Erdős Problem #959
Erdős problem #959 · erdosproblems.com/959
How large can the difference between the largest and second-largest distance multiplicities be among planar points?
- Result
- Proved(see note)
- Status
- Partial result
- AI contribution
- AI-discovered
- Method
- Argument
- Field
- Distinct Distances
- Posed by
- —
- Year posed
- —
- Years open
- —
- Solved
- 2026-07-13
- Model
- GPT-5.6 starships (Claude Fable 5 reviewer)
- Vendor
- OpenAI / Anthropic
- Collaborators
- —
- Verification
- Lean-verified
- Publication
- Announced
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
superlinear lower bound M(n) ≥ n^{1 + 1/(50000 log log n)}, improving Ω(n log n); the exact order remains open
What the AI did
Produced by the GPT-5.6 starships pipeline with Claude Fable 5 as reviewer.
Verification
Lean-checked construction; community status pending.
There is an even stronger bound, M(n)>n1+c, see erdos problem website