4$. It was argued in~\cite{deBoer-ml-2011wk,Hung-ml-2011xb} that the analog of the Ryu-Takayanagi formula~\eqref{eq:RTformula} for Einstein-Gauss-Bonnet should be the Jacobson-Myers entropy~\cite{Jacobson-ml-1993vj,Jacobson-ml-1993xs} \begin{equation} S_{JM}=\frac{1}{4G}\left(\textrm{Area}+2\lambda\int_{\Sigma} d^{D-2}\sigma\sqrt{\gamma}\,\mathcal{R}\right)+\dots\,, \label{eq:JMentropy}\end{equation} evaluated on a surface $\Sigma$ that extremizes~\eqref{eq:JMentropy}, or equivalently, on a surface which satisfies \begin{equation} \label{eq:JMeom} \left(\gamma^{ij}- 4 \lambda\mathcal{R}^{ij}\right)\mathcal{K}_{ijz}+ O\!\left(\lambda^2\right) =0\,. \end{equation} Here $\gamma_{ij}$ is the metric induced on $\Sigma$, and $\mathcal{R}_{ijkl}$ and $\mathcal{K}_{ijz}$ are its intrinsic and extrinsic curvatures. The first half of this conjecture, namely that the appropriate entropy functional is the Jacobson-Myers entropy, was shown in~\cite{Fursaev-ml-2013fta, Dong-ml-2013qoa, Camps-ml-2013zua}. However, the derivation of the extremality condition involves accounting for the divergences mentioned above. We find that the extra freedom afforded by our ansatz allows us to cancel all order $(n-1)$ divergences in the Einstein-Gauss-Bonnet field equations precisely when~\eqref{eq:JMeom} holds. As in the case of general relativity, this is the only constraint on $\Sigma$. We also find that the equations of motion allow replica symmetry breaking terms to contribute to the extrinsic curvature at $n=1$, but in a way that preserves~\eqref{eq:JMeom}. ]]>