Completeness and discreteness conjecture for the d-categorical nerve of a pasting shape

Let $I$ be a $d$-dimensional pasting shape. The notation $I$ denotes the $d$-categorical nerve of $I$, obtained by applying the reflector from $d$-uple categories to $d$-fold Segal spaces to the nerve of $I$.

Nerve completeness conjecture. The $d$-categorical nerve $I$ is a complete and discrete $d$-fold Segal space.

This is proposed as the expected computation of the reflector defining the $d$-categorical nerve. Establishing it would give an explicit description of the coherence data for maps from a pasting-shape nerve into a $d$-fold Segal space and would yield a pasting theorem for $(\infty,d)$-categories.