The Triffin Impossibility Theorem: Reserve Currency as an Adversarial Aggregation Channel

This paper proves the Triffin Dilemma as a theorem by embedding the reserve-currency system within the adversarial aggregation channel (AAC) framework. A reserve currency is formalized as an aggregation channel that must carry two signals — a credibility signal (the backing ratio) and a liquidity signal (the reserve-supply ratio) — through a single instrument (the currency's external balance). The fundamental structural constraint is that the product of the two signals equals R/G, the ratio of backing stock to global reserve demand, which is conserved independently of the deficit level. This hyperbolic constraint is the channel capacity bound. A monetary Nyquist theorem establishes a sharp phase transition at the Triffin threshold τ = c·ℓ. Below this threshold, a feasible interval of deficit levels satisfying both mandates exists and has width proportional to excess capacity. At the threshold, the feasible interval collapses to a single point. Above it, aliasing is forced: no deficit level can simultaneously satisfy both mandates, and the single-instrument channel cannot distinguish credibility-preserving from liquidity-providing monetary states. A Goodhart subsumption theorem proves that the positive feedback between reserve status and reserve demand accelerates threshold crossing: higher credibility attracts greater demand, which erodes the feasibility margin, making reserve-currency success self-undermining. A conservation identity proves that no institutional patch — including Special Drawing Rights, currency baskets, or multi-reserve arrangements — escapes the bound without genuinely expanding the channel architecture. A confidence dynamics theorem proves that once the Triffin threshold is crossed, the system enters a renewal trap: the credibility-restoring action and the liquidity-providing action are perfectly anti-correlated, and exit requires discontinuous regime change rather than marginal policy adjustment. A Bretton Woods phase-transition theorem characterizes the 1971 Nixon suspension of gold convertibility as the unique equilibrium response to threshold crossing, not a discretionary policy choice. These results place the Triffin impossibility alongside Arrow's theorem, the Cambridge Capital Controversy, Gibbard–Satterthwaite, Myerson–Satterthwaite, and the quantum no-cloning theorem as instances of a single conservation law governing adversarial aggregation channels.