Paper: arXiv 2407.02496
Authors: Mark B. Richardson, Stefan Loesch
Abstract
The scope of this article includes the three preeminent descriptions of concentrated liquidity from Bancor (2020 and 2022), and Uniswap (2021), as well as three additional descriptions informed by trigonometric analysis of the same. The purpose of this contribution is to organize the seminal and derivative forms of this cornerstone DeFi technology, and algebraically and geometrically elaborate these descriptions to achieve an authoritative and near-exhaustive overview of the underlying theory powering the current state-of-the-art in decentralized exchange infrastructure. This material was created for the Token Engineering Academy Study Season 2024, a cohort-based online program scheduled for April-July 2024. The Study Season offers access to a bachelor-level online learning program, and complementary live tracks with the most influential practitioners and researchers in the sector - all provided as free, public goods.
Complexity vs Empirical Score
- Math Complexity: 6.0/10
- Empirical Rigor: 2.0/10
- Quadrant: Lab Rats — theoretically deep, empirically untested
Why this score: The paper provides a thorough, pedagogical derivation of concentrated liquidity mechanics using algebra and trigonometry based on Uniswap v3 and Bancor models. However, it is purely theoretical and educational, completely lacking empirical backtesting or real-world data validation.
Research Flowchart
flowchart TD
A["<b>Research Goal</b><br>Unified theory of Concentrated Liquidity in DeFi"] --> B["<b>Core Inputs</b><br>Bancor (2020/22) & Uniswap (2021) Models"]
B --> C["<b>Algebraic & Geometric Analysis</b><br>Elaboration & Trigonometric Mapping"]
C --> D["<b>Comparative Framework</b><br>Organize Seminal vs. Derivative Models"]
D --> E["<b>Key Outcome</b><br>Exhaustive Overview of DEX AMM Mechanics"]
D --> F["<b>Educational Output</b><br>Open-Access Resource for TE Academy 2024"]