Many theorists agree that space-time geometry could be emerge from something else. That structure is often therefore described as "pregeometric." I.e. It is a common generic term in physics used to describe any hypothetical theory in which space and time is emergent. Wikipedia is always a good place to turn to when you don't understand a term and in this case it gives several good examples of mainstream pregeometric theories http://en.wikipedia.org/wiki/Pregeometry_(physics)
"The meta-laws" here just mean the theory of this pregeometry. They are meta-laws in the sense that the laws of physics we know are just one possibility of what could emerge from the meta-laws. They exist at a deeper level. I am talking here about theory whose exact form is unknown so in that sense it does have multiple meaning, but what I am saying applies generically to whatever those meta-laws are. Again the term "meta-laws" is in common use although it is less common than "pregeometry"
I think the meaning of my statement that it takes a purely algebraic form should be clear enough. If it is pregeometric is should not be a theory of geometry so it could be algebraic or combinatorial or something else. Quantum mechanics is very much algebraic so once the geometry has been transcended it seems reasonable to expect that what underlies the theory from which it emerges will be algebraic.
I don't think "relationships between systems of information" is very ambiguous even though I do not describe those systems in general. Also I think the words "symmetry" and "immutable" are unambiguous.
Possibly the problem here is not that this can mean different things, but rather that I am referring to generic concepts where the detailed implementation of the ideas is not yet worked out. I don't see how this can be avoided given the essay topic which forces us to consider questions of what fundamental means when we don't yet have a complete fundamental theory of physics to work from. I am pleased that others seem to have understood some of what I say in that context and sorry that you have not.