The minimally rigidity-connected stress-independence conjecture

Let $G$ be a minimally $\mathcal{R}_d$-connected graph, meaning that $G$ is $\mathcal{R}_d$-connected and deleting any edge destroys $\mathcal{R}_d$-connectedness.

Minimally $\mathcal{R}_d$-connected stress-independence conjecture. Every minimally $\mathcal{R}_d$-connected graph is $d$-stress-independent.

The statement is known in dimension $d=2$ from the preceding discussion, and the conjecture asks whether it extends to all dimensions.