  Fast variability of the X-ray corona in black hole binaries can produce a
soft lag by reverberation, where the reprocessed thermalized disc photons lag
behind the illuminating hard X-rays. This lag is small, and systematically
decreases with increasing mass accretion rate towards the hard-soft transition,
consistent with a decreasing truncation radius between the thin disc and X-ray
hot inner flow. However, the soft lag suddenly increases dramatically just
before the spectrum becomes disc-dominated (hard-intermediate state).
Interpreting this as reverberation requires that the X-ray source distance from
the disc increases dramatically, potentially consistent with switching to
X-rays produced in the radio jet. However, this change in lag behaviour occurs
without any clear change in hard X-ray spectrum, and before the plasmoid
ejection event which might produce such a source (soft-intermediate state).
Instead, we show how the soft lag can be interpreted in the context of
propagation lags from mass accretion rate fluctuations. These normally produce
hard lags, as the model has radial stratification, with fluctuations from
larger radii modulating the harder spectra produced at smaller radii. However,
all that is required to switch the sign is that the hottest Comptonized
emission has seed photons which allow it to extend down in energy below the
softer emission from the slower variable turbulent region from the inner edge
of the disc. Our model connects the timing change to the spectral change, and
gives a smooth transition of the X-ray source properties from the bright hard
state to the disc-dominated states.
