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We prove the periodicities of the restricted T and Y-systems associated withthe quantum affine algebra of type C_r, F_4, and G_2 at any level. We alsoprove the dilogarithm identities for these Y-systems at any level. Our proof isbased on the tropical Y-systems and the categorification of the cluster algebraassociated with any skew-symmetric matrix by Plamondon.

Periodicities of T and Y-systems, dilogarithm identities, and cluster algebras II: Types C_r, F_4, and G_2