Kontsevich's canonical semi-orthogonal decomposition conjecture

Let $X$ be a smooth projective variety and let $D^b\operatorname{Coh}(X)$ denote its derived category of coherent sheaves. A semi-orthogonal decomposition is a decomposition of this category into ordered admissible components, and mutations are the standard operations relating such decompositions. Kontsevich's conjecture. There should exist canonical semi-orthogonal decompositions, well-defined up to mutations, which are compatible with geometric operations. Such decompositions are intended to provide canonical categorical pieces compatible with the minimal model program and potentially yield obstructions to rationality. The source presents this as a conjectural principle and does not state a general resolution.