The Mechanism of Decay from the Bost–Connes System

The structure, thermalization, and motion of matter have been established on the state space of the Bost–Connes system; the change of identity has so far had no mechanism. We define decay as the change of identity of a stable standing wave, χj → χk, and it proceeds in only one way: the amplitude of the initial state merges into the background, the final state re-forms from the background, and an emitted pair carries the record away. Merging and formation are evaluated at the vertices against the background; the evaluation gives the conservation of electric charge, generation charge, and parity, the direction and rate of decay follow from it, and the Fermi constant and the muon lifetime are given by the numbers of the framework. The exponential decay law, the β spectrum, parity violation, the lifetime hierarchy, and nucleon stability are explained one by one from the same structure.