I think I can name an example, which is how I am approaching datalisp; https://sr.ht/~ilmu/tala.saman/ the first principles bit for my context refers to: fixing a standard encoding that is sufficient for the task, determining inputs and outputs of model, setting a general guideline for expressivity of model (space of conflict-free programs), sketching interaction modes and user interfaces.

These are the first principles in question, now from there your architecture is mostly determined, you can fall back on known patterns and decades of research. The axioms are the architecture.