The connectivity conjecture for globally rigid k-chains

Let $d$ be a positive integer, and let a $k$-chain be a graph of the type defined in the paper, with vertices embedded in $\mathbb{R}^d$. A graph is generically globally rigid if a generic realization is uniquely determined up to Euclidean congruence by its edge lengths.

Connectivity conjecture. Any $(d+1)$-connected $k$-chain in $\mathbb{R}^d$ with more than $\binom{d+2}{2}$ vertices is generically globally rigid.

The paper presents this as an experimentally supported conjecture about the unexplored range above $\binom{d+2}{2}$ vertices; its resolution is not supplied here.