The problem TheEqualizer solves

Once Uniswap V4 is released, it will host a multitute of pools for the same tokens but with different hooks. This will lead to bunch of pools experiencing price deviations, allowing for swaps between them with low transaction costs due to flash accounting (all pools' tokens stored in a single contract).

However, the majority of these pools might not attract sufficient attention from solvers/arbitragers due to a lack of liquidity and fees not allowing to perform profitable trade. At the same time, having trades is crucial for these pools as they might use hooks for TWAP, rebalancing, and other purposes.

The proposed solution suggests discounting fee rates and distibuting only small share of arbitrage profit to arbitrager. It consists of two components:

• Discounted Fee Hook: allows setting discounted fee for Arbitrager who is using Arbitrage Router (aka TheEqualizer) to perform trades much sooner than any MEV actor. The fee can be reduced by 10x or even set to 0, enabling Arbitrage Router to fron-trun toxic arbitrage before it becomes possible for later
• Arbitrage Router: takes 4 essential arguments: amount, tradeDirection, pool0 and pool1 (one with actual and outdated prices). It performs trades and estimates the profit. In case of positive outcome, minor 10% share (can be lowered) goes as a bounty to the initiator, while the major 90% goes back to LPs utilizing .donate() function available in UniV4

As a result, most of the slippage still benefits Liquidity Providers by capturing LVR. Pool Managers gain from updated prices and triggered hooks, while Arbitragers able to perform arbitrage more frequently

Challenges we ran into

Main challenge was to develop router that is able to do proper calculations and distribute profit