an>, p.3), where <span class="math display">\[\begin{multline*}
\mathcal{D}=\Biggl\{\mathbf{A}\in [0, \infty)^{d\times d}:
\boldsymbol{x}^\top\!\!\mathbf{A}\boldsymbol{x} &lt;0, \ \forall \
\boldsymbol{x} \in \mathbb{R}^{d}
\setminus\{\boldsymbol{0}\} \\ \qquad
\text{ with } \sum_{i=1}^d x_i=0, a_{ij}=a_{ji}, a_{ii}=0 \ \forall \ i,
j \in \{1,\ldots, d\}\Biggr\}
\end{multline*}\]</span> denotes the set of symmetric conditionally
negative definite matrices with zero diagonal entries. An avenue to
automatical