  We analyze the equivalent widths of HI Ly-$\alpha$ ($W_{Ly\alpha}$)
absorption from the inner (R < 160 kpc) circumgalactic medium (CGM) of 85
galaxies at $z \sim 0$ with stellar masses $M*$ ranging $\rm{8 \leq log M* /
M_{\odot} \leq 11.6}$. Across three orders of magnitude in stellar mass, the
CGM of present-day galaxies exhibits a very high covering fraction of cool
hydrogen gas ($f_C = 87\pm 4$\%) indicating that the CGM is ubiquitous in
modern, isolated galaxies. When HI Ly-$\alpha$ is detected, its equivalent
width declines with increasing radius regardless of the galaxy mass, but the
scatter in this trend correlates closely with $M*$. Using the radial and
stellar mass correlations, we construct a planar surface describing the cool
CGM of modern galaxies: $\log W^{\rm{s}}_{HI 1215} \; = \; (0.34 \pm 0.02) -(
0.0026 \pm 0.0005)\times (R) + (0.286 \pm 0.002) \times \log (M*/M_{\odot})$.
The RMS scatter around this bivariate relation is $\sim$0.2 dex. We interpret
the explicit correlation between $W_{Ly\alpha}$ and $M*$ to arise from the
underlying dark matter halo mass ($M_{halo}$), thereby suggesting a CGM
fundamental plane between $W_{Ly\alpha}$, $R$ and $M_{halo}$. This correlation
can be used to estimate the underlying dark matter halo mass from observations
of saturated HI Ly-$\alpha$ in the CGM of a modern galaxy.
