Non-Newtonian Hydrodynamics of Decentralised Markets: A Theory of Sandwich Attacks, Diophantine Protection, and the Inverse Cascade on Automated Market Makers

We present a unified non-Newtonian hydrodynamic theory of cryptocurrency markets spanning centralised limit order books (CEXs) and automated market makers (DEXs). The central mathematical innovation is the extension of the financialNavier–Stokes equations to variable-viscosity fluids, where the effective viscosity νeff is not a constant but a function of the local gauge enstrophy density: νeff ∝ ⟨ξ2⟩. This extension captures the defining feature of automated market makers—slippage that grows with trade size—as a non-Newtonian constitutive relation.We prove four main theorems. First, centralised crypto exchanges with classical limit order books are natively quasi-2D flows supporting the inverse Kraichnan cascade, and Diophantine lattices of limit orders with golden ratio spacing provide optimal KAM protection against HFT-induced resonances. Second, constant-function automated market makers in their native form have effective dimensionality deff = 1and cannot support an inverse energy cascade. Third, concentrated liquidity protocols raise the effective dimensionality to deff = 2 when liquidity positions areplaced at Diophantine price intervals, enabling the inverse cascade and providing a hydrodynamic mechanism for the stabilisation of AMM pools. Fourth, and most significantly, we prove that sandwich attacks on AMMs are non-Newtonian shock fronts in the liquidity velocity field, governed by a Burgers-type equation with variable viscosity. The shock amplitude is amplified when the attacker’s frequency is rationally related to the pool’s natural frequency, and is suppressed—exponentially in the Diophantine distance—when the pool’s liquidity is distributed at golden ratio intervals.This last result provides a fundamentally new class of MEV protection: hydrodynamic suppression of sandwich attacks through the geometric design of liquidity pools, requiring no changes to consensus protocols, no private mempools, and no additional transaction costs. The protection is a direct consequence of the Diophantine geometry of the liquidity distribution and the non-Newtonian constitutive law of the AMM.The theory contains no adjustable parameters. The critical threshold Kcrit = 28 is the Lorenz homoclinic explosion. The optimal liquidity spacing is the golden ratio. The shock suppression factor is determined by the Bruno Diophantine distance between the attacker’s frequency and the pool’s natural frequencies. All predictions are testable against on-chain data from Uniswap v3, PancakeSwap, and centralised exchanges.