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An improved upper bound for finite Sidon sets via vector-valued smoothing
Hou, Jianfeng, and Hongbin Zhao, An Improved Upper Bound for Finite Sidon Sets via Vector-Valued Smoothing, arXiv:2607.01169v3 (4 September 2026).
The abstract reports an upper bound of the form F(N) <= sqrt(N) + gamma_0 N^(1/4) + O(1), with gamma_0 < 0.9435, for Sidon subsets of {0,...,N-1}. Several smoothing kernels and their boundary corrections contribute to a joint covering inequality. The authors describe an eight-component candidate with an exact rational certificate. This improves a coefficient while retaining the fourth-root error exponent.
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Source: https://arxiv.org/abs/2607.01169v3.
Bears on. Problem 30: the stated scope above supplies a related result or a limitation of a possible route.