Generative AI compresses within-task skill differences while shifting economic value toward concentrated complementary assets, creating an apparent paradox: the technology that equalizes individual performance may widen aggregate inequality. We formalize this tension in a task-based model with endogenous education, employer screening, and heterogeneous firms. The model yields two regimes whose boundary depends on AI's technology structure (proprietary vs. commodity) and labor market institutions (rent-sharing elasticity, asset concentration). A scenario analysis via Method of Simulated Moments, matching six empirical targets, disciplines the model's quantitative magnitudes; a sensitivity decomposition reveals that the five non-$Δ$Gini moments identify mechanism rates but not the aggregate sign, which at the calibrated parameters is pinned by $m_6$ and $ξ$, while AI's technology structure ($η_1$ vs. $η_0$) independently crosses the boundary. The contribution is the mechanism -- not a verdict on the sign. Occupation-level regressions using BLS OEWS data (2019--2023) illustrate why such data cannot test the model's task-level predictions. The predictions are testable with within-occupation, within-task panel data that do not yet exist at scale.