Associativity conjecture for monoidal Jantzen filtrations

Let $K(\mathscr{C})_t=K(\mathscr{C})\otimes_{\mathbb{Z}}\mathbb{Z}[t^{\pm 1/2}]$ be the $t$-deformed Grothendieck module, with basis elements $[M(\boldsymbol{d})]_t$ obtained by decategorifying the monoidal Jantzen filtrations. For a skew-symmetric bilinear map $\gamma\colon\mathbb{N}^{\oplus J}\times\mathbb{N}^{\oplus J}\to\frac12\mathbb{Z}$, define

$$[M(\boldsymbol{d})]_t*[M(\boldsymbol{d}')]_t=t^{\gamma(\boldsymbol{d},\boldsymbol{d}')}[M(\boldsymbol{d})\star M(\boldsymbol{d}')]_t.$$

Associativity conjecture. The $\mathbb{Z}[t^{\pm1/2}]$-module $K(\mathscr{C})_t$ with this operation is a $\mathbb{Z}[t^{\pm1/2}]$-algebra, and hence gives a not necessarily commutative $t$-deformation of the Grothendieck ring $K(\mathscr{C})$. The conjecture asserts associativity of the operation constructed from the filtrations; the source gives no resolution.