  The purpose of this note is to unify the role of the lantern identity in the
proof of several finiteness theorems. In particular, we show that for every
nonnegative integer m, the vector space (over the rationals) of type m (resp.
T-type m) invariants of integral homology 3-spheres are finite dimensional.
These results have already been obtained by [Oh] and [GL2] respectively; our
derivation however is simpler, conceptual and relates to several other
applications of the lantern identity.
