State Structure: Institutional Sedimentation of Continuation Slot Allocation Rules and the Conditions for State Formation

The State and the power field are two distinct structures. History offers many examples of highly concentrated power without a State — warlord regimes, tribal chieftaincies, criminal organizations. What they lack is not power, but a second-order structure above the power field: the institutional sedimentation of the continuation slot allocation rule itself, whereby the question “how is governance conducted” becomes regularized and solidified into a stable, independently transmissible structure. This chapter provides a formal criterion for State formation within a sedimentation field dynamics framework: a State emerges only when the power field deepens beyond an institutionalization threshold and the continuation slot allocation rule itself also undergoes sedimentation — a structural transition, not a quantitative change. Three results follow. First, PowerCore succession (elections, coups, dynastic replacement) does not equal State replacement; the continuity of a State is determined by the depth of its rule structure, not the strength of its current ruler. Second, historical disputes over whether a given polity constitutes “the same State” reduce to the question of which parts of the rule structure remained continuous and which were replaced. Third, State destabilization occurs when the Legitimation Core and the Enforcement Core undergo structural separation — a necessary precondition for revolution, not a sufficient one.