Consider some universe at a moment in time which appears classical (all waves are unitary / point-like) and which contains a brain-like information-containing structure (ICS) that is encoding the present state of the static universe as a classical universe, along with sensors attached to the ICS which update the encoded information in the obvious way. Now time-evolve the system for a moment. The universe now will be in a superposition (ie: non-unitary) of possible classical and non-classical evolutions. The ICS will also be in a superposition of such states

There should be a possible unitary state now consistent with this time-evolved universe where the collapsed time-evolved ICS still encodes a classical universe. It only possibly encodes some variant of what it initially encoded, updated with new information from its sensors. Obviously its possible for the ICS to record information about the non-classical time-evolution of the system through statistical analysis of observations because we can actually do that -- thats how we know about quantum-mechanical effects. But did the ICS only observe what it believed were classical events?

If we define a classical universe as what an ICS in one term of a superposition of classical univseres encodes the universe as, then obviously the ICS will encode the universe as classical by definition

Is a scenario possible where you have some arbitrary non-unitary or unitary universe with some ICS + sensors within it, with some arbitrary time evolution operator T that isn't necessarily a classical or non-classical time evolution operator, such that the information the ICS encodes is consistent with T? What I'm getting at: is a classical / semi-classical time evolution operator arbitrary, and only relative to an arbitary ICS which happens to encode information using that operator?

I suppose in this scenario such a time evolution operator might treat certain superpositions which are unitary only after some transform as unitary. I'd imagine there are certain transforms corresponding to certain time evolution operators with this property