Let's get back to focus on what Percacci exactly did say. It is simple, important, and it is the topic of this thread:
...much of the literature does not address the issue of constructing workable emergent models for gravity. It seems to me that those that go furthest in this direction are people that do not usually talk much about emergence. For instance, you could argue that causal dynamical triangulations is currently the most successful way of actually calculating emergent properties of gravity.
Loll uses self-assembling swarms or flocks of small identical 4-simplices as her DoF and she gets largescale deSitter spacetime to emerge as an average.
The calculation is a MonteCarlo computer sim. The 4-simplices behave according to simple local rules---analogous to individual birds in a flying flock or fish in a school of fish or sheep in a herd. The individual interacts locally with its neighbors according to simple rules. An overall dynamic shape of the collective appears out of this.
The simple local rules reflect some Regge considerations. The computer is constantly randomizing the internal arrangement according to these rules. It may iterate the assemblage a million times before printout. It is very "thermodynamical" or "ergodic" in this way---like shuffling a deck of cards a million times before you examine it.
The method of CDT is not manifoldy, in the sense that the dimensionality at small scale is not even determined. A smooth manifold which is macro 4d must also be micro 4d. Loll has gone beyond the differential manifold and has found a 21st century way to do unsmooth geometry. However she requires a computer doing MonteCarlo sims in order to calculate.
Nevertheless she is doing what Percacci says, when she calculates that the smallscale dimensionality goes down from 4 to near 2. And when she calculates that the average large shape of the flock is deSitter. She and Ambjorn and Jurkiewicz and friends are calculating emergent properties of gravity
Calculating emergent properties of geometry from non-manifold micro degrees of freedom
, i.e. from active self-assembling building blocks.
That is just one example of a new thing which Percacci is pointing at. LQG models can also be seen in this light. In Loop cosmology one also runs small computer models of the universe, and the cosmology people are getting into doing this with spinfoam models (which will make them more like Loll CDT.)
I see Percacci just posted a second comment, amplifying what he said about CDT calculating emergent properties of gravity (actually of geometry but it's the same thing):