Delegating cognitive operations to generative artificial intelligence redistributes execution and raises a governance problem: where human direction of the task remains. We distinguish two routes. Specified delegation places that direction before execution, through instructions, constraints, or criteria that delimit the task. Iterative coproduction places it during production, through interventions that correct or redirect provisional outputs. To examine both routes, we use aggregate monthly cells from the Anthropic Economic Index for April and May 2026. The AEI distinguishes two modes of use: 1P API, which corresponds to direct traffic through Anthropic's API, and Claude.ai, which combines activity from Chat and Cowork. On this basis, we test whether a stronger work-related orientation of human-AI interaction is associated with more specified delegation within each mode and whether the increase in the iterative profile is greater in Claude.ai than in 1P API. The main analysis uses level-0 O*NET tasks and estimates how both profiles change when an eligible record reallocates ten percentage points from personal use to work-related use. The iterative comparison is restricted to 1,411 node-month pairs observed and eligible in both modes. Specified delegation increases by 2.76 points in 1P API (95% CI: [2.30, 3.22]) and by 1.45 in Claude.ai (95% CI: [0.93, 1.97]). On the common support, iterative coproduction changes by-0.30 points in 1P API and by 0.15 in Claude.ai, yielding a between-mode difference of 0.45 points (95% CI: [0.15, 0.75]). These findings show that work-related orien tation is associated with stronger traces of prior human direction and that the observable iterative response varies across modes of use. The article shifts attention from how much the AI executes to when human direction leaves observable traces.

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