Relative Field Localization (RFL): Microscopic Open-System Closure: Transition Dynamics, Q-ball Localization, and Event-Position Statistics

This supplement develops a connected microscopic treatment of the open-system sector of Relative Field Localization (RFL). Starting from the scalar-field action and a scalar-bath density coupling, it fixes an explicit working identification of the coupled system operator with the Noether charge density, specifies charge-preserving initial and final state sectors, and derives transition matrix elements and finite-temperature emission and absorption rates. The bath correlation function yields a Born-Markov reduced evolution and its energy-resolved jump operators. Finally, a spatially resolving detector is coupled to the emitted bath wavepacket. Its response kernel generates a normalized event instrument, a finite-resolution convolution of the position density, and the Born distribution in the sharp-resolution limit.