Strassen's asymptotic rank conjecture for tight concise tensors

Let $\mathbb{k}$ be the underlying field, and let $T\in\mathbb{k}^a\otimes\mathbb{k}^b\otimes\mathbb{k}^c$ be a tensor that is tight and concise. Here, concise means that the flattenings of $T$ are injective, and tight means that the support of $T$ satisfies an additive conservation law. Strassen's asymptotic rank conjecture.

$$\lim_{q\to\infty}\operatorname{rank}(T^{\otimes q})^{\frac{1}{q}}=\max\{a,b,c\}.$$

The conjecture predicts that the asymptotic rank of every tight concise tensor is determined solely by its format, despite the typically larger generic border rank of such tensors. It concerns the long-term complexity of tensor powers and is connected to algebraic complexity theory, including matrix multiplication; its resolution status is not established in the supplied source.