I think I respond to most earlier questions and comments below:
As to the "Laws of Logic" with respect to information [and I think I said this earlier] the information in a kernel is indeed static. The "laws of Logic" are just our locally grown [and apparently sequential] way of revealing it. The question I raise is the implicit inclusion of time in this process. Should we have the hubris to impose this somewhat questioned concept on all other universes? In my view the states of all universes preexist in the All [as some of the kernels] and "Physical Reality" washes over them in some sequentially inconsistent way. Just like being in Bruno's transporter etc. we would never notice.
My approach is designed to address the residual information problem and provide a basis for a dynamic.
I do not agree with your "rather" based cancelation of the residual information issue since I see it as an unnecessary complication of my own method.
Can a kernel of information be self inconsistent? From Bruno's last post I think it is possible to impose this idea on the All.
My interest was to have a dynamic which did not impose any residual information on the All. My current view is that each state of that dynamic has to be completely independent of the current state. The way I describe this is to say that the dynamic is inconsistent. It helps this idea if there are kernels that are pairwise inconsistent. I think that is straight forward enough. If there are kernels that are self inconsistent then all the better. Why should they be selected out?
Can any of this exclude a universe that has a sequence of successive states that follow a set of fixed rules? I think that one must insist that the inconsistency permeate every corner of the dynamic i.e. some level of external noise impressed on all state sequences.
As to does mathematics contain information, mathematics has the potential to erect boundaries so by my definition it is information. It also seems possible that there is room for what might be called bifurcated boundaries - inconsistencies.