= Solution
Here the conserved total <angular momentum> is $\mathbf J_t=(0,0,1)$, while the <black-hole spin> magnitude remains $\sqrt3$. The hole again aligns with the positive $z$ direction in the persistent-<torque> regime. Thus
$$
\boxed{\mathbf J_{h,f}=(0,0,\sqrt3),\qquad
\mathbf J_{d,f}=(0,0,1-\sqrt3).}
$$
Since $1-\sqrt3<0$, the disk points in the negative $z$ direction and has magnitude $\sqrt3-1$. This realizes <counteralignment of a black hole and accretion disk> even though the hole itself is aligned with the conserved total vector. \b[The black hole and disk do not always finish with aligned spins.]
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