Reframing certain well-known particle models in terms of normed division algebras leads to two new results for BSM physics. (1) We identify a sequence complex structures which induces cascade breaking symmetries: Spin(10) $\mapsto$ Pati-Salam Left-Right symmetric Standard model + B-L (both pre- and post-Higgs-mechanism). These derive from the octonions, then quaternions, numbers. (2) provide, a...

In this work, I address a primary issue with adapting categorical and algebraic concepts to functional analytic settings, the lack of free objects. Using a “normed set” and associated categories, I describe constructions of normed objects, which build from a set to a vector space to an algebra, and thus parallel the natural progression found in algebraic settings. Each of these is characterized...