Yang Enlin from Peking University and Zhao Yigeng resolved the quasi-projective case of the uniqueness conjecture for characteristic classes proposed by Saito in 2017. Specifically, they demonstrated that the cohomological characteristic classes of étale sheaves can be computed via their characteristic cycles. Cohomological characteristic classes are crucial invariants in geometric ramification theory, yet their geometric computation has remained a long-standing challenge. In 2007, Abbes and Saito addressed the computation for a special class of étale sheaves, but no substantial progress had been achieved since then. To tackle Saito’s conjecture, Yang and his collaborators introduced a novel cohomological class for the first time, which Prof. Saito proposed to name the non-acyclicity class. Building on this class, they established a fibration formula for cohomological characteristic classes and proposed cohomological analogues of three pivotal formulas in geometric ramification theory: the Grothendieck-Ogg-Shafarevich formula, the Milnor formula, and the Bloch conductor formula. Saito’s conjecture emerges as a corollary of the fibration formula and the cohomological analogue of the Milnor formula.