Organizations devote substantial resources to coordination, yet which tasks actually require it for correctness remains unclear. The problem is acute in multi-agent AI systems, where coordination cost is directly measurable and can exceed the cost of the work itself. Distributed systems theory provides a precise criterion: coordination is required when a task specification is non-monotonic, meaning that as histories grow, new information can invalidate prior conclusions. Here we show that Thompson's classic taxonomy of interdependence maps to that criterion, yielding a decision rule for when coordination is required for correctness. We formalize the correspondence in a bridge theorem, apply the rule to 65 APQC workflows and (with a calibrated LLM) 13,417 O*NET tasks, and illustrate it in multi-agent AI simulations. Under our decompositions, 74% of workflows and 42% of O*NET tasks are monotonic, implying that up to 24-57% of coordination spending is unnecessary for correctness.

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