Exact maximal average sensitivity of nested canalizing functions

Let $f$ be a Boolean nested canalizing function in $n$ variables. Write its layer parameters as $r,k_1,\ldots,k_r$, where $r$ is the layer number, and let $s^f$ denote its average sensitivity.

Exact maximal-average-sensitivity conjecture. The maximal value of $s^f$ is

$$s^f=\frac{4}{3}-\frac{3+(-1)^n}{3\times 2^n}.$$

It is attained when $r=n-1$, $k_1=\cdots=k_{n-2}=1$, and $k_{n-1}=2$. When $n$ is even, it is also attained for $n\geq 4$ with $r=n-2$, $k_1=\cdots=k_{n-3}=1$, $k_{n-2}=3$, or for $n\geq 6$ with $r=\frac n2$, $k_1=1$, $k_2=\cdots=k_{\frac n2-1}=2$, and $k_{\frac n2}=3$.

The claim is based on numerical calculations, an explicit average-sensitivity formula, and several evaluated parameter families. It refines the broader conjecture that maximal layer number gives maximal average sensitivity; its general optimality remains open.