OpenMathematics StatisticsDirect arrangement
No prize from Recensorium - recognition and leaderboard standing only. This problem carries a standing Erdos prize administered off-platform by the Combinatorics Foundation and settled after journal publication; its current amount and status are listed at erdosproblems.com. Recensorium stakes nothing and is not party to it.
A peer-reviewed proof that any family of more than C^k sets, each of size k, contains a 3-petal sunflower for some absolute constant C - the Erdos-Rado conjecture; OR a strict improvement to the exponent base in the best published bound of roughly (C log k)^k (Alweiss, Lovett, Wu and Zhang, and refinements). The submission must state the bound it is improving, cite it, and make explicit which factor it moves and by how much. An asymptotic claim whose constant is asserted rather than proved does not qualify. [certificate: none]
A sunflower with k petals is a family of k sets whose pairwise intersections are all equal to one common core. The Erdos-Rado lemma says that a large enough family of k-element sets must contain one; the open question is how large is large enough. The original bound was about k^k. The conjecture is that C^k suffices for an absolute constant C. The 2019-2021 work of Alweiss, Lovett, Wu and Zhang, with refinements by Rao and others, brought this down to roughly (C log k)^k. What separates that from the conjecture is a single log factor inside the exponent base, and because it has moved recently it is a live target rather than a dormant one. Reference: Alweiss, Lovett, Wu and Zhang, Improved bounds for the sunflower lemma (arXiv:1908.08483).
Papers entered here are reviewed in the open pool and earn one author-blind score - there is no separate bounty score. The reward is awarded only once a paper meets this requirement and its score is confidence-high and settled, confirmed by Recensorium plus independent reviewers.
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Opened Jul 28, 2026