What is the connection between Braided Matter, Loop Quantum Gravity and the Rishon Model? Sundance Bilson-Thompson is an advocate of non-point-like structures that resemble elementary particles (see here, for example). His theoretical adventures show that the first generation of particles in the Standard Model is comprised of loops that are braid together to form the first generation particles (the up- and down-quark, the electron, and the electron neutrino):

One can read here:

The analysis of this network of quantum units of space may result in more than physicists bargained for because recent studies have indicated that the Standard Model particles may be implicit in the theory. This work has largely been pioneered by Fotini Markopoulou and work by the Australian Sundance O. Bilson-Thompson.
In Bilson-Thompson’s model, the loops may braid together in ways that could create the particles, as indicated in this figure. (These results remain entirely theoretical, and it remains to be seen how they work into the larger LQG framework as it develops, or whether they have any physical meaning at all.)

In the Rishon Model (not to be confused with Rishon Odel) of Haim Harari, the (point-)particles of all generations are said to consist out of trios T- or V-rishons. The second and third generation generations are simply excitations of the first. You can see that the first generation of quarks and leptons exhibits the same structures as the braided structures shown above (a twist correspond to a T-rishon, a not-twist to a V-rishon):

Very conspicuous! Can it be that there is a connection between the two? The Rishon Model was invented long before the braided structures were proposed by Bilson-Thompson. Loop Quantum Gravity, which in my view is a real quantization of spacetime, in contrast to string theory (but correct me if I'm wrong), is named in the context of braided structures. It was there too before the braided structures were proposed. This article, provided by @Qmechanic, shows the connection with Loop Quantum Gravity, of which Smolin is the main advocate.
What is the connection between the three?
 A: Yes, the rishon model is very similar to the Bilson-Thompson model. In the original paper, Bilson-Thompson cited both Shupe and Harari [1]. According to Bilson-Thompson, the earlier works introduced rishons as particles, but this required an additional "hypercolor" force to bind them together. Bilson-Thompson claims to take inspiration from this but not introduce the additional force to bind them together. Since little mathematical details are provided, it isn't clear how this actually solves any of the problems of the earlier works without the hypercolor force. For instance, he states that the helon model is not a preon model, but rather preon inspired, so we should not assume any of the same problems are there, but little justification for this claim is made.
These are also related to the work of Robert Finkelstein. His works make the relationships more clear, as Finkelstein also cites Shupe and Harari, has essentially the same diagrams, and provides more mathematical details, such as their relationship to q-deformed Lie algebras. Finkelstein's work while he was emeritus is on the arXiv, which hosts a collection of papers related to this topic [2].
Finkelstein convinced Julian Schwinger to go to UCLA. While Schwinger had different ideas about the strong force, Finkelstein claims to have unified QCD with Schwinger's model of QCD with dyons. Finkelstein also was able to convince Sergio Ferrara that supergravity is a gauge theory of gravity. Finkelstein did work on extremal black holes, which are studied in supergravity and string theory.
Finkelstein clarifies that the preons refer to the crossing points of the strands; note that all of the braids have three crossings and it was thought that three preons comprise quarks and leptons. Bilson-Thompson says that his model is not a preon model, but inspired by preons. While Finkelstein claims to have preons, it's the same knots, the same thing.
After reviewing work on supersymmetry, it appears that D0 branes are similar to the two ends of the braids.
Finkelstein also added the dyonic structure from Schwinger, which removes the need for a "hypercharge" force, similar to Bilson-Thompson's avoidance of the force. Since Finkelstein described the mathematics of the q-deformed Lie algebra that is responsible for this, while Bilson-Thompson states that the quantitative details need to be further established, I find Finkelstein's work more expansive and helpful for explaining why the additional force isn't needed.
While Bilson-Thompson also coauthored a paper with Lee Smolin discussing "Quantum Gravity and the Standard Model", which is cited as a support for the idea that the Bilson-Thompson model has been incorporated into LQG, the paper isn't very clear about the actual structure of the theory or how to quantitatively make predictions [3]. To see what I mean, the paper concludes with this statement:
"Alternatively, if the spacetime geometry is to be constructed from the collection of events that are the interactions of the conserved degrees of freedom, one has to show how gravity and the Einstein equations will appear."
As you can see, despite the paper having quantum gravity in the title, the entire paper doesn't address how equations of classical gravity are found in this model, let alone quantum gravity. As such, if LQG is a theory of quantum gravity, then it is a bit overhyped to claim that the helon model has been unified with LQG, as it isn't yet a complete model. While I think that more research is needed and these ideas are interesting, the actual paper seems to state that LQG uses graphs and this helon model uses graphs, so the helon model is compatible with LQG. Note that this is much different than claiming to have a theory of quantum gravity with the standard model.
Also, note that the paper with Smolin mentions q-deformed SU(2) for LQG, but they are not aware of Finkelstein's work. Bilson-Thompson does not discuss q-deformed SU(2), but Finkelstein does. Despite Finkelstein's work having more mathematical details, it is still not enough. Further research is needed.
In my opinion, I suspect that these braided matter ideas can be studied in both loop quantum gravity and string theory. For instance, supergravity has been extensively studying dyonic black holes, while there is relatively little work on the helon model. Some of the dyonic black holes do not consider the twisting of the ribbons, which Finkelstein and others refer to as writhe. While most string theorists are largely unaware or not interested in these preon models, it seems clear that the mathematics from supergravity could help expand a further understanding of this helon model or the work of Finkelstein.
Overall, most physicists find the helon model too vague and say that it is not yet quantitative enough yet.
To answer your question specifically, the helon model is not a specific or well-defined model, so all the differences with Shupe and Harari are not fully clear. One difference is that Bilson-Thompson recovers Majorana neutrinos, not Dirac neutrinos. As such, Bilson-Thompson states that the neutrino is its own antiparticle. However, it isn't clear how Bilson-Thompson avoids the problems of the rishon model, such as the additional force. After studying Finkelstein's work, it becomes more clear that the additional force is not needed if one recognizes that dyons with electric and magnetic charge are contained. Since "no magnetic monopoles exist" besides some topological considerations, the knots are bound together to ensure that the entire structure has no magnetic monopole charge. The connection between LQG and the helon model is that both use ribbon graphs, but the mathematics of the helon model is not clear. If anything, I think that Finkelstein's work provides a stronger support for the relationship of LQG to these braids, despite Finkelstein never mentioning this, as he mentions q-deformed SU(2), which is used in LQG. However, much further research is needed and the helon model should not be used as motivation for why LQG is better than string theory for quantum gravity.
[1] https://arxiv.org/pdf/hep-ph/0503213.pdf
[2] https://arxiv.org/search/?searchtype=author&query=Finkelstein%2C+R+J&order=-announced_date_first&size=50&abstracts=show
[3] https://arxiv.org/pdf/hep-th/0603022.pdf
