Period-six conjecture for misère Sprouts

Let $S_p^-$ denote the misère version of Sprouts starting with $p$ spots. Period-six conjecture for misère Sprouts. The first player has a winning strategy in $S_p^-$ if and only if $p$ is equal to $0$, $4$ or $5$ modulo $6$, except if $p=1$ or $4$. The paper presents this conjecture after listing computed values through $S_{17}^-$. Its general validity is not established in the supplied text.