Boundary rigidity of CAT(0) cube complexes (Q6615759)

The authors prove that finite CAT(0) cube complexes are \textit{boundary rigid}, meaning that any finite CAT(0) cube complex \(X\) is determined up to isomorphism by the distances (in the 1-skeleton) between the vertices of its boundary. Here the \textit{boundary} of a finite CAT(0) cube complex is the subcomplex consisting of all cubes lying in a unique larger cube, together with their faces. (For example, the boundary of a finite tree is its set of leaves.) This result was conjectured by \textit{J. Haslegrave} et al. [``Boundary rigidity of 3D CAT(0) cube complexes'', Preprint, \url{arXiv:2309.04385}].