The projection-area conjecture for three-dimensional cube dismantling

Let $[n]^3$ be the $n\times n\times n$ cube, and let $s_3(n)$ denote the minimum possible area covered by the three orthogonal projections onto the faces of a solution to the faces of $[n]^3$. Projection-area conjecture.

$$s_3(n)\ge n^2+6n-4$$

for all $n$. The conjecture, attributed in the source to Hjorth et al., asserts that the solution whose black cubes lie in three orthogonal facial sections achieves the minimum projection area.