Optical clocks with accuracy validated at the 19th digit

We report a comprehensive evaluation of all known sources of systematic uncertainty for two independent ${}^{176}$Lu${}^{+}$ single-ion optical references, finding total systematic uncertainty of $1.1\times {10}^{-19}$ and $1.4\times {10}^{-19}$ for the two individual systems and $9.6\times {10}^{-20}$ for the difference. Through direct comparison via correlation spectroscopy, we demonstrate a relative frequency agreement of $-2.4\pm (5.7{)}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm (1.0{)}_{\mathrm{s}\mathrm{y}\mathrm{s}}\times {10}^{-19}$, where stat' and sys’ indicate the statistical and systematic uncertainty, respectively. The comparison uncertainty is statistically limited after approximately 200 hours of averaging with a measurement instability of $4.8\times {10}^{-16}(\tau \mathrm{/}\mathrm{s}{)}^{-1\mathrm{/}2}$.