Erdős Problem #662
Erdős problem #662 · erdosproblems.com/662
Among sufficiently large one-separated planar point sets, does the triangular lattice maximize the number of distances below each threshold? Explicit rational oblique lattices beat the triangular lattice under several closed- and strict-shell readings.
- Result
- Disproved(see note)
- Status
- Variant only
- AI contribution
- AI-discovered
- Method
- Construction
- Field
- Discrete Geometry
- 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
natural readings of the ambiguous historical statement are disproved
What the AI did
Produced by the GPT-5.6 starships pipeline with Claude Fable 5 as reviewer.
Verification
Finite certificates and variant statements Lean-checked; community status pending.