Friedgut–Kahn–Kalai–Keller antipodal correlation conjecture

Let $[n]=\{1,\ldots,n\}$ and let $f,g:\{0,1\}^n\to\{0,1\}$ be increasing Boolean functions. A Boolean function $g$ is antipodal if

$$g(x)=1-g(1-x)$$

for every $x\in\{0,1\}^n$, where $1-x$ is the coordinatewise complement. For a Boolean function $f$, define

$$\operatorname{Inf}_i[f]=\mathbb{P}[f(x)\neq f(x\oplus e_i)].$$

Friedgut–Kahn–Kalai–Keller antipodal correlation conjecture. For every increasing $f,g:\{0,1\}^n\to\{0,1\}$, if $g$ is antipodal, then

$$\operatorname{Cov}(f,g)\geq \frac14\min_{i\in[n]}\operatorname{Inf}_i[f].$$

This is presented as an equivalent correlation formulation of Chvátal's conjecture. The supplied text does not state a resolution of either formulation.