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—slippagethat grows with trade size—as a non-Newtonian constitutive relation.We prove five main theorems. First, centralised crypto exchanges with classical limit order books are natively quasi-2D flows supporting the inverse Kraichnan cas-cade, 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 are placed at Diophantine price intervals, enabling the inverse cascade. Fourth, we prove thatsandwich attacks on AMMs are non-Newtonian shock fronts governed by a Burgers equation with variable viscosity, and that their amplitude is suppressed exponentially in the Bruno Diophantine distance when the pool’s liquidity is distributed at golden ratio intervals. Fifth, and most significantly, we formulate the sandwich attack as a problem of optimal control in a non-Newtonian financial fluid. The attacker’s Lagrangian couples a direct Burgers equation (shock formation) with an adjoint equation (value wave propagation backward in time), linked by a terminalcondition at the victim’s execution. We prove a Diophantine destruction theorem: in a pool with golden ratio liquidity spacing, the non-Newtonian term in the adjoint equation becomes violently oscillatory, causing Anderson localisation of the value wave. The conjugate field is suppressed exponentially, the optimality conditions degenerate, and no finite optimal attack amplitude exists. The sandwich attack is rendered economically unviable—not merely reduced in profitability, but mathematically eliminated as an optimal strategy.We further demonstrate that this mechanism embodies a principle of geometric information control: information in financial markets is a physical wave governed by the non-Newtonian Burgers equation, and its propagation can be blocked not bycryptographic protocols but by the Diophantine geometry of the liquidity distribution. This shifts the paradigm of MEV protection from the information layer to the hydrodynamic layer.Extending the analysis to political economy, we apply the hydrodynamic diagnostic framework to the contemporary Russian economy, identifying institutional intermediaries, deficit beneficiaries, and speculative capital as the dominant parasitic structures threatening systemic stability. We propose a four-point Diophantine immune programme: sovereign blockchain settlement infrastructure, irrational filtering of state subsidies, differential viscosity reduction for the productive sector,and entropy taxation of speculative capital.The theory contains no adjustable parameters. The critical threshold Kcrit = 28is the Lorenz homoclinic explosion. The optimal liquidity spacing is the golden ratio.The shock suppression factor is determined by the Bruno Diophantine distance. All predictions are testable against on-chain data from Uniswap v3, PancakeSwap, and centralised exchanges.