  The nature and geometry of the hard state in black hole binaries is
controversial. The broadband continuum spectrum and fast variability properties
can be explained in a model where the inner disc evaporates into a
geometrically thick, hot flow. However these models are challenged by the
persistent detection of an extremely broad iron line, which requires that the
disc extends down to the last stable orbit of a high spin black hole. This line
width can be considerably reduced if the Comptonisation continuum is
multi-component rather than single temperature, but such models are highly
degenerate. Here we show a specific model of a radially stratified continuum
coupled to a model of propagating fluctuations, fit to some of the best hard
state data from GX 339-4. This full spectral-timing model can fit the time
averaged spectrum, the power spectra in different energy bands, and the
frequency dependent lags between these bands. For the first time we also
include disc reverberation and show that this same spectral-timing model
successfully \textit{predicts} the lag-energy spectra on all timescales. This
gives a more robust method to determine the inner radius of the disc, which is
of order $20~R_g$, i.e. significantly truncated. This opens up the way to use
the fast variability spectral-timing data to trace the source geometry of black
hole binaries in all states.

High Energy Astrophysical Phenomena