  The pursuit of ever more precise measures of time and frequency is likely to
lead to the eventual redefinition of the second in terms of an optical atomic
transition. To ensure continuity with the current definition, based on a
microwave transition between hyperfine levels in ground-state $^{133}$Cs, it is
necessary to measure the absolute frequency of candidate standards, which is
done by comparing against a primary cesium reference. A key verification of
this process can be achieved by performing a loop closure$-$comparing frequency
ratios derived from absolute frequency measurements against ratios determined
from direct optical comparisons. We measure the $^1$S$_0\!\rightarrow^3$P$_0$
transition of $^{171}$Yb by comparing the clock frequency to an international
frequency standard with the aid of a maser ensemble serving as a flywheel
oscillator. Our measurements consist of 79 separate runs spanning eight months,
and we determine the absolute frequency to be 518 295 836 590 863.71(11) Hz,
the uncertainty of which is equivalent to a fractional frequency of
$2.1\times10^{-16}$. This absolute frequency measurement, the most accurate
reported for any transition, allows us to close the Cs-Yb-Sr-Cs frequency
measurement loop at an uncertainty of $<$3$\times10^{-16}$, limited by the
current realization of the SI second. We use these measurements to tighten the
constraints on variation of the electron-to-proton mass ratio, $\mu=m_e/m_p$.
Incorporating our measurements with the entire record of Yb and Sr absolute
frequency measurements, we infer a coupling coefficient to gravitational
potential of $k_\mathrm{\mu}=(-1.9\pm 9.4)\times10^{-7}$ and a drift with
respect to time of $\frac{\dot\mu}{\mu}=(5.3 \pm 6.5)\times10^{-17}/$yr.
