OSSS inequality

For a Boolean function of independent coordinates and a randomized decision tree that determines it, the OSSS inequality bounds its variance by a sum of coordinate influences weighted by their revealment probabilities.

Choosing an intermediate radius uniformly and exploring the open cluster meeting that sphere gives a decision tree for a one-arm event. Translation and a union bound control each revealment by a constant times the average of the one-arm probabilities over the possible radii.