Triple-indexed Gaussian supremum conjecture

Let $p\geq 1$, let $n,m$ be positive integers, let $(a_{ijk})_{i,j\leq n,k\leq m}$ be a triple-indexed real matrix, let $T\subset\mathbb R^m$ be bounded and nonempty, and let $g_i$ and $g'_j$ be independent standard Gaussian random variables. Write $C$ for a universal constant. Triple-indexed Gaussian supremum conjecture. One has

$$\begin{aligned} \mathbb E\sup_{\|x\|_2\leq 1,\,t\in T}\left|\sum_{ijk}a_{ijk}g_ix_jt_k\right|\leq C\Bigg(&\frac{1}{\sqrt p}\mathbb E\sup_{t\in T}\left|\sum_{ijk}a_{ijk}g_ig'_jt_k\right|\\ &+\sup_{\|x\|_2\leq1}\mathbb E\sup_{t\in T}\left|\sum_{ijk}a_{ijk}g_ix_jt_k\right|+\sup_{t\in T}\left(\sum_{ij}\left(\sum_k a_{ijk}t_k\right)^2\right)^{1/2}\\ &+\sqrt p\sup_{\|x\|_2\leq1,\,t\in T}\left(\sum_i\left(\sum_{jk}a_{ij}x_jt_k\right)^2\right)^{1/2}\Bigg). \end{aligned}$$

This is the reformulation of the preceding Banach-space conjecture in finite-dimensional tensor coordinates, with $T$ representing a bounded nonempty subset of the coefficient space. The supplied source does not give evidence that the conjecture has been resolved.