A formula for risk in chains of AI agents (Formula note, revision 5)

When AI agents work in a chain, one agent's error can become the next agent's input. This note gives a formula, exact within the stated model, for the chance of at least one high-stakes outcome in a chain of N agents, each taking n steps, where an anomaly upstream raises the anomaly rate downstream by a contamination multiplier c and contaminates the next agent's input with probability g. It reduces to the standard independent result when c = 1 and when g = 0. Preprint, not peer reviewed.