PatternBoost paper. The paper gives new bounds on .
- Result
- Proved(see note)
- Status
- Partial result
- AI contribution
- AI co-developed
- Method
- Construction
- Field
- Extremal Combinatorics, Covering Problems
- Posed by
- Leader, Miličević and Tan
- Year posed
- —
- Years open
- —
- Solved
- 2026-07-10
- Model
- Claude
- Vendor
- Anthropic
- Collaborators
- Patrick White
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
Improved bounds rather than a settled question: the asked-for inequality is not established in general.
What the AI did
The author credits large language models used as reasoning engines with producing several of the key ideas, naming the modular refinement of Section 3, the crossing lemma of Section 5 and the constructions of Section 7.
Verification
No independent check. The disclosure is unusually specific about which sections the model produced. Preprint, not refereed.