Paper: arXiv 2510.10171
Authors: Alexander McFarlane
Abstract
We derive a slippage-aware toxicity condition for on-chain liquidations executed via a constant-product automated market maker (CP-AMM). For a fixed (constant) liquidation incentive $i$, the familiar toxicity frontier $ν< 1/(1+i)$ tightens to $ν< 1/((1+i)λ)$ for a liquidity penalty factor $λ$ that we derive for both the CP-AMM and a generalised form. Using a dynamic health-linked liquidation incentive $i(h) = i(1 - h)$, we obtain a state-dependent bound and, at the liquidation boundary, a liquidity-depth-only condition $ν< 1/λ$. This reconciles dynamic incentives with the impact of the CP-AMM price and clarifies when dynamic liquidation incentives reduce versus exacerbate spiral risk.
Complexity vs Empirical Score
- Math Complexity: 5.5/10
- Empirical Rigor: 2.0/10
- Quadrant: Lab Rats — theoretically deep, empirically untested
Why this score: The paper presents a concise mathematical derivation extending toxic liquidation spiral conditions to dynamic incentives and CP-AMMs. While mathematically clear and conceptually novel for DeFi risk parameters, it completely lacks empirical backtesting, historical liquidation data analysis, or real-world simulation.
Research Flowchart
flowchart TD
A["Research Goal: Reconcile Dynamic Liquidation Incentives with AMM Slippage & Spiral Risk"] --> B["Inputs: CP-AMM Pool State, Collateral Price Drop (ν), Health Factor (h)"]
B --> C["Derive Liquidity Penalty Factor (λ) for CP-AMM & General AMMs"]
C --> D["Evaluate Toxicity Bounds:<br/>Static: ν < 1 / ((1+i)λ)<br/>Dynamic: i(h) = i(1-h)"]
D --> E["Key Outcome 1: Liquidation Boundary Condition Tightens to ν < 1/λ"]
D --> F["Key Outcome 2: Clarified Conditions Where Dynamic Incentives Mitigate vs Exacerbate Liquidation Spirals"]