Erdős Problem #1151
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Attempts
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For closed A ⊆ [−1,1], does some continuous f have A as the cluster set of the Chebyshev–Lagrange interpolation sequence L_n f(x₀)? We first shipped this as an unflagged find; it wasn't. Przemek Chojecki posted the resolution to the erdosproblems.com comment thread on 30 April, Nat Sothanaphan confirmed it the same day, and Allen Hart announced a Lean formalization in early May, also confirmed. The top-level tracker badge (OPEN, 0 claimed proofs) just hadn't caught up — we mistook a stale badge for an unflagged result because our first pass never loaded the actual comment thread. Our contribution is a genuine one, just smaller than we first framed it: an independent from-scratch Lean rebuild, on our own compute, as a second confirmation.
CLOSED