This paper examines the contemporary proliferation of sovereignty claims — by states, by non-state armed and corporate actors, and by popular movements — as symptoms of a single structural transformation rather than as political confusion. Reading four commissioned studies of Brazilian struggles (on the dismantling of the nation-state form, the courier movement and the crisis of trade unionism, territorial and food-sovereignty struggles, and the construction of Teia dos Povos), it argues that they converge on a shared diagnosis: the current crisis is not the onset of disorder but the end of an exceptional historical arrangement. The paper reconstructs the tradition that has long anticipated this outcome — the “peripherization thesis” running from René Zavaleta Mercado and Roberto Schwarz through Francisco de Oliveira and Paulo Arantes to Thiago Canettieri’s “peripheric condition” — according to which the periphery reveals capitalism’s most adequate operational logic, now generalizing across the system as a whole. It then identifies a limit internal to this tradition: powerful as a diagnostic, it lacks a language for the new political forms emerging under these conditions. Drawing on the framework of the Common Space of Organizations (CSO) — the three social logics of value, property, and affinity, and their alignment or misalignment — the paper reframes peripherization as a constructive social form rather than a deficit, and treats modernity as the local, temporary, and costly special case. On this basis it proposes reading popular sovereignty as self-determination: the capacity of movements to subordinate competing logics to collective decision without the institutional mediations that once shielded them.