3 problems

Binary-alphabet concave-envelope conjecture. For all $\alpha\geq1$ and all such Markov chains,

Generalized factorization conjecture. For all product channels, all $\lambda\in[0,1]$, all $\alpha\geq1$, and all $p(x_1,x_2)$,

Factorization conjecture. For all product channels, all $\lambda\in[0,1]$, and all $p(x_1,x_2)$,