Contributions

  In order to organize the contributions of my work, I present Figure 37 which is a modified version of the claims hierarchy which appeared in Chapter 1. Added to the original figure are indications of what proof has been provided for each of the lowest level claims, as well as what chapter the associated discussion appeared in. These lowest level claims, in turn, provide the support for the higher-level claims, building to the overall claim of this research. By examining these claims, it is possible to see the contributions of this research.