Let $X$ be a second-countable Hausdorff smooth manifold, let $T^*X \setminus 0$ denote its cotangent bundle with the zero section removed, and let $P \in \Psi^m_{\mathrm{cl}}(X)$ be a properly supported scalar classical pseudodifferential operator acting on distributions $\mathcal{D}'(X)$. Let $p \in C^\infty(T^*X \setminus 0; \mathbb{R})$ denote the real homogeneous principal symbol of $P$ of degree $m$, and let $H_p$ denote the Hamilton vector field of $p$ with respect to the canonical symplectic structure on $T^*X \setminus 0$. Assume that $P$ is of real principal type, meaning that

\begin{align*} \operatorname{Char}(P) := \{(x,\xi) \in T^*X \setminus 0 : p(x,\xi) = 0\} \end{align*}

is a conic hypersurface and $H_p(\rho) \neq 0$ for every $\rho \in \operatorname{Char}(P)$.

For $v \in \mathcal{D}'(X)$, write $WF(v) \subset T^*X \setminus 0$ for the $C^\infty$ wavefront set of $v$, regarded as a closed conic subset. A null bicharacteristic of $P$ means a connected parametrized integral curve $\gamma: I \to \operatorname{Char}(P)$ of $H_p$, where $I \subset \mathbb{R}$ is an interval and $\gamma'(t) = H_p(\gamma(t))$ for all $t \in I$. A maximally extended null bicharacteristic in an open subset $O \subset \operatorname{Char}(P)$ means such a curve with image in $O$ that admits no proper extension as an integral curve of $H_p$ with image still contained in $O$.

For every $u \in \mathcal{D}'(X)$, the set

\begin{align*} WF(u) \setminus WF(Pu) \end{align*}

is a union of maximally extended connected null bicharacteristics of $P$ in

\begin{align*} \operatorname{Char}(P) \setminus WF(Pu). \end{align*}

Equivalently, if $\gamma: I \to \operatorname{Char}(P) \setminus WF(Pu)$ is an integral curve of $H_p$ and $\gamma(t_0) \notin WF(u)$ for some $t_0 \in I$, then $\gamma(t) \notin WF(u)$ for every $t \in I$.