This paper applies the structural supranational criterion to Economic and Monetary Union and the single currency. The supranational criterion holds that an entity is a supranational cascade attractor when its binding residue density spans jurisdictions so that no single jurisdiction's reversal dissolves the network, and it reads density as a multiplicative product of extent, depth, and interconnection in which a necessary component at near-zero nullifies the whole. The Euro is classified by outcome-independent markers. A single legal-tender currency that replaces the national currencies, the exclusive competence of the European Central Bank over euro-area monetary policy, and the absence of any provision for leaving the single currency supply maximal monetary depth. The Euro area supplies extent. The single settlement system, the banking union, and the stability mechanism supply interconnection. The combination is a high-density monetary attractor. The binding residue is monetary, while the fiscal rules are a low-depth layer whose repeated breach does not dissolve the monetary union, so the attractor does not rest on the fiscal component. Reversal-resistance is tested within case against the sovereign-debt crisis, the prospect of a member's exit, and the national-court challenges to the crisis instruments, all of which the monetary union absorbed, and the supranational criterion discriminates against a voluntary monetary-coordination contrast that retained reversal-flexibility. The same residue density that makes the Euro reversal-resistant attenuates the capacity of a national electorate to reverse its monetary conditions through a vote, so the constraint on monetary sovereignty is read as the accountability-face of reversal-resistance. The reading is structural and is offered alongside the existing debate, not as a verdict within it.