The intersection-triple bound conjecture for closed curves on the pair of pants

Let $M$ be the pair of pants, and let $aB$, $Cb$, and $aC$ be the three curve classes with self-intersection number $1$. For any curve $\alpha$ on $M$, define its intersection triple by

$$t(\alpha)=\left(\operatorname{i}(\alpha,aB),\operatorname{i}(\alpha,Cb),\operatorname{i}(\alpha,aC)\right).$$

The intersection-triple bound conjecture. For any curve $\alpha$ on the pair of pants,

$$\max(t(\alpha))\leq 2\cdot\min(t(\alpha)).$$

Moreover, equality holds if and only if $t(\alpha)$ is a permutation of $(q,q,2q)$, where $q$ is an even positive integer.

This conjecture describes a restriction on the three intersection numbers associated with $1$-equivalence. The source explains the parity condition using the fact that intersection numbers of two deformation classes of curves on the pair of pants are even, but gives no resolution of the asserted bound and equality characterization.