# Gated self-evolution

Treating the individual instances inside a gated self-evolving LLM agent (DSH-plugin-based, with plugins satisfying four architectural properties: permutation symmetry, reversibility, acyclicity, and typed contracts) as identical hard spheres, the work builds a rigorous layer (any-time hitting-time certificate, resolution law, separation theorem), a kinetic layer (a master equation over the plugin x version x task grid with collision, reaction, external field, and gate operators plus its moment hierarchy), and a measured layer (a faithful minimal instance in a one-model, one-task-family WebShop environment), finding that population fluctuation scaling is density-gated: invisible at sparse edit density and emerging at the predicted rate under tripled density.

Treating the individual instances inside a gated self-evolving LLM agent (DSH-plugin-based, with plugins satisfying four architectural properties: permutation symmetry, reversibility, acyclicity, and typed contracts) as identical hard spheres, the work builds a rigorous layer (any-time hitting-time certificate, resolution law, separation theorem), a kinetic layer (a master equation over the plugin x version x task grid with collision, reaction, external field, and gate operators plus its moment hierarchy), and a measured layer (a faithful minimal instance in a one-model, one-task-family WebShop environment), finding that population fluctuation scaling is density-gated: invisible at sparse edit density and emerging at the predicted rate under tripled density.