The decision problems of the NP core are bundled with a proof that they do not distinguish isomorphic structures. For the problems of this submission the bundling is done once and for all: the problem given by a property $P$ of structures has as yes-instances the structures isomorphic to one satisfying $P$, which is invariant by construction. When $P$ is itself invariant, as every property here is, this is the problem whose yes-instances are exactly the structures satisfying $P$; that equivalence is stated, problem by problem, beside each definition.