We focus on the uniqueness for the Gross-Pitaevskii hierarchy. Away from being the toughest part for the derivation of NLS from quantum many-body dynamics, it hints a fresh idea of proving new NLS results. Specificly, we consider the cubic and quintic NLS under the $\mathbb{R}^{d}$ and $\mathbb{T}^{d}$ energy-supercritical setting. Via a newly developed unified scheme, we prove the unconditional uniqueness for solutions to NLS at critical regularity for all dimensions. One application of our theorem is to prove that blowup solutions are the only possible $C([0,T);\dot{H}^{s_{c}})$ solutions if exist in these domains. This is joint work with Xuwen Chen and Zhifei Zhang.