Competitive Heresthetic Reachability: Strategic Dimension Creation, Alternative Preservation, and Counter-Manipulation

Political actors rarely manipulate a choice structure against a passive environment. Rivals can preserve threatened alternatives, restore capacity, create counter-dimensions, and carry current losers into the future because those alternatives may later become valuable. This paper develops a finite complete-information game in which a temporary controller and one or more strategic opponents alter both the majority tournament and the executable domain, with cardinal preferences over the full post-handoff consequence, action costs, residual resources, and possibly different tenure horizons. For finite durability windows the primary object is one common general-sum game, not a family rebuilt around a designated target. Its Equilibrium Heresthetic Reachability Correspondences are projections of a set-valued backward recursion that recovers exactly every subgame-perfect-equilibrium law over post-handoff consequences. Possible and robust reachability are the maximum and minimum durable-target probabilities over that set, so the target is selected endogenously under one payoff system. A continuation-option-value theorem characterizes decentralized preservation: in every pure preserving equilibrium,contributors form a minimal winning coalition whose members' continuation gains cover their private resource costs. Coordination can separate possible from robust reachability even when the physical technology is deterministic. A primitive voter-threshold and capacity specialization derives complementarity rather than assuming it. Order statistics of voter-level criterion thresholds determine which majority edges a new dimension reverses, and integer capacity stocks determine exact deletion costs. The paper gives necessary and sufficient conditions under which reshaping alone fails, erosion alone is infeasible, and some reshape-and-interdict route succeeds, then derives the exact least-cost defense decomposed intopreservation and creation, and shows separately when an affordable blocker is worth financing. A target-specific opposed-interest benchmark supplies a Shapley value, a probability-one predecessor kernel, and an exact security cost in min-max form. That object is an adversarial stress test, not a general-sum equilibrium prediction. The contribution is the integration of endogenous political preferences, dimension creation,option-preserving capacity choice, and persistent reachability in one strategic state.