Process for discovery of suitable apps for a resource

I would like to confirm my understanding of use cases where a user receives a uri and wishes to check whether an app can open it, or identify an app to open it with.

My understanding is that the intention would be that the shape tree of the resource is identified, and then compared with the registered shape trees provided by application identity profile documents.

Following the spec, it appears there is no link from a data instance to its data registration. Is this correct?

Instead, this use case seems to be covered by the shape tree spec, with the link header providing the shape tree manager.
If so, is there a link between the data registration and shape tree manager that needs to be specified?
And would this link header be a should or a must? Will servers consistently provide it? (it's a must for shape trees)

As a point of comparison, I like the way I can:

1. dereference a resource
2. look up its rdf:type
3. check whether apps support that type

I understand the need to check shapes rather than just types, but my preferred option would be to replace step (2) with looking up the shape or shape tree expressed in a single triple rather than by checking headers or loading registries. I expect that might be too simplistic, but I don't yet understand why.

Start with the shape tree spec, data registration, application identity profile, and link-header questions described in the issue. Trace how a data instance is associated with its registration and how an app discovers supported shapes. Done means resolving the proposed discovery flow and documenting the required links and their obligation level.