This is a challenging document to assimilate because it mixes unfamiliar mathematics with unfamiliar physics. But here is a rough outline.

Chapters 2 through 5 are spent defining many simple combinatorial objects in the not-so-simple language of category theory. There are numbers, sets, trees, braids, polytopes, and matrices, among other objects.

In chapter 6, we make contact with current applications of twistors to quantum field theory. This is already an area in which combinatorial objects and simple symbolic calculi are playing a role, and Sheppeard wants to interpret the subject using concepts and results introduced in the preceding chapters.

In chapter 7, some of this apparatus is employed to introduce an extended version of Bilson-Thompson’s correspondence (of braids and Standard Model particles) and an explanation of Koide formulae in terms of circulant matrices associated with the braids.

So to summarize, chapter 6 is about the frontier of current theory and chapter 7 is about phenomenology, and in both cases there is an attempt to make the categorical combinatorics of chapters 2 through 5 relevant.

Chapters 8 and 9 return to pure math – knots, polytopes, and categorical diagrams.

Chapter 10 is about black holes – the “black hole / qubit correspondence” – and chapter 11 is about cosmology – the dark sector and cosmic time.