Yes, it's official NASA has recently reported that the Moon has shrunk significantly over the past few decades. The key to this is a particular type of Moon cliff known as a "lobate scarp". Pictures from NASA's selenomapping satellite, the Lunar Reconnaissance Orbiter (LBO) now in orbit around the Moon, have been trawled through and large numbers of the key scarps identified.
Tellingly, many of these scarps - essentially wrinkles in the lunar crust caused as the middle of the moon shrinks and it's outer cover is forced to adapt - run right through small craters, which are generally assumed to be quite new. Large craters which are considered to be older do not cover any of the cliffs.
This means that the scarps have formed recently and that the Moon is not geologically "dead" but very much still alive and shrinking.
