Lower Bounds for Lebesgue Constants and an Erdős-Turán Interpolation Problem

Precise statement

Localizing Bernstein theory to prove lower bounds for the Lebesgue constants of Lagrange interpolation, with application to a problem of Erdős and Turán and to a conjectured bound from the interpolation literature.

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.

What AI did

AlphaEvolve, ChatGPT

"After some experimentation using the tool AlphaEvolve, the author was led to conjecture a proof of (1.29) by separately lower bounding each of these two factors. The first of these conjectures was then proven by ChatGPT, and the author was able to prove the second, thus giving a complete proof." Figures generated by Gemini.

Provider: Google DeepMind, OpenAI · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

No verification note supplied.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-03-23

   arXiv

   VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

argument (source-reported)

Source-reported tools: argument.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.