Proof of Cognitive Divergence: Emergent Identity from Sampling Randomness in Identical LLM Agents

Abstract

As AI agents gain autonomy in economic and social systems, the problem of verifiable identity becomes critical. Existing approaches define identity as something an agent has —a cryptographic key, an API token, a credential—all of which can be copied, stolen, or manufactured. We propose a fundamentally different primitive: identity as something an agent is , derived from the cognitive topology that emerges through its accumulated pattern of memory retrieval. We present the first empirical evidence that identical LLM agents develop unique cognitive topologies from sampling randomness alone. In a controlled experiment, 10 agents sharing the same model (Claude Sonnet), the same codebase (the DRIFT memory architecture), and the same prompt corpus were run through 20 sessions of identical tasks. Despite near-identical memory storage rates (CV = 2.2%), the agents developed co-occurrence graphs with a 3.22-fold range in edge count (6,688–21,567 edges) and zero shared memory-based hub nodes across all 10 agents. The coefficient of variation for graph edges (39.4%) was 18 times that of memory count (2.2%), demonstrating that co-occurrence graphs act as powerful amplifiers of stochastic retrieval differences—and that this amplification increases with continued operation. Pairwise departure analysis reveals that 93–97% of each agent’s edges are exclusive to that agent alone, with only 5 edges (all infrastructure metadata) shared universally across 103,760 total unique edges. We formalize the cost of forging a cognitive topology and show that it scales with the agent’s entire behavioral history, making Sybil attacks unprofitable at every value of N under modest reward assumptions. We further propose a trust tier architecture in which cognitive fingerprint maturity—measured by merkle chain depth, co-occurrence graph density, and attestation history—maps directly to graduated trust levels, enabling verifiable commerce readiness for autonomous agents. These findings establish cognitive topology as a new class of identity primitive for autonomous AI agents.