= Quantum equilibrium equivariance
{title2=$\rho(t_0)=|\psi(t_0)|^2\ \Longrightarrow\ \rho(t)=|\psi(t)|^2$}
Both the ensemble position density transported by the <guidance equation> and the squared wave amplitude satisfy the same <probability continuity equation>. Subject to existence and uniqueness of that transport, an initial <Born rule> distribution stays a <Born rule> distribution. This is a preservation statement, not a derivation that every initial ensemble is already in equilibrium.
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