This document presents a convergent synthesis across logic, number theory, geometry, and group theory, unified by a single primitive: the act of drawing a distinction, the Mark. We define the Mark as a self-embedding operator and show that repeated application generates an ultrametric tree whose leaves are the objects of mathematics. The Classification of Finite Simple Groups, the p-adic numbers, and the ultrametric topology of hierarchically organized systems are proposed as manifestations of a single generative engine: the recursive act of distinction.
Rowan Brad Quni-Gudzinas (2026) studied this question.