When Do LLM Agents Reproduce Human Social Structure? An Identifiability Audit of Generative Social Simulators

Large language models (LLMs) are increasingly used as agents to simulate human societies, and such simulators are often evaluated by whether the social structures they generate resemble real ones. However, realistic-looking social structure does not necessarily imply realistic agent behavior: the observed structure may arise from simulator architecture or even from superficial features of the prompt. We introduce the Simulator Identifiability Audit, a framework for testing whether emergent social structure is actually attributable to an LLM agent policy. The audit compares each simulator with an architecture-matched random twin that replaces LLM choices by chance while holding the rest of the simulator fixed, evaluates both at matched edge counts, and permutes labels to separate effects of simulated individuals from effects of their representations. Across six social-simulation architectures, real and synthetic social networks, three commercial LLM providers, and an open-weight model, we find three consistent patterns. First, a minimal persona-agent architecture distilled from recurring design choices in published simulators is structurally silent: none of its evaluated network properties differs detectably from its random twin. Second, exposing peer traits makes the policy detectable, improving clustering through convergent selection of the same trait-attractive peers rather than homophily, while degrading degree structure. Third, apparent successes can be artifacts: memory-driven community formation disappears at matched edge counts, while names and list positions systematically bias partner selection, with female-associated names selected up to 8.7x as often as male-associated names in a synthetic-name probe.