Let $V$ be a finite set of observed variables. For each $v\in V$, let $(\mathcal X_v,\mathcal E_v)$ be a measurable state space, and let $X_v:(\Omega,\mathcal F,\mathbb P)\to(\mathcal X_v,\mathcal E_v)$ be a [random variable](/page/Random%20Variable). For $A\subset V$, write $X_A=(X_v)_{v\in A}$, let $(\mathcal X_A,\mathcal E_A)=(\prod_{v\in A}\mathcal X_v,\bigotimes_{v\in A}\mathcal E_v)$, and let $P=\mathbb P\circ X_V^{-1}$ be the observational law of $X_V$ on $(\mathcal X_V,\mathcal E_V)$. Let $G=(V,E)$ be a directed acyclic graph on the observed variables, where $E\subset V\times V$ and no edge has the form $(v,v)$. Write $x\sim_G y$ when either $(x,y)\in E$ or $(y,x)\in E$, so the skeleton of $G$ is the undirected graph with edge set $\{\{x,y\}:x\neq y\text{ and }x\sim_G y\}$. An unshielded collider of $G$ is a triple of distinct vertices $a,b,c\in V$ such that $(a,b),(c,b)\in E$ and $a\not\sim_G c$. Assume that $P$ is Markov with respect to $G$ and faithful to $G$: for all pairwise disjoint subsets $A,B,C\subset V$, $X_A \perp\!\!\!\perp X_B \mid X_C$ under $P$ if and only if $A$ and $B$ are d-separated by $C$ in $G$. Run the population PC algorithm with a perfect conditional-independence oracle for $P$ as follows. It starts from the complete undirected graph on $V$. In the skeleton-deletion phase, for each distinct pair $u,v\in V$, every conditioning set $S\subset V\setminus\{u,v\}$ is an admissible candidate, and the phase is exhaustive in the sense that it deletes $\{u,v\}$ whenever at least one such set satisfies $X_u\perp\!\!\!\perp X_v\mid X_S$ under $P$; when it deletes $\{u,v\}$, it records one oracle-positive set as $\operatorname{Sep}(u,v)$. In the collider phase, it orients each unshielded triple $a-b-c$ as $a\to b\leftarrow c$ exactly when $b\notin\operatorname{Sep}(a,c)$. It then applies the standard Meek orientation rules to closure, where Meek closure is understood as the sound and complete closure operation which, from a partially directed graph with the correct skeleton and exactly the unshielded colliders of a finite DAG Markov equivalence class, orients precisely the compelled edges and leaves precisely the reversible edges unoriented. The Markov equivalence class of $G$ is the set of directed acyclic graphs on $V$ with the same d-separation relations as $G$. The completed partially directed acyclic graph of a Markov equivalence class means the unique partially directed graph on $V$ whose skeleton is the common skeleton of the class, whose directed edges are exactly the edges oriented the same way in every DAG in the class, and whose undirected edges are exactly the reversible edges. Then the graph returned by the population PC algorithm is the completed partially directed acyclic graph of the Markov equivalence class of $G$.