Problem detail · source-aware
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Let $\mathcal{L}^nf$ be the Lagrange interpolation polynomials of a continuous $f$ on the Chebyshev nodes. Prove that, for any closed $A\subseteq [-1,1]$, there exists a continuous function $f$ such that $A$ is the set of limit points of $\mathcal{L}^nf(x)$.
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The solution was obtained with GPT-5.5 Pro using an explicit primitive-row decomposition of the Chebyshev-node measures; Theorem 1.1(a), the main contribution, was subsequently formalized largely autonomously by ChatGPT and Codex.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
Theorem 1.1(a), the main part of the contribution, is formalized in Lean and the formalization was confirmed correct on the forum; part (b) is unformalized because it depends on an Erdős result absent from mathlib. erdosproblems.com still lists the problem open.
Correctness: supported · statement fidelity: audited · peer review: none
An elementary solution via a primitive-row decomposition of the Chebyshev-node measures; the main theorem is formalized in Lean, but erdosproblems.com still lists the problem open
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.