How is trust established across pod providers?

There are lengthy answers to your question here :
https://forum.solidproject.org/t/solid-pod-with-jwt-verification/. The short answer is : Any Solid Identity Provider can provide an app with a JWT associated with a given WebID that allows that app to act as that WebID.
Any Solid Pod provider the app contacts can recognize it as authenticated via the JWT and as belonging to that WebID and can therefore apply authorization restrictions accordingly. That is all part of the spec.

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