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. With $10^5$ atoms in Wannier-Stark eigenstates of this lattice, we measure record atomic coherence time and measurement precision reaching below $1 \times 10^{-19}$ [arXiv:2109.12238]. Such clock precision, together with imaging spectroscopy, enables precise control of collisional shifts as well as the lattice light shift [arXiv:2201.05909, arXiv:2210.16374]. To address two remaining large systematic effects, we measure the second order Zeeman coefficient on the least magnetically sensitive clock transition, and we precisely determine the $5s4d$ $^3D_1$ lifetime to reduce the dynamic black body radiation shift uncertainty. All other systematic effects have uncertainties below $1 \times 10^{-19}$.