geopoliticsCert
plain-language theorem explainer
geopoliticsCert constructs the canonical certificate asserting five geopolitical power categories together with vanishing recognition cost at equilibrium. Sociologists applying Recognition Science to state interactions would cite this instance when modeling balance of power. The definition is a direct structure constructor that supplies the cardinality theorem for the power types and the unit equilibrium lemma.
Claim. Let GeopoliticsCert be the structure requiring that the cardinality of geopolitical power types equals five and that the recognition cost satisfies $J(1)=0$. The instance geopoliticsCert satisfies the first requirement by the theorem establishing five power types and the second by the lemma proving $J(1)=0$.
background
The module treats international order as a recognition equilibrium between states, with balance of power corresponding to zero recognition cost $J=0$ and power transitions to positive $J$. Jcost is the recognition cost function imported from the Cost module; its unit value vanishes by the equilibrium theorem. GeopoliticalPower is the finite type whose cardinality is fixed at five, matching the five canonical categories (military, economic, diplomatic, cultural, technological) stated in the module documentation.
proof idea
This is a one-line structure constructor that directly supplies the five_powers field from the geopoliticalPowerCount theorem and the equilibrium field from the geopolitical_equilibrium theorem.
why it matters
The definition supplies the concrete GeopoliticsCert instance required by the sociology module, instantiating the five-power count and the $J=0$ equilibrium condition. It extends the Recognition Science equilibrium concept (Jcost 1 = 0) from the NonlinearDynamicsFromRS upstream result into the social domain, consistent with the module's framing of order as recognition equilibrium. No downstream theorems yet depend on it.
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