What question did this study set out to answer?

This research aims to model money laundering as a cost-minimization problem influenced by detection risks.

April 28, 20260 citationsOpen Access

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

Key Points

This research aims to model money laundering as a cost-minimization problem influenced by detection risks.
Developed a launderer's cost equation that considers operational overhead and detection risks.
Decomposed total costs into four components: overhead, expected loss, opportunity cost, and trust risk.
Evaluated the impact of KYC compliance on the cost structure of laundering strategies.
Identified a phase transition at a threshold amount of $5,600; below this, artisanal methods are preferred, above which ZK strategies are cost-efficient.
ZK compliance could reduce on-chain laundering volume by 65-80%, but artisanal methods remain prevalent.
Validated the model by showing significant drops in mixer deposits following regulatory actions.

Abstract

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).

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