Radix to Ultrametrics to Page-Wootters to Wheeler-DeWitt to Bruhat-Tits: A Convergent Synthesis

When the Wheeler-DeWitt equation eliminates external time, Page-Wootters emergent clock states produce conditional quantum states whose correlations form an ultrametric hierarchy. The radix (prime p) characterizes the clock spectrum's self-similarity. Bruhat-Tits buildings become the geometric space of temporal reference frames — uniting quantum gravity, number theory, and algebraic geometry through a single structural principle.