The following are some important advantages of this theory:

- There is a small set of fundamental assumptions with very few independent parameters. This implies that almost all of the parameters can be derived from first principles. This has already been done for the fine structure constant.
- In this theory, quantum properties are a consequence of the dynamics of the branched manifold. We show that the discrete behavior of the branched manifold can be modeled using a continuous approximation, which is a path integral. Because the underlying system is discrete and finite, the pathological infinities of the path integral never appear.
- From the fundamental assumptions, we show that the manifold can spontaneously produce pairs of knots of the form ℝ
^{3}#(S^{1}×P^{2}). We show that these knots have the properties of the elementary fermions. Different embedding types of these knots explain the different generations of fermions. We therefore find that the theory spontaneously produces the elementary particles without additional assumptions. Furthermore, the theory tightly constrains the types of knots that can be created, and we therefore can mathematically constrain the types of possible particles. - The spacetime manifold is constrained by our assumptions, but it is under-constrained. We therefore expect the manifold to maximize entropy. Using this principle of entropic maximization, we can derive a description of the dynamics of the spacetime manifold. We find that the manifold behavior is best described by a Lagrangian. In that Lagrangian, we find terms for gravity (scalar curvature R) and electromagnetism (the term F
^{μν}F_{μν}). Including the effects of particle geometry and topology produces electroweak and strong forces.

In this theory, we assume a few constraints on the spacetime manifold. One important result of those constraints is that the ways that the manifold can change topology are tightly constrained. If particles are knots on the manifold, then every production of particle/anti-particle pair is a change of topology of the manifold. Therefore a particular topology is only a viable particle topology if it can be created on the spacetime manifold subject to the constraining assumptions.

We prove that it is possible to produce pairs of knots of the form ℝ^{3}#(S^{1}×P^{2}) subject to our constraining assumptions. The type ℝ^{3}#(S^{1}×P^{2}) is relatively simple, analogous to a twist in the manifold. We then go on to show that those knots have the same properties as the elementary fermions. It remains to be shown that no other topology type is possible. It may be that there are other possible particle topologies and the only reason we see just the type ℝ^{3}#(S^{1}×P^{2}) is that it has the lowest energy. While it is possible to mathematically eliminate many classes of particle topology, a complete list of possible particle topologies has not yet been determined.

The mathematical theory of knot theory has a very specific meaning for the word "knot". A knot is an embeddding of S^{n} in S^{n+2}. The constraint on the dimensions (an n-manifold in an n+2-manifold) is a tight constraint. For any other dimensionality, the embedding would not be knotted. For example, a knot of the form S^{n} in S^{n+3} would spontaneously untie.

Every elementary fermion in this theory has topology ℝ^{3}#(S^{1}×P^{2}). This is not a knot in the sense of knot theory. Also, this 3-dimensional topology can be embedded in ℝ^{n} for n≥5. A hadron, for example a proton, contains linked copies of ℝ^{3}#(S^{1}×P^{2}), each of which is a quark. Those quarks will remain linked to each other only if the 3 spatial dimensions of the spacetime manifold are embedded in a 5-dimensional space. For that reason, we see that the dimension of the embedding space is perfectly constrained by the particle topology of hadrons.

In this theory, we need a word to describe particle topology. There are two reasons that we use the word "knot". The first reason is that the word is convenient and approximately describes the particle topology. The second reason is that, for hadrons, the 3-dimensional particle topology must be embedded in an 5-dimensional space, which is the same constraint (n=3 and n+2=5) that applies in the mathematical theory of knot theory.

In this theory, all elementary fermions are knots in the spacetime manifold that have topology ℝ^{3}#(S^{1}×P^{2}). Leptons are elementary fermions and therefore they also have this topology. In this theory, we assume that the spacetime manifold is constrained by Ricci flatness, and we find that Ricci flatness strongly constrains the geometry of the particles. In particular, as charged leptons approach other particles, Ricci flatness forces the lepton radius to shrink. As the distance of approach goes to zero, the lepton radius also goes to zero. For this reason, leptons appear to be pointlike in collisions.

This description allows us to describe the spin angular momentum of leptons in familiar terms. For the case of pointlike leptons, spin angular momentum must be considered to be an inherent quantity that is not obtained in the normal sense of p×r, because the calculation would be meaningless if the lepton radius is r=0. In this description, radius is non-zero and the spin angular momentum can be calculated as a function of field strength from first principles.