  We measure the radius-velocity phase-space edge profile for Abell S1063 using
galaxy redshifts from arXiv:1409.3507 and arXiv:2109.03305. Combined with a
cosmological model and after accounting for interlopers and sampling effects,
we infer the escape velocity profile. Using the Poisson equation, we then
directly constrain the gravitational potential profile and find excellent
agreement between three different density models. For the NFW profile, we find
log$_{10}$(M$_{200},{\rm crit}$)= $15.40^{+0.06}_{-0.12}$M$_{\odot}$,
consistent to within $1\sigma$ of six recently published lensing masses. We
argue that this consistency is due to the fact that the escape technique shares
no common systematics with lensing other than radial binning. These masses are
2-4$\sigma$ lower than estimates using X-ray data, in addition to earlier
velocity dispersion estimates. We measure the 1D velocity dispersion within
r$_{200}$ to be $\sigma_{v} = 1477^{+87}_{-99}$ km/s, which combined with our
escape velocity mass, brings the dispersion for AS1063 in-line with
hydrodynamic cosmological simulations for the first time.
