“…It is stronger than the K-polystability which is equivalent to the existence of Kähler-Einstein metric [6,7,8,32]. Birational superrigidity and K-stability are unexpectedtly related according to Odaka-Okada and Stibitz-Zhuang [23,30], and it is conjectured by Kim-Okada-Won [18] that every birationally superrigid Fano manifold is K-stable. Both the notions are intensively studied in the case of smooth Fano complete intersections of index 1: birational superrigidity by Iskovskih-Manin, Pukhlikov, Cheltsov, de Fernex-Ein-Mustat ¸ȃ, de Fernex, Suzuki, and Zhuang [17,24,25,26,28,29,2,12,9,10,31,34] (see also the note [20] written by Kollár), and K-stability by Fujita and Zhuang [14,34].…”