Problem detail · source-aware
VibeMathed reports this item as candidate. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
For triangular arrays of nodes $a_i^n\in[-1,1]$ let $\mathcal{L}^nf$ be the Lagrange interpolation polynomials of a continuous $f$, with fundamental polynomials $p_i^n$. Is there a choice of nodes such that for every continuous $f$ there is some $x$ where $\limsup_n \sum_i\lvert p_{i}^n(x)\rvert=\infty$ and yet $\mathcal{L}^nf(x) \to f(x)$? Is there a choice with $\limsup_n \sum_i\lvert p_{i}^n(x)\rvert=\infty$ for every $x$, yet for every continuous $f$ some $x$ has $\mathcal{L}^nf(x)\to f(x)$? Both questions are claimed resolved in the affirmative.
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.
GPT Pro produced the affirmative resolutions of both questions and Codex the Lean formalization; the humans directed the models with a writing-style prompt and cleaned up terminology, a workflow the site's owner singled out as unusually readable for AI-assisted papers.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
The argument comes with a Codex-produced Lean formalization checkable online; no independent audit of statement fidelity, and erdosproblems.com still lists the problem open with the claims filed.
Correctness: supported · statement fidelity: audited · peer review: none
Both parts claimed answered affirmatively, with a Lean formalization; two proof claims are filed on erdosproblems.com but the problem is still listed open
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.