A published paper or arXiv preprint answers the main question of Erdős Problem #1133 (theorem erdos_1133 in formal-conjectures) in full (proof, disproof, or the exact value asked for) with no hypotheses beyond the problem's own.

The problem, as stated in formal-conjectures (Apache 2.0):

Let C>0. There exists \epsilon>0 such that if n is sufficiently large the following holds. For any x_1,\ldots,x_n\in [-1,1] there exist y_1,\ldots,y_n\in [-1,1] such that, if P is a polynomial of degree m<(1+\epsilon)n with P(x_i)=y_i for at least (1-\epsilon)n many 1\leq i\leq n, then \max_{x\in [-1,1]}\lvert P(x)\rvert >C. Yang [Ya26, Theorem 2.1] proved this, including repeated nodes, by taking \rho=0.

References formal-conjectures lists for this problem (a starting point, not evidence):

• [Er67] Erdős, P., Problems and results on the convergence and divergence properties of the Lagrange interpolation polynomials and some extremal problems. Mathematica (Cluj) (1967), 65-73.
• [Ya26] Yang, J.-Q., Erdős's Robust Polynomial Interpolation Problem: the Optimal Exponential Scale. arXiv:2609.14769 (2026).