  Precision measurements of the free neutron lifetime $\tau_n$, when combined
with measurements of the axial vector form factor, can be used to test
unitarity of the CKM matrix. Non-unitarity is a signal for physics Beyond the
Standard Model (BSM). Sensitivity to BSM physics requires measurements of
$\tau_n$ to a precision of 0.1~s. However, the two dominant techniques to
measure $\tau_n$ (colloquially beam and bottle measurements) disagree by nearly
10~s. UCN$\tau$ is a neutron lifetime experiment using a magneto-gravitational
trap and an in-situ neutron detector. Neutrons in this trap are not susceptible
to loss on material walls as in previous bottle measurements. Additionally, the
in-situ detector allows spectral monitoring of the trapped Ultracold Neutrons.
In this talk, I will present our most recent result -
$\tau_n=877.7\pm0.7_\text{(stat.)}+0.4/-0.2_\text{(sys.)}$~s. I will also
present Monte Carlo simulations of systematic effects in the experiment
including heating and spectral cleaning.
