Gamma-positivity conjecture for dissonant canon polynomials

Let $P=[m]$, let $Q$ be a subposet of $P\times[n]$, and let $C^{Q,\operatorname{id}}(x)$ denote the dissonant canon polynomial associated with $Q$. Gamma-positivity conjecture. The polynomial

$$C^{Q,\operatorname{id}}(x)$$

is $\gamma$-positive whenever $P=[m]$. This conjecture arises from the question of which subposets yield $\gamma$-positive dissonant canon polynomials. The claim is known for canon permutations, corresponding to the poset $[m]\times[n]$, and for the poset corresponding to all multiset permutations; a unified interpretation of the $\gamma$-coefficients remains open for general subposets.