This article introduces the concept of Spectral Sovereignty, a form of authority that operates through predictive systems without the presence of a subject. Unlike classical sovereignty, where command is anchored in an identifiable sovereign, spectral sovereignty emerges when structures compel compliance while concealing their source. Through examples including automated financial compliance, predictive scoring in health and credit systems, and decentralized DAO governance, the paper demonstrates how institutions increasingly enact authority in absence, generating obedience without command and legitimacy without presence. It develops a formal analytic framework to describe this spectral mode of governance and examines its consequences for accountability, traceability, and institutional responsibility within predictive societies. DOI Primary archive: https://doi.org/10.5281/zenodo.17063518 Secondary archive: https://doi.org/10.6084/m9.figshare.30061939 SSRN: Pending assignment (ETA: Q3 2025)