we will not utilize this discrete-time result in this paper, we consider it important to discuss random events to more closely match reality. Further, this result will implicitly appear in the construction and analysis of the continuous-time Eisenberg-Noe formulation of the next section.

\[cor:discrete\] Consider the setting of Theorem \[thm:discrete\] where the random network parameters $(c,L)$ adapted to the filtered probability space $(\Omega,{\mathcal{F}},({\mathcal{F}}(t))_{t \in {\mathbb{T}}},{\mathbb{P}})$. If $c(s) \in {\mathcal{L}}_s^p({\mathbb{R}}^{n+1})$ and $L(s) \in {\mathcal{L}}_s^p({\mathbb{R}}^{(n+1) \times (n+1)}_+)$ for all times $s \leq t$ for some $p \in [0,\infty]$, then the unique clearing solution at time $t$ has finite $p$-norm, i.e., $V(t) \in {\mathcal{L}}_t^p({\mathbb{R}}^{n+1})$.

With the construction of the existence and uniqueness of the solution we now want to emphasize the *fictitious default algorithm* from [@EN01] to construct this clearing wealths vector over time. This algorithm is presented for the deterministic setting; if a stochastic setting is desired then Algorithm \[alg:discrete\] provides a method for computing a single sample path. We note that at each time $t$ this algorithm takes at most $n$ iterations. Thus with a terminal time $T$, this algorithm will construct the full clearing solution over ${\mathbb{T}}$ in $nT$ iterations.

\[alg:discrete\] Under the assumptions of Theorem \[thm:discrete\] in a deterministic 