The real symmetric substitution conjecture

Let $I$ be an index set, let $d$ be a positive integer, let $\mathcal{C}\in(\mathbb{R}^{I})^{\otimes d}$ be a symmetric tensor, and let $\mathcal{M}\subset(\mathbb{R}^{I})^{\otimes(d-1)}$ be a finite set of symmetric tensors. The real symmetric substitution conjecture.

$$\operatorname{srk}\operatorname{SAdj}(\mathcal{C},\mathcal{M})\geq\min\operatorname{srk}(\mathcal{C}\operatorname{mod}\mathcal{M})+d\dim\operatorname{Span}\mathcal{M}.$$

Equality holds if $\mathcal{M}$ consists of decomposable tensors. This is the real symmetric analogue of a conjecture of Shitov and concerns lower bounds for the symmetric rank of tensors constructed by symmetric adjunction; the supplied text does not establish whether the conjecture is resolved.