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We compute bounds in the expected Ollivier curvature for the Browniancontinuum random tree $\mathcal{T}_{\mathbb{e}}$. The results indicate thatwhen the scale dependence of the Ollivier curvature is properly taken intoaccount, the Ollivier-Ricci curvature of $\mathcal{T}_{\mathbb{e}}$ is boundedabove by every element of $\mathbb{R}$ for almost all points of$\mathcal{T}_{\mathbb{e}}$. This parallels the well-known result that everycontinuum tree is a $CAT(K)$ space for all $K\in\mathbb{R}$.

Oliver Curvature Bounds for the Brownian Continuum Random Tree