In the very broad scope addressed by digital preservation initiatives, a special place belongs to the scientific and technical artifacts that we need to properly archive to enable scientific reproducibility. For these artifacts we need identifiers that are not only unique and persistent, but also support integrity in an intrinsic way. They must provide strong guarantees that the object denoted by a given identifier will always be the same, without relying on third parties and external administrative processes. In this article, we report on our quest for this identifiers for digital objects (IDOs), whose properties are different from, and complementary to, those of the various digital identifiers of objects (DIOs) that are in widespread use today. We argue that both kinds of identifiers are needed and present the framework for intrinsic persistent identifiers that we have adopted in Software Heritage for preserving billions of software artifacts.