Institutional structure can stabilize collective choice, but the structure is itself an object of collective choice: a coalition defeated under one arrangement may try to amend the arrangement. This paper does not claim to originate endogenous rule choice or to solve the unrestricted infinite regress. It asks a finite operational question, placing rule amendment together with verified criterion creation, alternative capacity, agenda choice, and strategic voting in one priced public state, with the operative constitution itself part of that state, and asks which post-amendment outcomes are possible or universal in subgame-perfect equilibrium and which are coalitionally secure. A finite closure theorem flattens every bounded amendment tower into a single rule-coded extensive form, and a set-valued recursion recovers every subgame-perfect equilibrium, including the global-consistency condition required for Markov compression. The flattening is explicit about its own limit: it identifies a fixed semantic interpreter that no finite model can endogenize, so the regress is stopped by exogenous interpretation rather than dissolved. The central result is an exact constitutional budgeted-core characterization. A target is coalitionally secure if and only if some installation route is affordable and every hostile coalition's pooled budget is strictly below its constitutional blocking price, where that price is the minimum, over terminal rule codes, of a shortest counter-amendment cost plus a local criterion-capacity blocking cost. The singleton-rule case reduces to the earlier two-player security price. Equilibrium possibility and coalition security remain distinct, since affordable opponents may fail to coordinate in an ordinary equilibrium, so no price-only formula is asserted for the possible set. Instrument invariance is stated precisely. Costed history isomorphism preserves all constitutional heresthetic equilibria and costed probabilistic bisimulation preserves globally consistent Markov equilibria, but equality of total manipulation prices alone does not, so the aggregate price is not a sufficient statistic. On a finite discounted stochastic domain, pure stationary equilibria and their recurrent regimes occupy semialgebraic cells. A pair of two-state games shows that contraction, prices, discounting, and budgets do not by themselves determine whether recovery or deterrence prevails, and resource symmetry alone does not confine equilibrium-possible outcomes to the top cycle, uncovered set, or Banks set. Pure equilibrium membership is PSPACE-complete for a succinct polynomial-horizon encoding and polynomial on an explicit tree. What remains open is stated narrowly: the resource and payoff frontier for history-dependent mixed equilibria when the amendment catalog itself can expand.
K. Fathi (Sat,) studied this question.