The degree conjecture for the associated Boolean function of odd-variable APN functions

Let $F$ be a quadratic APN function of $n$ variables, where $n$ is odd, and let $\varphi_F:\mathbb{F}_2^n\to\mathbb{F}_2$ be the associated Boolean function in the representation of $\gamma_F$.

Degree conjecture. Then

$$\deg(\varphi_F)<n,$$

or, equivalently, $\operatorname{wt}(\varphi_F)$ is even.

The case of odd $n$ is stated to remain open. The conjecture is supported by computational experiments for all known quadratic APN functions in at most 11 variables.