Whitepaper
The Zest Protocol CLMM whitepaper: the bin model, the deposit fee and the integer implementation on Stacks, with proofs.
Abstract
Concentrated liquidity lets a provider commit capital to a bounded price range. Zest CLMM, an automated market maker for Stacks, partitions liquidity into a fixed geometric grid of bins, each with its own bounded constant-product curve and fungible shares. Liquidity and price are derived from a bin’s reserves, retained fees compound into those reserves, and a deposit that changes a bin’s composition is charged the swap fee on the exchange implied by adding and immediately redeeming liquidity. The paper presents the model, proves its liquidity and valuation properties, and describes a Clarity implementation on 128-bit integers whose liquidity estimates err only downward, by at most 2⁻⁵⁶ of the exact value plus one frame-liquidity unit.
What the Paper Covers
| Section | Contents |
|---|---|
| Introduction | The three contributions: reserve-derived bins, the deposit fee and conservative integer execution |
| Related Work | Uniswap v3, Liquidity Book and DLMM, Maverick v2, Bitflow HODLMM, and loss-versus-rebalancing |
| Discrete Liquidity | Price intervals on a geometric grid, liquidity derived from reserves, and how much capital it concentrates |
| Swaps | Execution within a bin, fees and the liquidity provider share, and routing across bins |
| Liquidity Accounting | Shares, the exchange implicit in a deposit, deposit fees and share issuance, and private pools |
| Implementation on Stacks | Normalized price coordinates, conservative liquidity evaluation, exact multiword arithmetic and routes |
| Risks and Limitations | Risks for liquidity providers, traders and tokens, numerical limits, governance and review status |
| Appendices A to D | Proofs of the liquidity properties and integer bounds, the finite-word error bound, and route benchmarks |
Scope
The paper describes the Zest Protocol CLMM contracts at commit 258021b, which includes the fixes from the Clarity Alliance audit . The paper does not cover Liquidity Vaults, cross-chain bridging or off-chain route selection.
For how pools behave in practice, start with How Concentrated Liquidity Works. The contract functions are listed under Contracts.