A Proofs A.1 Proof of Theorem 2.2

Then statement 2 follows from statement 1 and the Banach fixed point theorem. A.5 Proof of Theorem 4.2 Due to (L3), it is clear that the derivative bounds (16) hold if and only if null null null null dN We created datasets from 6 AC power network test cases. We selected 6 test cases, listed in Table 2. Fortunately, branch resistances are typically small before this modification. We then computed the resulting power flows using the runpf function and recorded the results. Geometric data object, with the following attributes: edge_index, the edge index tensor, containing the topology from the test case.