Researchers treat plugin instances inside a gated self-evolving LLM agent as hard spheres, derive a kinetic theory, and observe density-gated population fluctuation scaling

It proposes moving the unit of study in self-evolution research from the agent as a whole down to the individual instances inside it, and provides a usable theoretical framework on a DSH-plugin-based agent. Prior self-evolution research treated the agent as the unit; here the individual instances inside it are studied instead, and the four architectural properties the plugins satisfy (permutation symmetry, reversibility, acyclicity, typed contracts) license treating these instances as identical hard spheres. The theory is explicitly scoped to DSH-class plugin populations; the four architectural properties are stated as conditions licensing the analogy rather than as universally holding premises.

The rigorous layer delivers three results independent of any analogy: an any-time hitting-time certificate, a resolution law that prices held-out validation budgets, and a separation theorem. The hitting-time certificate bounds the expected rounds to any prescribed improvement; the resolution law connects held-out validation budgets to resolvability; the separation theorem states that the daemon must stay outside the population, because merging evaluator with evaluated voids the certificate. This layer is explicitly described as independent of the fluid analogy and as rigorous; the separation theorem is argued by the fact that merging evaluator with evaluated voids the certificate.

The kinetic layer sets up a master equation over the plugin x version x task grid with four operators (collision, which is co-activation, reaction, external field, and gate), and generates falsifiable statistical signatures through its moment hierarchy. The moment hierarchy, the step that turns a gas into fluid equations, is used here to derive testable statistical signatures from the master equation. The fluid reading is repeatedly framed as a bounded analogy: momentum is not conserved, so no Navier-Stokes limit exists; falsifiability comes from the statistical signatures derived via the moment hierarchy.

The measured layer observes density-gated population fluctuation scaling on a faithful minimal instance. That instance is a large library of four-parameter skill plugins retrieved one per episode with a co-activation probe, in a one-model, one-task-family WebShop environment, with every element mapped to the DSH loop by architectural role. The fluctuation scaling is invisible at sparse edit density and emerges at the predicted rate under tripled density, which the authors position as directional evidence.

The scope of the theory is explicitly limited to DSH-class plugin populations, that is, plugins satisfying the four architectural properties of permutation symmetry, reversibility, acyclicity, and typed contracts. The rigorous layer is independent of the fluid analogy and can be used to bound expected rounds to any prescribed improvement, to price held-out validation budgets, and to support designs that keep the daemon separate from the population. The kinetic layer applies to systems on the plugin x version x task grid where collision is co-activation and where reaction, external field, and gate processes are present, with its moment hierarchy used to derive falsifiable statistical signatures. The measured layer's conclusions are aimed at the faithful minimal instance of a one-model, one-task-family WebShop environment with a four-parameter skill plugin library, where density-gated fluctuation scaling is observed.

The fluid reading is framed as a bounded analogy: momentum is not conserved, so no Navier-Stokes limit exists, and readers should note which conclusions depend on the analogy and which belong to the rigorous layer. The measured layer is a minimal instance in a one-model, one-task-family WebShop setting, and the fluctuation scaling is positioned by the authors as directional evidence; whether the emergence rate under tripled density holds at other densities, in other task families, or in other plugin libraries remains an open question. Whether the four architectural properties hold for plugin populations outside the DSH class determines whether the theory transfers. In addition, the currently visible text is the abstract and bibliographic tool sections without figures or full derivation details, so the concrete forms of the hitting-time certificate, resolution law, and separation theorem cannot be checked against this text.