Let (X,d) be a finite metric space with elements Pi, i=1,…,n and with distances dij≔d(Pi,Pj) for i,j=1,…,n. The “Gromov product” Δijk, is defined as [Formula presented]. (X,d) is called Δ-generic, if, for each fixed i, the set of Gromov products Δijk has a unique smallest element, Δijiki. The Gromov product structure on a Δ-generic finite metric space (X,d) is the map that assigns the edge Ejiki to Pi. A finite metric space is called “quadrangle generic”, if for all 4-point subsets {Pi,Pj,Pk,Pl}, ...