  We report an optical lattice clock with a total systematic uncertainty of
$8.1 \times 10^{-19}$ in fractional frequency units, representing the lowest
uncertainty of any clock to date. The clock relies on interrogating the
ultra-narrow ${}^1S_0 \rightarrow {}^3P_0$ transition in a dilute ensemble of
fermionic strontium atoms trapped in a vertically-oriented, shallow,
one-dimensional optical lattice. Using imaging spectroscopy, we previously
demonstrated record high atomic coherence time and measurement precision
enabled by precise control of collisional shifts and the lattice light shift.
In this work, we revise the black body radiation shift correction by evaluating
the $5s4d$ $^3D_1$ lifetime, necessitating precise characterization and control
of many body effects in the $5s4d$ $^3D_1$ decay. Lastly, we measure the second
order Zeeman coefficient on the least magnetically sensitive clock transition.
All other systematic effects have uncertainties below $1 \times 10^{-19}$.
