The non-viability criterion for the $(110)$-space

Let $E_{110}$ be a subspace with associated mixed-kernel dimensions $\kappa_m$ and $\kappa_m'$ for the $(210)$- and $(120)$-tests, respectively.

Non-viability criterion. If

$$\kappa_m=\kappa_m'=0,$$

then $E_{110}$ is not viable.

This criterion supplies a sufficient condition for ruling out viability in the tensor-border-rank analysis. The supplied text does not state whether the criterion is intended as a conjecture or whether any further cases remain open.