The unique-shape conjecture for $(\tmo,n)$-prismatic polyominoes

Let a (\begin{tikzpicture}[scale=.25] \draw (1,0)--++(.5,0)--++(0,.5)--++(-1.5,0)--++(0,-.5)--++(1,0)--++(0,1)--++(-.5,0)--++(0,-1); \end{tikzpicture},n)-prismatic polyomino be a prismatic polyomino formed using the tile represented by the source's diagram and parameter $n$, and let a ziggurat of height $h$ denote the corresponding stepped polyomino shape of height $h$. Unique-shape conjecture. The unique shape of (\begin{tikzpicture}[scale=.25] \draw (1,0)--++(.5,0)--++(0,.5)--++(-1.5,0)--++(0,-.5)--++(1,0)--++(0,1)--++(-.5,0)--++(0,-1); \end{tikzpicture},n)-prismatic polyominoes is the ziggurat of height $n^2+1$. The preceding theorem gives evidence for this shape, but the conjecture remains unproved because a satisfactory coloring of the ziggurat has not been established.