improve abstract flow

Author: euler-mab

.DS_Store

@@ -40,18 +40,22 @@
 \maketitle
 
 \begin{abstract}    
-    EulerSwap is an Automated Market Maker (AMM) that uses unique features of Euler lending vaults to dramatically magnify capital efficiency using leverage. Unlike traditional AMMs that require fragmented liquidity pools, EulerSwap enables a single, cross-collateralized vault to provide liquidity across multiple asset pairs simultaneously, maximising capital efficiency and scaling liquidity across DeFi. Using the Ethereum Vault Connector (EVC), EulerSwap allows market makers to borrow the out token of a swap using the in token as collateral, unlocking deep liquidity without requiring large static deposits. This liquidity-sharing model allows EulerSwap to achieve up to 40x the liquidity depth of traditional AMMs, efficiently repurposing idle assets for optimal capital utilisation. At the core of EulerSwap is a highly customisable AMM curve that governs swap exchange rates, ensuring deep, just-in-time liquidity while dynamically incentivising market balance. By combining on-demand borrowing, shared liquidity, and flexible AMM mechanics, EulerSwap eliminates inefficiencies in existing liquidity provisioning, offering superior depth, reduced costs, and greater control for liquidity providers.
+EulerSwap is an Automated Market Maker (AMM) that improves capital efficiency using Euler lending vaults. Unlike traditional AMMs that fragment liquidity across multiple pools, EulerSwap allows a single, cross-collateralised vault to support multiple asset pairs at once. Through the Ethereum Vault Connector (EVC), market makers can borrow the out token of a swap using the in token as collateral, unlocking deep liquidity. This model enables up to 40x the liquidity depth of traditional AMMs by making idle assets more efficient. At its core, EulerSwap uses a flexible AMM curve to optimise swap pricing, ensuring deep liquidity while maintaining market balance. By combining on-demand just-in-time liquidity, shared liquidity across pools, and customisable AMM mechanics, EulerSwap reduces inefficiencies in liquidity provision, offering deeper markets, lower costs, and greater control for liquidity providers.
 \end{abstract}
 
 \section{Introduction}
 
-EulerSwap enhances trade execution by increasing the size of swaps that can be serviced compared to traditional AMMs. This is made possible by combining a novel AMM curve with the advanced \href{https://docs.euler.finance/developers/evc/keyConcepts?_highlight=operator#batch-operations}{check deferrals} and \href{https://docs.euler.finance/developers/evc/keyConcepts?_highlight=operator#operators}{operator} features of the Ethereum Vault Connector (EVC). Market makers supply an initial amount of liquidity to a `swap account' which can then be amplified through borrowing. Specifically, when a user swaps an `in token,' EulerSwap borrows the corresponding `out token,' using the `in token' as collateral. Later, when a swap occurs in the reverse direction, the incoming `in token' repays the outstanding loan, and any excess collateral is returned as the `out token,' effectively closing the position. This leveraged approach significantly increases the available liquidity provided by EulerSwap and multiplies swap fees. It is somewhat analogous to MEV bots that provide just-in-time single-tick liquidity to Uniswap v3 in order to capture fees on large trades.
+EulerSwap is a novel Automated Market Maker (AMM) that increases capital efficiency and liquidity depth beyond traditional AMMs. By leveraging Euler lending vaults and just-in-time liquidity provisioning, EulerSwap enables market makers to service significantly larger swaps while reducing the need for fragmented liquidity pools.
 
-Beyond individual swap accounts, EulerSwap takes capital efficiency further by taking advantage of Euler's modular design to allow multiple swap accounts to be built on top of the same lending vaults. This means that the same idle liquidity inside a single vault can provide depth for swaps across multiple asset pairs simultaneously. Much like Curve’s 3pool, but generalised to any number of asset pairings, a USDC vault could provide deep liquidity for 10+ correlated assets without requiring separate liquidity pools for each.
+This is achieved through a combination of advanced liquidity mechanisms and customisable AMM curves. Unlike conventional AMMs that require separate liquidity pools for each asset pair, EulerSwap utilises a single, cross-collateralised vault to support multiple asset pairs simultaneously. When a user initiates a swap, EulerSwap borrows the required out token against the in token as collateral using the Ethereum Vault Connector (EVC), dynamically scaling liquidity without requiring large static deposits.
 
-As illustrated in Figure \ref{fig:fig1}, EulerSwap’s exchange rates are governed by a highly customisable AMM curve which incentivises swappers to maintain market maker positions in balance over time. The EulerSwap AMM curve is a novel construction blending constant-sum and constant-product models, allowing swap account creators to tailor their AMM parameters. Like \href{https://berkeley-defi.github.io/assets/material/StableSwap.pdf}{Stableswap}, it supports concentrated liquidity for correlated assets, as well as \href{https://app.uniswap.org/whitepaper.pdf}{Uniswap v2}-style distributed liquidity for uncorrelated pairs. However, unlike those more traditional AMMs, EulerSwap allows asymmetric liquidity deposits, where different amounts of liquidity can be added to each side of the pool, and single-sided liquidity concentration, enabling deeper concentration of liquidity on one side of the pool relative to the other. This enables it to simulate the behaviour of atypical AMM protocols, like the MakerDAO \href{https://mips.makerdao.com/mips/details/MIP29}{Peg Stability Module} (PSM).
+This liquidity-sharing model increases capital efficiency, allowing EulerSwap to achieve up to 40x the liquidity depth of traditional AMMs. The integration of \href{https://docs.euler.finance/developers/evc/keyConcepts?_highlight=operator#batch-operations}{check deferrals} and \href{https://docs.euler.finance/developers/evc/keyConcepts?_highlight=operator#operators}{operator features} further enables market makers to automate liquidity provisioning and optimise capital usage.
 
-For end-users, EulerSwap functions like a typical Uniswap-style interface. However, behind the scenes, it incorporates advanced mechanisms such as borrowing and repaying, custom pricing curves, and dynamic liquidity provisioning. The main target audience for liquidity providers in EulerSwap AMMs are professional market makers, token issuers, and other DAOs, whilst the main target audience for swappers are leverage traders on Euler, aggregators, intent solvers, and MEV bots.  
+Beyond individual swap accounts, EulerSwap enhances liquidity further by allowing multiple swap accounts to operate within the same lending vault. This modular design ensures that idle liquidity is repurposed efficiently across multiple trading pairs. Much like Curve’s 3pool, but generalised to any number of asset pairings, a USDC vault could provide deep liquidity for 10+ correlated assets without requiring separate liquidity pools for each.
+
+EulerSwap’s exchange rates are governed by a highly customisable AMM curve (illustrated in Figure \ref{fig:fig1}), which dynamically adjusts incentives to maintain market balance. Unlike traditional AMMs that use constant-sum or constant-product formulas, EulerSwap’s curve allows for asymmetric liquidity deposits and single-sided concentration. This flexibility enables it to simulate the behaviour of atypical AMM protocols, such as the MakerDAO \href{https://mips.makerdao.com/mips/details/MIP29}{Peg Stability Module} (PSM).
+
+For end-users, EulerSwap functions like a typical Uniswap-style interface. However, behind the scenes, it incorporates advanced mechanisms such as dynamic borrowing and repaying, customisable pricing curves, and shared liquidity provisioning. The primary target audience for liquidity providers includes professional market makers, token issuers, and DAOs, while swappers include leverage traders on Euler, aggregators, intent solvers, and MEV bots. 
 
 \section{Example}