  The Neutron Star Interior Composition Explorer (NICER) monitoring campaign of
Cyg X-1 allows us to study its spectral-timing behavior at energies ${<}1$ keV
across all states. The hard state power spectrum can be decomposed into two
main broad Lorentzians with a transition at around 1 Hz. The lower-frequency
Lorentzian is the dominant component at low energies. The higher-frequency
Lorentzian begins to contribute significantly to the variability above 1.5 keV
and dominates at high energies. We show that the low- and high-frequency
Lorentzians likely represent individual physical processes. The lower-frequency
Lorentzian can be associated with a (possibly Comptonized) disk component,
while the higher-frequency Lorentzian is clearly associated with the
Comptonizing plasma. At the transition of these components, we discover a
low-energy timing phenomenon characterized by an abrupt lag change of hard
(${\gtrsim}2$ keV) with respect to soft (${\lesssim}1.5$ keV) photons,
accompanied by a drop in coherence, and a reduction in amplitude of the second
broad Lorentzian. The frequency of the phenomenon increases with the
frequencies of the Lorentzians as the source softens and cannot be seen when
the power spectrum is single-humped. A comparison to transient low-mass X-ray
binaries shows that this feature does not only appear in Cyg X-1, but that it
is a general property of accreting black hole binaries. In Cyg X-1, we find
that the variability at low and high energies is overall highly coherent in the
hard and intermediate states. The high coherence shows that there is a process
at work which links the variability, suggesting a physical connection between
the accretion disk and Comptonizing plasma. This process fundamentally changes
in the soft state, where strong red noise at high energies is incoherent to the
variability at low energies.
