Four atom conjecture

Statement
The four atom conjecture is a conjecture in information theory/entropy that has a purely group-theoretic formulation due to Dougherty, Freiling, and Zeger. The formulation includes a certain number $$u$$, whose decimal approximation is $$0.089373$$, and makes the claim that for every finite group, and every 4-tuple of subgroups of that finite group, the Ingleton score for this tuple is less than or equal to the number $$u$$.