The Buckley–James estimator (BJE) is a classical extension of least squares for linear regression with right-censored responses. Because the Buckley–James estimating function is nonsmooth and piecewise linear, defining the BJE simply as a root of the estimating equation can be ill-posed: roots may fail to exist, may be non-unique, or may form flat regions that include uninformative candidates. This talk develops a well-posed definition of the BJE through a sequence of examples, each motivating a refinement from roots to zero crossings (ZC), then to strict zero crossings (SZC), and finally to a refined multivariate SZC based on sign changes and the geometry of connected zero-crossing components.