Quote from a proof on page 9 of this paper:
Let $\hat{w}$ be the $\mathbf{(s[j] \bot 1)st}$ write by $p_i$. (emphasis mine)
$s[j]$ is an integer. My initial guess was that this was typo/misprint and either $+$ or $-$ was intended, but I can't seem to make sense of the proof assuming $\bot$ is either of those, so I'm wondering if there's some perhaps meaning of $x \bot y$ for integers $x,y$ that I'm unaware of?
Looking at page 7 (the algorithm), $\bot$ is used as a symbol for undefined. This is confirmed on page 4 ('...$v=\bot$. That is a read with no write must return the initial value'). This leads me to assume the two occurences of $s[j]\bot 1$ are a typo and meant to say $s[j]+1$.