Suppose a simple linear regression model $Y = \beta_0 + \beta_1 X + \epsilon$ is fitted using Ordinary Least Squares. If the vector of residuals $\mathbf{e}$ is orthogonal to the column space of the design matrix $\mathbf{X}$, which of the following is a necessary condition for the OLS estimate $\hat{\beta}$ to exist and be unique?