The Ramachandra-Natarajan Pairwise Independent Correlation Gap Conjecture
Ramachandra and Natarajan conjectured a bound on the pairwise independent correlation gap in their 2025 Operations Research Letters paper. An explicit counterexample refutes it.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Construction
- Field
- Optimization
- Posed by
- Arjun Ramachandra, Karthik Natarajan
- Year posed
- 2025
- Years open
- 1y
- Solved
- 2026-06-18
- Model
- GPT-5.5 Pro
- Vendor
- OpenAI
- Collaborators
- Arjun Ramachandra, Karthik Natarajan
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The abstract credits the counterexample to GPT-5.5 Pro in its first sentence. The authors add that earlier attempts with free tiers of ChatGPT and Claude made no progress, which is a useful data point on where the capability threshold sat. They are refuting their own conjecture.
Verification
The refutation is an explicit counterexample, so it is a finite check. Short arXiv note, not peer-reviewed.