The block-and-hole minimal-rigidity conjecture in $\ell_p^3$

Let $p\in[1,\infty]$ with $p\not=2$, and let $\hat{G}$ be a block-and-hole graph with a single block. Assume that the block is minimally rigid in $\ell_p^3$.

Block-and-hole minimal-rigidity conjecture. The following statements are equivalent:

1. $\hat{G}$ is minimally rigid in $\ell_p^3$.
2. $\hat{G}$ is $(3,3)$-tight.

This is proposed as a special case of the conjecture that every $(3,3)$-tight simple graph is minimally rigid in $\ell_p^3$. The statement remains open.