  More than 30 years ago Edwards and co-authors proposed a model to describe
the statistics of granular packings by an ensemble of equiprobable jammed
states. Experimental tests of this model remained scarce so far. We introduce a
simple system to analyze statistical properties of jammed granular ensembles to
test Edwards theory. Identical spheres packed in a nearly two-dimensional
geometrical confinement were studied in experiments and numerical simulations.
When tapped, the system evolves towards a ground state, but due to incompatible
domain structures it gets trapped. Analytical calculations reproduce relatively
well our simulation results, which allows us to test Edwards theory on a
coupled system of two subsystems with different properties. We find that the
joint system can only be described by the Edwards theory if considered as a
single system due to the constraints in the stresses. The results show
counterintuitive effects as in the coupled system the change in the order
parameter is opposite to what is expected from the change in the compactivity.
