Peak–valley antichain statistic conjecture for odd uniform self-dual fences

Let $a$ be a positive integer, let $t$ be odd, and let $F=\breve{F}(a^t)$ be the uniform self-dual fence with $t$ segments. For each peak $p$ and valley $v$ of $F$, let $\chi_p$ and $\chi_v$ be their antichain indicator statistics. Peak–valley conjecture. The statistic

$$\sum_{p:\text{ peak}}\chi_p-\sum_{v:\text{ valley}}\chi_v$$

is 0-mesic under rowmotion.

This is presented as an equivalent formulation of the order ideal cardinality conjecture above.