This chapter interrogates the transformation of US global influence from material supremacy to algorithmic governance, revealing how political engineering, economic manoeuvring, and platform control converge into a new architecture of hegemony. It traces the operational evolution from kinetic dominance to cognitive orchestration and algorithmic pre-emption—mapping how power now operates through data infrastructures, predictive governance, and the codification of trust. The analysis moves beyond traditional geopolitics to theorise algorithmic power as a governance ecology, where political, economic, and ethical instruments intertwine in recursive feedback loops that both sustain and subvert hegemony. Through detailed case studies—Iraq (spectacle of control), Ukraine (anticipatory governance), and Venezuela (legitimacy engineering)—the chapter demonstrates the metamorphosis of American power from force projection to epistemic design. Integrating Realism, Idealism, HST, AICST, and Constructivism, it conceptualises hegemony as a cognitive-technical phenomenon sustained through algorithmic infrastructures and normative frameworks. Yet, this architecture faces mounting limits: technological saturation, epistemic rebellion, and quantum countermeasures herald a shift towards Hegemony 2.0, where legitimacy is rebuilt through ethical stewardship, transparency, and plural governance. The chapter concludes by situating the US algorithmic dominance within the emergent quantum order, where the contest for global leadership transcends information control to encompass the governance of uncertainty itself. It challenges readers to reconsider hegemony not as domination, but as ontological stewardship—an evolving struggle to harmonise technology, ethics, and cognition in a world where code has become the grammar of power.