A 
-dimensional
framework is a pair 
where 
is a graph with vertex set 
and edge set 
and 
is a map that assigns a point in 
to each vertex of 
. The length of an edge 
in 
is the Euclidean distance between 
and 
. Call 
a realization of 
in 
. The framework is said to be generic if the set of the coordinates
of its points is algebraically independent over 
, and is said to be globally rigid if every other realization
of 
in 
in which corresponding edges have the same length is congruent to 
, i.e., the graph 
and its edge lengths in 
uniquely determine the pairwise distances of all vertices
in 
.
After defining the above terminology, 
is generically globally rigid in 
if every (equivalently, if some) generic realization of
in 
is globally rigid (Garamvölgyi et al. 2021).
If 
is globally rigid in 
on 
vertices, then 
is fully reconstructible
in 
(Garamvölgyi et al. 2021).
is Fully Reconstructible in 
." Submitted to Disc. Math., 2022.Garamvölgyi,
D.; Gortler, S. J.; and Jordán, J. "Globally Rigid Graphs Are Fully
Reconstructible." 10 May 2021.