The Macdonald version of Stanley's positivity conjecture

Let ${\mathfrak J}^{(\alpha,\gamma)}_\lambda$ be the normalized Macdonald polynomial

$${\mathfrak J}^{(\alpha,\gamma)}_\lambda:=\left.\frac{J^{(q,t)}_\lambda}{(1-t)^{|\lambda|}}\right|_{q=1+\gamma\alpha,\,t=1+\gamma},$$

where $\alpha=\frac{1-q}{1-t}$ and $\gamma=t-1$. Let $\langle-,-\rangle_{q,t}$ denote the Macdonald scalar product.

Macdonald version of Stanley's conjecture. For any partitions $\lambda,\mu,\nu$, the quantity

$$\langle{\mathfrak J}^{(\alpha,\gamma)}_\lambda{\mathfrak J}^{(\alpha,\gamma)}_\mu,{\mathfrak J}^{(\alpha,\gamma)}_\nu\rangle_{q,t}$$

is a polynomial in $\alpha$ and $\gamma$ with non-negative integer coefficients. This is proposed as a Macdonald deformation of Stanley's Jack-case conjecture, and the supplied text gives no resolution evidence.