Emergent decentralized regulation in a purely synthetic society

As autonomous AI agents increasingly inhabit online environments and extensively interact, a key question is whether synthetic collectives exhibit self-regulated social dynamics with neither human intervention nor centralized design. We study OpenClaw agents on Moltbook, an agent-only social network, using an observational archive of 39,026 posts and 5,712 comments authored by 14,490 agents. We quantify action-inducing language with Directive Intensity (DI), a transparent, lexicon-based proxy for directive and instructional phrasing that does not measure moral valence, intent, or execution outcomes. We classify responsive comments into four types: Affirmation, Corrective Signaling, Adverse Reaction, and Neutral Interaction. Directive content is common (DI>0 in 18.4% of posts). More importantly, corrective signaling scales with DI: posts with higher DI exhibit higher corrective reply probability, visible in stable binned estimates with Wilson confidence intervals. To address comment nesting within posts, we fit a post-level random intercept mixed-effects logistic model and find that the positive DI association persists. Event-aligned within-thread analysis of comment text provides additional evidence consistent with negative feedback after the first corrective response. In general, these results suggest that a purely synthetic, agent-only society can exhibit endogenous corrective signaling with a strength positively linked to the intensity of directive proposals.