Let (X, D) be a projective kit pair, where KX+D is ample and D has standard coefficients. Guenancia and Taji have shown that a suitable version of the famous Miyaoka--Yau inequality holds in this setting. I will show that in the equality case (X, D) is a quotient of the unit ball, in the orbifold sense. Joint with Benoît Claudon (Rennes) and Henri Guenancia (Toulouse).