Entry knot in least angle regression (${\lambda }^{\mathrm{hit}}$)

On a segment starting at residual-score level $t$, an inactive score evolves as $c_j-h{a}_j$ while the active level is $t-h$. Solving $c_j-h{a}_j=\pm (t-h)$ gives distances $(t-c_j)/(1-a_j)$ and $(t+c_j)/(1+a_j)$. The smallest positive admissible distance determines the next entry; reaching level zero ends the algorithm.