Constructing and Validating an Agent-Based Simulator for Uniswap v3 Concentrated Liquidity

We construct a quantitatively interpretable agent-based simulator of a Uniswap v3concentrated-liquidity pool and validate it against six months of Ethereum mainnet datafor the WETH/USDC 5 bps pool. The simulator represents liquidity providers by finite tickranges, executes swaps with the square-root price update of concentrated liquidity, removespositions through burns, and allocates fees only to active liquidity. Every calibrated param-eter admits a market interpretation: the initial price fixes the pool state; tick spacing definesthe admissible range grid; the fee tier governs LP income; the training-derived range widthsand sizes, together with a nested range ladder and a periodically re-centred core sleeve,control capital concentration; and a conditional Student-t jump diffusion governs aggregateorder flow.The empirical sample comprises 181 daily OHLCV bars from 2026-01-22T00:00:00 UTCto 2026-07-21T00:00:00 UTC, with recorded dollar volume of approximately $24.79 billion,together with the complete indexed mint/swap/burn stream. Calibration is chronological:price-process and structural LP parameters are fit on the first 120 days and frozen for a 61-day holdout evaluated over 6 independent paths. The calibrated model uses 8 compressedevent slots per daily bar, multi-LP mint bundles (mean size 12), empirically informed widths,a core sleeve re-centred every 8 slots, state-dependent burns, and LP refreshes. The diffusionscale is daily and is converted to slot variance by the square-root time rule; slot and dailysupport caps prevent a single compressed event from creating an implausible price jump.Diffusion scale, degrees of freedom, jump probability and jump scale are s = 0.028, ν = 3.5,λ = 0.500% and σJ = 0.08.Out of sample, the pooled daily log-return standard deviation is 0.0301 against 0.0292empirically, while the simulated and empirical mean high-low ranges are 0.0291 and 0.0411,respectively, and excess kurtosis is 3.6994 versus 3.4888. Protocol diagnostics remain atfloating-point precision for the concentrated-liquidity invariant. Distributional distances ona representative path are KS = 0.1000 and Wasserstein = 0.0058. We report an explicitbootstrap ablation and a fixed-time liquidity-by-tick comparison (correlation 0.8568). Thesimulator is therefore a mechanistic baseline rather than a price-forecasting engine: everystate transition preserves the Uniswap v3 equations, while remaining volatility and inactive-liquidity gaps are stated explicitly.