Dude, Where's My State? Execution Information Requirements for Stateful Agents

Long-running agents must preserve information that later steps depend on. We introduce the Execution Information Requirement (EIR), a lower bound on the information that must remain accessible for correct completion under specified task and access conditions. We develop LACUNA, a framework that generates tasks with known dependencies and varies information demand, retention, and recovery separately from the difficulty of individual operations. Across four models, restoring a missing result raises accuracy on affected recall steps to 100%, compared with 0% for equal-length irrelevant information. Sufficient storage alone does not ensure success: retention policies can discard required results, errors can propagate through later computations, and agents can stop before recovery is complete. We also introduce VESTIGE, which uses agent execution traces to construct semantic graphs and measure information demand for real tasks. Across 72,562 software-agent trajectories, VESTIGE reveals a steeper distance-related decline in solution-relevant rereading for failed runs (RR 0.951 per distance doubling), while adjusted peak demand alone is not associated with failure. Together, these contributions support evaluating whether agents preserve and recover the information their tasks require.