  In this report we summarize in an informal way the main advances made in the
last 3 years and give a unified scheme of our theoretical work. This scheme
aims at connecting in a consistent physical picture (by the introduction of
some working hypotheses when necessary) the technical work published in several
single articles. The part of our model concerning the purely gravitational
aspects of the weak shielding phenomenon is almost complete; the part
concerning the density distribution of the superconducting carriers in the HTC
disks is still qualitative, also due to the very non-standard character of the
experimental setup. The main points of our analysis are the following: coherent
coupling between gravity and a Bose condensate; induced gravitational
instability and "runaway" of the field, with modification of the static
potential; density distribution of the superconducting charge carriers;
energetic balance; effective equations for the field; existence of a threshold
density.
