The Internet is a transport medium. It sounds like you are asking if it possible to (somehow) associate universal, intrinsic, and immutable attribution metadata with some or all (not sure what "viral" distinguishes in this context) Internet _content_ and have all receivers of that content accept the implications of that attribution metadata.
I think the failure of pretty much all the various digital rights management efforts applied on a MUCH smaller scale to infinitesimal subsets of content types that are now being schlepped across the Internet would suggest that no, there are no technical approaches that would realistically work.
And music, film, and television ownership/credit being tracked carefully? In certain law abiding environments, it's possible the owners/creators get a small fraction of what they believe they are entitled to, but in the majority of the world, not so much.
The distinction I’m thinking about is less about restricting the movement of content and more about tracking provenance. In other words, not trying to prevent copying or remixing, but making it easier to identify where something first appeared and who originally created it.
Music is an imperfect example, but the infrastructure around identifiers, registries, and rights databases at least creates a shared reference point for attribution. Internet-native media doesn’t really have anything comparable yet.
So the question I’m curious about is whether a similar kind of reference layer could exist for images, memes, and short-form media, even if the content itself continues to move freely?