Sunflower-free base-size exponential bound conjecture

For a sunflower-free $k$-uniform family, its base elements are the elements contained in at least one set of the family. Sunflower-free base-size exponential bound conjecture. The maximum number of base elements in a sunflower-free $k$-uniform family is at most $c^k$ for a suitable constant $c>0$. This conjecture was posed in the first version of the paper and is presented as a separate weakening related to the Erdős–Rado sunflower problem; the paper does not report a resolution.