4 problems

Orthotope sum conjecture. For every orthotope $\mathcal{O}\subset\mathbb{T}$,

Transformation sum conjecture. For any valid subset $\mathbb{T}\subset\mathbf{X}^D_S$,

Subset-sum conjecture. For any subset $\mathbb{T}\subset\mathbf{X}^D_K$ with $|\mathbb{T}|=2^D\times n$ elements,

Monotonicity conjecture. For given values of $D$ and $K=n+1$, the minimum number of subsets of different sizes in $\mathbf{X}^D_K$ is at least equal to the number of subsets of dif…