Applegate–Jacobson–Sleator conjecture for misère Sprouts

Let $S_p^-$ denote the misère version of Sprouts starting with $p$ spots. Applegate–Jacobson–Sleator conjecture. The first player has a winning strategy in $S_p^-$ if and only if $p$ is equal to $0$ or $1$ modulo $5$. Josh Purinton's computation disproved this claim at $p=12$, where the first player wins.