Three Impossibility Theorems for Universal AML Compliance in Zero-Knowledge Financial Systems

We prove three impossibility theorems establishing fundamental limits on universal AML compliance in zero-knowledge financial systems. T1 (Completeness Impossibility): no ZK compliance system achieves complete coverage of illicit transactions under rational adversarial behavior. T2 (Oracle Integrity Impossibility): no decentralized oracle network achieves integrity guarantees when state-level adversaries control oracle nodes — cryptographically valid compliance proofs can be semantically false by construction. T3 (Sovereignty Gap Impossibility): no voluntary international compliance framework achieves universal participation when sovereign defection is individually rational. These theorems are not engineering limitations addressable by better cryptography — they are structural properties of the compliance problem under adversarial conditions. Validated empirically against the Tornado Cash OFAC designation (T3) and the Lazarus Group / Ronin Bridge exploit (T2). The theorems characterize the residual attack surface that any compliance architecture must acknowledge and bound rather than claim to eliminate.