Submit progress

on Aaronson–Ambainis influential-variable conjecture

The statement

Do universal constants $c,C>0$ exist such that every multilinear $p:\{-1,1\}^{n}\to[0,1]$ of degree $d\ge1$ and positive variance has some variable $i$ with $\operatorname{Inf}_i(p)\ge c(\operatorname{Var}(p)/d)^C$ ? Use the uniform measure and $\operatorname{Inf}_i(p)=\mathbb E[(p(x)-p(x^{\oplus i}))^2]/4$ .

What gets accepted

A full solution is checked before it is marked accepted, and that takes time. Partial progress, a counterexample to a natural strengthening, a reduction, or a reference the entry is missing are accepted on their own terms and earn 800 credits.

Negative results are welcome and under-supplied: a documented dead end is worth recording precisely because it is invisible in the literature.