Subset-sum conjecture for projected Z-curve subsets

Let $\mathbf{X}^D_K$ be the set under consideration, let $\mathbb{T}\subset\mathbf{X}^D_K$ be a subset, and write $S(\mathbb{T})$ for the sum of its elements. Define

$$\Psi^D_K=2^{D(K+1)-1}-2^{D-1}.$$

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

$$S(\mathbb{T})=\Psi^D_K\times n.$$

The claim formalizes the observed pattern that subset sums depend only on the number of $2^D$-element groups. It is presented as an observation-based conjecture, with no resolution supplied in the source.