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Thresholds and spread in set systems of bounded VC-dimension
Shangguan, Chong, Thresholds and spread in set systems of bounded VC-dimension, arXiv:2609.30263v1 (24 September 2026).
The abstract reports an absolute-constant comparison between the threshold and expectation threshold with a factor log(d+1) for VC dimension at most d. A spread-measure estimate gives a sunflower consequence: an n-uniform family of VC dimension at most d with more than (C r log(d+1))^n members contains an r-sunflower. The restriction on VC dimension is part of the statement; this does not establish the unrestricted sunflower conjecture.
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Source: https://arxiv.org/abs/2609.30263v1.
Bears on. Problem 20: the stated scope above supplies a related result or a limitation of a possible route.