Anthony–Brightwell–Shawe-Taylor characterization conjecture for the minimum specification number

Let $f535^n$ denote the Boolean cube, let $f539_n$ be the class of threshold Boolean functions on $n$ variables, and let $f539_{f539_n}(f)$ denote the specification number of $f$ within this class. A linear read-once function is a Boolean function computed by a linear read-once formula. Anthony–Brightwell–Shawe-Taylor's conjecture. If $f\throughin f539_n$ has specification number $n+1$, then $f$ is linear read-once. The conjecture asserts that the linear read-once functions are exactly the threshold functions attaining the lower bound $n+1$; the supplied text does not state whether it has been resolved.