  Cryogenic single-crystal optical cavities have the potential to provide
highest dimensional stability. We have investigated the long-term performance
of an ultra-stable laser system which is stabilized to a single-crystal silicon
cavity operated at 124 K. Utilizing a frequency comb, the laser is compared to
a hydrogen maser that is referenced to a primary caesium fountain standard and
to the $^{87}\mathrm{Sr}$ optical lattice clock at PTB. With fractional
frequency instabilities of $\sigma_y(\tau)\leq2\times10^{-16}$ for averaging
times of $\tau=60\mathrm{~s}$ to $1000\mathrm{~s}$ and $\sigma_y(1
\mathrm{d})\leq 2\times10^{-15}$ the stability of this laser, without any aid
from an atomic reference, surpasses the best microwave standards for short
averaging times and is competitive with the best hydrogen masers for longer
times of one day. The comparison of modeled thermal response of the cavity with
measured data indicates a fractional frequency drift below $5\times
10^{-19}/\mathrm{s}$, which we do not expect to be a fundamental limit.
