When Concealed Links Cannot Be Recovered: A Structural Identifiability Bound and Evaluation Pitfalls in Offshore Leak Networks

Abstract

Leaks such as the Panama and Paradise Papers expose large networks of offshore entities, and they invite an obvious question for network learning. Can the relations these structures are built to hide---above all, who beneficially owns what---be recovered from the public part of the leak by link prediction? We argue that the answer is mostly no, and that the analyses which suggest otherwise are measuring the wrong thing. Our main result is a distribution-free identifiability bound. For any recovery rule that respects graph isomorphism, and that covers every topological link-prediction score together with every message-passing graph neural network, a concealed endpoint left isolated in the observed graph is interchangeable with its structural twins, so its hidden edge cannot be recovered above chance. Isolation is only the sharpest case. In general the ceiling on recovery is set by the size of a node's structural-indistinguishability class, for which the Weisfeiler--Leman colour class is a computable stand-in, and node degree is at best a loose proxy. On the full ICIJ Offshore Leaks graph (814K entities and 84K labelled beneficial-owner edges) a classifier-free, degree-controlled probe reproduces an exact $0.5$ floor for isolated owners, who make up $20.6\%$ of all owners, and a trained graph neural network lands on the same floor. Recovery climbs only as structural distinctiveness grows, and the floor reappears in every one of the five leaks. Along the way we document five evaluation traps. Each one makes a bound that cannot be beaten look beaten, and we give a short rule that avoids them. The practical upshot is to redirect effort from the hidden principal, which is close to unrecoverable, toward the machinery of concealment, and to spell out why fusing external data helps far less than one would hope.