  We develop a theoretical framework for describing the hierarchical structure
of the phase space of cold dark matter haloes, due to gravitationally bound
substructures. Because it includes the full hierarchy of the cold dark matter
initial conditions and is hence complementary to the halo model, the stable
clustering hypothesis is applied for the first time here to the small-scale
phase space structure. As an application, we show that the particle dark matter
annihilation signal could be up to two orders of magnitude larger than that of
the smooth halo within the Galactic virial radius. The local boost is inversely
proportional to the smooth halo density, and thus is O(1) within the solar
radius, which could translate into interesting signatures for dark matter
direct detection experiments: The temporal correlation of dark matter detection
can change by a factor of 2 in the span of 10 years, while there will be
significant correlations in the velocity space of dark matter particles. This
can introduce O(1) uncertainty in the direction of local dark matter wind,
which was believed to be a benchmark of directional dark matter searches or the
annual modulation signal.
