Will AGI Accelerate Algorithmic Patriarchy? Digital Gender Circularity in the Generative AI Era

As generative AI systems become pervasive tools for knowledge work, a central socioeconomic question is whether their diffusion reduces inequality through broad-based productivity gains or reproduces existing hierarchies through unequal participation and control. We introduce \emph{digital gender circularity} as a measurable risk model for the generative AI era: digital gender inequality and offline gender inequality can co-evolve in feedback loops, so unequal access and skills shape who benefits from AI adoption, while AI-mediated labor markets and information systems can in turn reshape offline gender outcomes. We argue that the most policy-relevant inequality mechanisms may occur before downstream model audits, at the diffusion stage: who adopts, what uses are legitimized, and which institutions convert AI usage into rewards. This perspective reframes \emph{algorithmic patriarchy} as an institutional-diffusion phenomenon, not only a model-behavior problem. To make these dynamics testable, we propose a compact empirical agenda: (i) construct country-level indicators of generative AI diffusion (awareness, access constraints, intensity, and use-case mix), (ii) link diffusion parameters to established gender-development indices and pre-existing digital parity, and (iii) test whether earlier digital gender parity predicts faster convergence in AI usage and outcomes, versus divergence driven by skill, safety, and legitimacy barriers. We close with actionable measurement and governance implications for capability building, affordability, safety, and auditability so that productivity gains do not amplify entrenched inequality.