= Causally minimal nonfaithful Gaussian model
Let $E_1,E_2,E_3$ be <independent random variables> with the <standard normal distribution> and set $Z_1=E_1$, $Z_2=Z_1+E_2$, $Z_3=Z_2-Z_1+E_3$. The complete acyclic graph with edges $1\to2$, $1\to3$, $2\to3$ is causally minimal: deleting each edge imposes a false marginal or conditional independence. Yet $Z_1\perp Z_3$ because $Z_3=E_2+E_3$, so <faithfulness of a directed acyclic graph> fails. Nonzero structural coefficients alone do not ensure faithfulness.
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