Lasso sign recovery under compatibility ($|{\beta }_k^0|>(1+c)\lambda s/{\varphi }^2$)

The fast-rate Lasso prediction bound under compatibility implies $\Vert {\hat{\beta }}_S-{\beta }_S^0{\Vert }_1\le (1+c)\lambda s/{\varphi }^2$. Each true coefficient larger in absolute value than this bound has the correct estimated sign. This conclusion alone does not ensure absence of false positives.