When Are Agents Irreplaceable? A Task-Level Theory of Acquisition and Computation

The success of an agent does not establish which capabilities the task requires. We introduce task-level resource diagnosis to determine when an agent is irreplaceable and when simpler configurations suffice. For each fixed-target task, we compare class-optimal risks with the interface and query budget held fixed across solver classes, allowing solvers in each class to redesign their solutions within the specified resource constraints. Exact evidence-coverage frontiers and processing risk bounds, together with successful agent constructions, establish conditions under which acquisition and enhanced computation are jointly necessary. Computation shapes both evidence acquisition and the answers derived from observations. Broader coverage need not reduce risk, and complete evidence can still require stronger computation. These mechanisms explain why tasks requiring the same agent capabilities can benefit from different resource investments. Controlled tasks test these predictions. Natural-language experiments show how interventions on acquisition and processing improve answer quality and affect resource use. The framework connects agent irreplaceability to task structure, identifying indispensable capabilities and guiding interventions on the limitations that prevent success.