  We construct a conformal map from $\mathbb{R}^3$ to a three-dimensional
spheriod, which includes $\mathbb{S}^3$, a double-cover of the 3-ball, and
$\mathbb{R} \times \mathbb{S}^2$ as limiting cases. Using the data of the
critical three-dimensional Ising model on $\mathbb{R}^3$ that was computed
using the conformal bootstrap method, we numerically estimate the fourth-order
Binder cumulant of the critical three-dimensional $\phi^4$ theory on
$\mathbb{S}^3$. We expect this estimate will enable an interesting comparison
between the conformal bootstrap and future calculations of critical $\phi^4$
theory on $\mathbb{S}^3$ using the Quantum Finite Element (QFE) method.

High Energy Physics - Lattice;High Energy Physics - Theory