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Geodesic Execution Slippage: A Statistical Physics Framework for Cryptocurrency Liquidity Risk.

Ntebogang Dinah Moroke¹, Lebotsa Daniel Metsileng¹

¹Department of Statistics and Operations Research, Faculty of Economic and Management Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa.

Entropy (Basel, Switzerland)

|June 26, 2026

Summary

GEODEX models cryptocurrency transaction costs using geometric principles, improving prediction accuracy and providing early warnings for market instability. This novel approach enhances financial market intelligence for regulators and participants.

Keywords:

Curvature-Fragmentation Law Fisher information metric Riemannian manifold Wasserstein distance complex financial systems early warning signals econophysics geodesic execution slippage market microstructure persistent homology

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Area of Science:

Quantitative Finance
Computational Economics
Financial Econometrics

Background:

Traditional cryptocurrency transaction cost models are limited by flat geometry assumptions.
Execution costs are typically modeled as proportional fees, failing to capture complex market dynamics.

Purpose of the Study:

To introduce GEODEX, a novel framework for modeling cryptocurrency execution slippage.
To utilize geometric and topological methods for enhanced financial market analysis.

Main Methods:

Modeling execution slippage as geodesic arc length on a Fisher information manifold.
Employing a Markov-switching GARCH maximum-entropy model with a joint curvature-topological fragmentation alarm.
Analytically deriving and empirically validating the Curvature-Fragmentation Law.

Main Results:

GEODEX demonstrates competitive prediction error across five major cryptocurrencies (BTC, ETH, XRP, LTC, BCH).
Ablation studies confirm the unique contribution of geometric components (geodesic, topological data analysis, curvature).
The joint curvature-topological alarm provides timely warnings, preceding circuit breaker thresholds by a median of two days during crises.

Conclusions:

GEODEX offers a geometrically grounded approach to understanding cryptocurrency transaction costs and market dynamics.
The framework provides valuable, accessible liquidity intelligence supporting financial stability and regulatory oversight.
Supports Sustainable Development Goals 10 and 16 through enhanced market transparency and institutional strength.