A CKM blind spot: probing $b$-column rescaling with kaons

CKM unitarity triangle constraints are insensitive to New Physics scenarios in which the $b$-column is uniformly rescaled. This is because B physics data over-constrain the angles of the (bd) unitarity triangle, but only calibrate its normalization. We identify this flat direction and derive model-independent constraints on the rescaling. We find that $|\varepsilon_K|$ already constrains the rescaling at the same level as the direct measurement of the $b$-column normalization, with current data allowing for ${\cal O}(4\%)$ deviations. Projected inputs promote the kaon sector to be the leading probe. A toy model employing mixing with a vector-like up-type singlet provides a proof of principle for a possible UV realization.