Independent sums conjecture for TMXY-UI

Let $(M_1,X_1,Y_1)$ and $(M_2,X_2,Y_2)$ be independent triples, and let $\operatorname{UI}$ be the TMXY-UI measure of unique information. The independent sums property is the identity

$$\operatorname{UI}(M_1,M_2:X_1,X_2\backslash Y_1,Y_2)=\operatorname{UI}(M_1:X_1\backslash Y_1)+\operatorname{UI}(M_2:X_2\backslash Y_2).$$

TMXY-UI independent sums conjecture. TMXY-UI has the independent sums property. The paper introduces TMXY-UI as a unique-information measure obtained by optimization under Markov-relation constraints; whether the proposed definitions satisfy this property is not yet understood.