 Instantaneous Lorenz error growth at a zero-y crossing

At $y=0$, the symmetric Jacobian sum is ${\mathrm{diag}}_{\mathrm{block}}([[-2\sigma ,\sigma +r-z],[\sigma +r-z,-2]],-2b)$. Its planar largest eigenvalue is positive exactly under the displayed condition. Thus both $z<\sigma +r-2\sqrt{\sigma }$ and $z>\sigma +r+2\sqrt{\sigma }$ permit instantaneous error growth. The vertical direction initially contracts, but skew couplings can rotate errors later; this local criterion is not a claim of persistent growth along a trajectory. For $\sigma =10,r=28,z=26,b=3$, the eigenvalues are $4,-26,-6$ and the growing direction is $(1,2,0)/\sqrt{5}$.