Sign compatibility of LAR and Lasso

If every nonzero active coefficient has the sign of its residual score along the least angle regression path, the LAR active correlation invariant and inactive bounds give the Karush-Kuhn-Tucker conditions for the Lasso. A unique Lasso solution then equals the LAR path. Zero coefficients use a subgradient interval; literal sign equality with sign(0)=0 is not appropriate for a newly entering coefficient at a positive knot.