9 problems

Let $P_{MXY}$ be the joint distribution of random vectors $M$, $X$, and $Y$. Define the … -PID is also Gaussian, so the $_G$-PID is identical to the … -PID rather than only the sta…

Let $P_{MXY}$ be an arbitrary joint distribution, and let $UI^I(M: X \setminus Y)$ denote the unique-information atom of the $I$-PID. The relation $Y \succcurlyeq_M X$ denotes that…

Let $k$ denote the number of elements in a discrete, maximum-entropy system, and consider its redundant and synergistic information structures alongside its unique terms. Asymptoti…

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-r…

Fourier–PID conjecture. There exists a mapping

Secret-sharing intuition conjecture. The intuitive assignment of values to the shared-information nodes in the partial information lattice for perfect secret sharing schemes should…

Separate-lattice monotonicity conjecture. Both of these lattices would be monotonic, and the non-monotonicity of the $I_\text{ccs}$ partial information decomposition would arise as…

Pairwise maximum-entropy conjecture. The inequality holds when using the pairwise maximum entropy solution $\hat{P}$, with no higher-order interactions.

Continuity and differentiability conjecture. $I_\text{ccs}$ is continuous in the underlying probability distribution, but is not differentiable because of the thresholding with $0$…