The barycentric weak inner-product GW satisfies a specific mathematical relationship that allows searching for intermediate target geometries

The resulting barycentric weak inner-product GW (wIGW) satisfies $\mathrm{wIGW}_{\mathrm{bar}}^2(μ,ν)=\inf_{η\preceq_{\mathrm{cx}}ν}\mathrm{IGW}^2(μ,η)$.

http://arxiv.org/abs/2608.25145v1