and static clearing solutions will generally not coincide. In fact, the set of defaulting and solvent institutions can be altered by rearranging the timing of obligations. As such, using the static Eisenberg-Noe framework for stress testing may result in an incorrect assessment of the health of the financial system. The proofs of the main results are provided in the Appendix.

Static clearing systems {#sec:setting}
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We begin with some simple notation that will be consistent for the entirety of this paper. Let $x,y \in {\mathbb{R}}^n$ for some positive integer $n$, then $$x \wedge y = \left(\min(x_1,y_1),\min(x_2,y_2),\ldots,\min(x_n,y_n)\right)^{\top},$$ $x^- = -(x \wedge 0)$, and $x^+ = (-x)^-$. Further, to ease notation, we will denote $[x,y] := [x_1,y_1] \times [x_2,y_2] \times \ldots \times [x_n,y_n] \subseteq {\mathbb{R}}^n$ to be the $n$-dimensional compact interval for $y - x \in {\mathbb{R}}^n_+$. Similarly, we will consider $x \leq y$ if and only if $y - x \in {\mathbb{R}}^n_+$.

Throughout this paper we will consider a network of $n$ financial institutions. We will denote the set of all banks in the network by ${\mathcal{N}}:= \{1,2,\ldots,n\}$. Often we will consider an additional node $0$, which encompasses the entirety of the financial system outside of the $n$ banks; this node 