  Let $Q$ be a quiver of $A_n$ type and $\mathbb{K}$ be an algebraically closed
field. A nilpotent endomorphism of a quiver representation induces a linear
transformation of the vector space at each vertex. Generically among all
nilpotent endomorphisms of a fixed representation $X$, there exists a
well-defined Jordan form of each of these linear transformations
$\operatorname{GenJF}(X)$, called the generic Jordan form data of $X$. A
subcategory of $\operatorname{rep}(Q)$ is Jordan recoverable if we can recover
$X$ up to isomorphism from its generic Jordan form data.
  There is a procedure which allows one to invert the map from representations
to generic Jordan form data. The subcategories for which this procedure works
are called canonically Jordan recoverable. We focus on the subcategories of
$\operatorname{rep}(Q)$ that are canonically Jordan recoverable, and we give a
combinatorial characterization of them.
