This kind of "simple" emergence of spacetime geometry, in the perturbative approach from a classical geometry and a given topology is a very weak form of emergence that I dont think is not what Smolin means, and for sure not what i have in mind, without going into details.
Smolin generically talks about emergent statespaces in an evolutionary sense, but this is in his later books, i dont remember how far these ideas was expressed in the early books like three roads.
Thanks for mentioning this book. I didn't know he wrote this. I just bought one and it completes my collection of all Smolin books. I like the part where he mentioned:
"* the fundamental theory will not be quantum mechanical.. but quantum mechanics will emerge in the case of small subsystem.
* the fundamental theory will not exist in space, but space will be emergent in some eras of the universe."
Do you know of authors or papers where they explored the "dna of physical law" as you put it? Where there is perhaps some idea of elementals that embody certain forces of nature... this is the truly radical theory.. smolin stuff is just not radical or powerful enough to explain all of nature.
The connection between "evolution of law", and the emergence of symmetry, and the concept of observer depdenent observer invariance as an hierarchy of observers, is probably not too easy to explain briefly simply because noone to my knowledge does it this way, but you can understand the vision maybe by as a synthesis of the below spirits exemplified by some quotes, like take the good parts of each, try to deform it to make it selfconsistent, dump the rest, and what do you get? ;-)
"However, the rules of classical probability theory can be determined by pure thought alone without any particular appeal to experiment (though, of course, to develop classical probability theory, we do employ some basic intuitions about the nature of the world). Is the sametrue of quantum theory?"
-- Lucien Hardy, https://arxiv.org/pdf/quant-ph/0101012.pdf
"Entropic dynamics, a program that aims at deriving the laws of physics from standard probabilistic and entropic rules for processing information, is developed further."
-- Ariel Caticha, https://arxiv.org/abs/0808.1260
The problematic common denominator of all the various statistical emergence problems is that they fail to give the appropriate observational physical footing to the probability spaces. One part of this is also how lightly the concept of uncountably many alternatives are introduces in the theory, becuase it destroys computability of the inference system. It also seems intuitive that finite physical systems does not encode infinite amounts of information. So why the need for continuum models? That is often easier to work with from the point of view of analytical appraoches, but computers prefer finite sets. And nature might well too, who knows?
Then add these ideas..
" We need determinism only in alimited set of circumstances, which is where an experiment has been repeated many times. In these cases we have learned that it is reliable to predict that when we repeat an experiment in the future, which we have done many times in the past, the probability distribution of future outcomes will be the same as observed in the past. Usually we take this to be explained by the existence of funda mental timeless laws which control all change. But this could be an over-interpretation of the evidence. What we need is only that there be a principle that measurements which repeat processes which have taken place many times in the past yield the same outcomes as were seen in the past."
Lee Smolin, https://arxiv.org/pdf/1205.3707.pdf
To be honest i dont think that Smolin managed to explain this as good as it maybe could. As i see it, you can easily misread this suggestion and find it completely ridiculous, but then think again. The idea is, could the reason for the APPARENT timeless law, that most of use think of as constraints, simply be explained as a principle where nature tends to (in a sense of induction) respond as it always did? Seen the right way, this is a rational action principle in disguise. It also is a kind of solution to the problem of induction, as we know the problem is that the induction can be flat our wrong (ie no black swans). But this might not be how nature works! Its not a matter ot true or false, its a matter of best guess. If you only have seen white swans, betting on another white swan may still be a goot bet. Sometimes the best guess is wrong, and sometimes its exactly this explains certain interactions.
You can apply this reasoing also to "symmetries" if you consider the actual observer symmetries of an observer. If a certain observer has evidence for a certain symmetry, it will itself proabably behave "as if" this was law. But it is not. And sometimes a black swan actaully appears and breaks the illusion. But nature might be a stable illusion, and how else to explain it?
This is a way to also then understand evolution of law.
Then add the ideas of evolving laws of smolin, and you arrive at my position.