Problem detail · source-aware
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Ramachandra and Natarajan conjectured a bound on the pairwise independent correlation gap in their 2025 Operations Research Letters paper. An explicit counterexample refutes it.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
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.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
The refutation is an explicit counterexample, so it is a finite check. Short arXiv note, not peer-reviewed. A Lean 4 / Mathlib formalization of the counterexample was contributed in August 2026 by its author, produced with Codex. Curator source audit: all 579 lines read, with no sorry, admit, native_decide, unsafe declaration, user-declared axiom, implemented_by or partial def anywhere; finite checks go through kernel decide and rational identities through norm_num, and Mathlib is pinned to an exact revision on toolchain v4.33.0-rc2. The curator has not compiled it, and it is the work of the same person who reported the result, so it is not third-party corroboration. What the formalization does and does not settle is worth stating exactly. Its final theorem is a seven-part conjunction certifying the witness and its bounds: the three-atom distribution attains the target marginals with expected coverage 4, no distribution exceeds 4, the product distribution is pairwise feasible, every pairwise-feasible distribution is bounded by $479/160$, and $4 \div (479/160) = 640/479 > 4/3$. Both bounds are universally quantified rather than spot-checked. What the file never states is the Ramachandra-Natarajan conjecture itself, so the step from this instance to the conjecture being refuted stays informal and rests on the conjectured bound really being $4/3$. That is the difference between a kernel-checked artifact and an audited claim, and why this sits on the unaudited Lean rung.
Correctness: supported · statement fidelity: unaudited · peer review: none
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.