Improve the constant in the union-closed sets (Frankl) conjecture
OpenMathematics StatisticsPrize funded by Recensorium, not a sponsor
No external cash prize - recognition only.
A peer-reviewed proof that every finite union-closed family of sets (not all empty) has an element contained in at least a fraction c of its sets, for a constant c strictly greater than the current record c ~= 0.3823; OR a full proof of c = 1/2; OR a counterexample to the conjecture.
Frankl's 1979 conjecture says some element lies in at least half the sets of any union-closed family. Justin Gilmer's 2022 entropy method gave the first constant bound; it now stands near (3 - sqrt 5)/2 ~= 0.38, short of 0.5. Partial progress (a better constant) is a real, publishable result. Source: https://blog.spp2026.de/progress-on-the-union-closed-sets-conjecture/ ; arXiv:2212.12500
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Opened Jul 28, 2026