Finite expected angular condition number for identifiable tensors

Let $\mathpzc{A}\in\sigma_{r;n_1,\ldots,n_d}$ be a generically identifiable tensor (GIT) of rank $r$, and let $\kappa_{\mathrm{ang}}(\mathpzc{A})$ denote its angular condition number, which measures sensitivity of the directions of the decomposition vectors. The expectation is taken with respect to the paper's tensor distribution.

Finite expected angular condition number conjecture.

$$\operatorname*{\mathbb{E}}\kappa_{\mathrm{ang}}(\mathpzc{A})<\infty.$$

The paper proves finiteness for rank-two tensors but does not know whether that theorem extends to higher ranks; the conjecture is posed based on experiments.