Zitterbewegung as the Physical Realization of p-Adic Anyon Braiding

Abstract

The p-Adic Anyons program (Phases 1-4) developed the mathematical framework for anyons whose braid statistics are defined on Bruhat-Tits trees rather than in continuous spacetime. The ZBW program (P1-P3) demonstrated that Zitterbewegung — the rapid trembling motion of Dirac fermions at the Compton scale — has ultrametric (p-adic) structure, and that the Majorana condition creates topological fixed points on the Bruhat-Tits tree. This paper bridges the two programs: ZBW is the physical mechanism that makes p-adic anyon braiding experimentally accessible. The ZBW transition graph at the Compton scale is a Bruhat-Tits tree (Gromov $\delta$ = 0, `[CODE-EXECUTED]`), and the ZBW current correlator is a Z$_2$ topological invariant that encodes the anyon fusion space grading `[CODE-EXECUTED]`. We show that a Majorana zero mode at a Bruhat-Tits fixed point has the same topological charge as a p-adic Fibonacci anyon in the ultrametric braid group formalism. This establishes ZBW spectroscopy as an experimental probe of adelic anyon physics — the p-adic analog of interferometric anyon braiding in the Archimedean domain. **Keywords:** Zitterbewegung, p-adic anyons, Bruhat-Tits tree, Majorana zero modes, topological quantum computing, adelic synthesis ---