= Solution
For the normalized standard <Gaussian density>,
$$
\nabla\gamma=-v\gamma,\qquad
\Delta\gamma=(|v|^2-d)\gamma,\qquad
\nabla\cdot(v\gamma)=(d-|v|^2)\gamma.
$$
The two terms cancel, so \b[the <Ornstein-Uhlenbeck Fokker-Planck equation> has <stationary density for a Fokker-Planck equation>]
$$
\boxed{\partial_t\gamma=0,\qquad
\Delta\gamma+\nabla\cdot(v\gamma)=0.}
$$
Equivalently its <Fokker-Planck probability current> $-\nabla\gamma-v\gamma$ vanishes identically. The normalization follows from the <Gaussian integral> in each coordinate.
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