It seems to me that several quantum interpretations rely on the idea that there exists a wavefunction that completely specifies the state of the universe. Of these, the Many Worlds Interpretation is perhaps the most famous but it seems even the Bohm Interpretation requires a Universal Wavefunction in order to specify the complete, nonlocal waveguide that determines the trajectories of locally isolated particles.
This Universal Wavefunction is difficult to explicitly construct as it requires a specification of a complete set of observables. However, one can imagine that in the limit of infinite experiments, it might be possible to enumerate a complete set of observables and determine the form of the Universal Wavefunction on these observables (or more specifically on some maximal subset of commuting observables).
The difficulty I'm encountering is that I do not see how this limit necessarily converges to a fully specified Universal Wavefunction. Just considering how the final object would have to be constructed, a simple paradox immediately arises: There must be a self-encoding (i.e. a model) of the Universal Wavefunction within a subset of itself. This model would be constructed using strictly less information than the "real" Universal Wavefunction. Naively this seems not only unlikely to me, but completely contradictory. One could consider the universe itself as the model, but this is not a representation of the universe and it contains no physical content about its laws or any means of prediction.
It's clear that some approximate model might exist in a subset of the Universal Wavefunction, but a number of these quantum interpretations rely on the existence of such a wavefunction in order to justify their ontological ramifications. Often the stipulation is made, "if calculated from an outside observer," but it isn't fair to assume that an "observer outside the universe" is a sensible ontological framework to work with either.
I haven't really been able to find discussions of the Universal Wavefunction from this angle, are there any resources that are able to define the Universal Wavefunction in such a way and circumvent (or show the potential naive flaw of) my concerns?
Is there an argument that such a Universal Wavefunction need not exist in order to carry out the program implied by these interpretations?
Are the ontological pictures of Bohmian mechanics and the many worlds interpretation insensitive to the existence of a Universal Wavefunction in the first place?
I apologize if this is a repost but similar questions seem to be focused on the existence of the many worlds that follow from this stipulation in the many worlds interpretation or whether the universal wavefunction exists and neither approach seem to be getting at my question.