The Launderer's Cost Equation: A Phase-Transition Model of Money Laundering Strategy Selection from Artisanal to Zero-Knowledge

We model money laundering as a cost-minimization problem under detection risk, formalizing the trade-off between two polar strategies: the ant plan (plan hormiga) — high-volume artisanal fragmentation using human couriers and informal networks — and ZK-native laundering via cryptographic privacy protocols. We derive the launderer's cost equation, decomposing total cost into four additive components: operational overhead, expected detection loss, opportunity cost of time, and counterparty trust risk. The equation reveals a phase transition at a critical amount threshold A*: below A* the ant plan dominates; above A* ZK strategies become cost-competitive through near-zero marginal cost and elimination of human counterparties. Under KYC bypass conditions, the ZK strategy dominates for amounts above approximately 5, 600. ZK-Sentinel-class mandatory compliance infrastructure shifts this cost structure by raising effective detection probability of ZK on-ramps, making the ZK channel economically irrational under honest oracle conditions. On-chain ZK compliance eliminates 65--80% of digital on-chain laundering volume but leaves the artisanal layer — 99% of operations by count, 45% by volume — structurally inaccessible to any cryptographic detection mechanism. Validated against the August 2022 OFAC designation of Tornado Cash (85% collapse in mixer deposits within 72 hours).