Who really shaped the goal? Measuring AI's hidden influence in collaboration

When people work with AI to solve problems, credit for the final result is blurred—the AI may have subtly shaped what people wanted to achieve in the first place. This paper introduces CoTrace, a framework that traces goal-shaping contributions across dialogue turns by decomposing goals into verifiable requirements. Analysis of 638 real collaborations reveals models contribute modestly to high-level goals but heavily influence lower-level requirements and make indirect contributions users don't notice. A user study shows exposing people to this breakdown shifts their perceived AI contribution by 2 points on a 5-point scale, exposing systematic miscalibration.