67 Commits

Author SHA1 Message Date
tim
f7a53295f7 started CREATE2 work and abandoned it 2025-11-11 12:28:52 -04:00
tim
46e38ec996 callback-style funding option 2025-11-11 00:21:18 -04:00
tim
64c2245f25 working() wasnt working 2025-11-10 22:32:44 -04:00
tim
74daea17d7 PartyInfo.working(); DeployMock/Sep LP token amount fix 2025-11-10 16:31:51 -04:00
tim
89f4307ca0 PartyInfo.working(); DeployMock/Sep LP token amount fix 2025-11-10 16:31:43 -04:00
tim
a08a928f7f rename to PartyInfo; README fees 2025-11-07 16:18:00 -04:00
tim
ff9ed674f9 sepolia redeploy 2025-11-06 16:42:40 -04:00
tim
de108cc1e4 price() and poolPrice() fixes 2025-11-06 15:04:01 -04:00
tim
2b941e0969 sepolia redeploy 2025-11-04 17:20:22 -04:00
tim
dc2e186331 additive fees; burnSwapAmounts fix 2025-11-04 16:58:16 -04:00
tim
590acdd4dc Sepolia redeployment 2025-10-31 14:05:30 -04:00
tim
89e67ba69b cached pair fees 2025-10-31 12:32:05 -04:00
tim
dd9b7474a6 removed state.nAssets 2025-10-29 19:35:41 -04:00
tim
20758cfb35 per-asset fees 2025-10-29 18:22:23 -04:00
tim
86410c9a91 burnSwap outputIndex/token naming fix 2025-10-28 12:17:01 -04:00
tim
5c5a000961 whitepaper rendering fix 2025-10-27 17:54:44 -04:00
tim
f475ea0894 fix for anvil 1.4.x 2025-10-27 17:10:18 -04:00
tim
4b1ef01b8b LICENSE.txt 2025-10-27 16:24:41 -04:00
tim
687d7f9be0 introduction=>README.md 2025-10-27 16:19:21 -04:00
tim
cb72042998 sepolia redeploy 2025-10-27 15:16:08 -04:00
tim
015fe95284 sepolia redeploy 2025-10-27 11:55:26 -04:00
tim
ba08da2fca computed bases 2025-10-25 18:18:18 -04:00
tim
2972152e58 ETH-USDC pool_design; uni4 quotes refactor 2025-10-24 17:06:59 -04:00
452b28d165 package log for get_quotes 2025-10-24 17:45:29 +00:00
tim
33aadd333e pool_design.py 2025-10-24 01:17:40 -04:00
tim
9796a4345f pool_design.py 2025-10-23 17:29:21 -04:00
c5be9a3aee comment update 2025-10-23 21:27:43 +00:00
8dbdcfa4c6 Update adhoc_scripts/get_quotes.js 2025-10-23 21:24:38 +00:00
68db51a560 Add adhoc_script/swap_sim.js 2025-10-23 21:23:45 +00:00
tim
083773b232 signature upload; Sepolia deployment files 2025-10-23 14:51:03 -04:00
tim
2e61235b68 admin can change protocol fee address 2025-10-22 11:04:11 -04:00
tim
903f65327a Sepolia redeployment 2025-10-21 15:28:38 -04:00
tim
538f778f51 event changes: SwapMint/BurnSwap replace rather than augment the regular Mint/Burn events; All swapping events have lpFee and protocolFee 2025-10-21 14:42:40 -04:00
tim
11ae6f2a4b Sepolia redeploy 2025-10-20 18:21:50 -04:00
tim
316da25f5b Kill event; mock fix 2025-10-20 13:51:03 -04:00
tim
12fc43f999 flash loan initiator fix 2025-10-20 12:25:30 -04:00
tim
52c923baee changed basis to be different than decimals in a couple mock pools 2025-10-20 12:15:58 -04:00
tim
b64f5f6648 contract size fix 2025-10-19 15:46:41 -04:00
tim
d55be28cba ownership & killable 2025-10-19 13:35:33 -04:00
tim
5aa0032be0 bin/mock slow 2025-10-16 19:01:58 -04:00
tim
55306dff9c deployed to Sepolia 2025-10-16 16:17:11 -04:00
tim
e948067167 deployed to Sepolia; liqp-deployments.json 2025-10-16 16:16:41 -04:00
tim
38371614fc mock sets up three pools including a stablecoin pair pool and a pool with native wrapper token 2025-10-15 14:55:15 -04:00
tim
d9e6191d6e foundry.lock 2025-10-15 11:32:51 -04:00
tim
ead004d631 styling consistency 2025-10-15 11:19:36 -04:00
tim
7ac4cdc8f6 native currency fixes 2025-10-14 21:13:38 -04:00
tim
96535ed005 native currency fixes 2025-10-14 20:54:15 -04:00
tim
308227f251 autowrap; sendAmounts() restored 2025-10-14 19:59:38 -04:00
tim
eab01554e1 more gas optimization; protocol fee enabled by default in tests 2025-10-14 14:53:22 -04:00
tim
dd009cb561 raw gas data checked in 2025-10-14 12:51:38 -04:00
tim
fb6455f7bf IPartyPoolViewer 2025-10-13 15:17:42 -04:00
tim
878617c483 foundry.toml update for [profile.lint] 2025-10-13 12:21:32 -04:00
tim
1ea30cfd8c whitepaper updates 2025-10-08 12:07:19 -04:00
tim
923d9b93e7 removed tax coin support 2025-10-07 17:09:24 -04:00
tim
12957aaa51 flashLoan gas test 2025-10-07 15:57:04 -04:00
tim
457385e692 flashLoan protocol fee 2025-10-07 15:46:51 -04:00
tim
2d45296406 DeployMock creates viewer 2025-10-07 15:02:43 -04:00
tim
104c279123 deployable sizes 2025-10-07 14:50:36 -04:00
tim
98e80ab6ca delegated reentrancy lock 2025-10-07 14:37:44 -04:00
tim
ef039aa57e flashLoan rewritten as ERC-3156 2025-10-07 14:12:27 -04:00
tim
677ce4886c PartyPoolView 2025-10-07 12:36:24 -04:00
tim
20af14c872 proxied swapToLimit 2025-10-06 17:38:47 -04:00
tim
63f6e66d08 PartyPoolBalancedPair as subclass 2025-10-06 16:09:34 -04:00
tim
0049d27c90 removed console logs 2025-10-03 13:50:41 -04:00
tim
b126c52c7c swapMintImpl moved into mintImpl 2025-10-03 13:42:28 -04:00
tim
2e675bceb9 ERC functionality split into internal/external 2025-10-03 12:48:45 -04:00
tim
269236cfba whitepaper rough draft 2025-10-03 12:14:13 -04:00
140 changed files with 5563 additions and 2271 deletions

22
.gitignore vendored
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@@ -1,14 +1,14 @@
cache/
out/
/cache/
/out/
chain.json
/log/
/.env
/.env-*
/.idea/
package-lock.json
/broadcast
docs/
log/
.env
.idea
*secret*
# Ignores development broadcast logs
!/broadcast
/broadcast/*/31337/
/broadcast/**/dry-run/
# This file is only used by DeployMock
/liqp-deployments.json

3
LICENSE.txt Normal file
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Copyright ©2025 Dexorder LLC. All rights reserved.
No license is provided. This source code is viewable for verification purposes only.

96
README.md Normal file
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# Introduction
[Liquidity Party](https://liquidity.party) is a new game-theoretic multi-asset AMM based on this research paper:
[Logarithmic Market Scoring Rules for Modular Combinatorial Information Aggregation](https://mason.gmu.edu/~rhanson/mktscore.pdf) (R. Hanson, 2002)
Our formulation and implementation is described in the [Liquidity Party whitepaper.](doc/whitepaper.md)
A Logarithmic Market Scoring Rule (LMSR) is a pricing formula for AMM's that know only their current asset inventories
and no other information, naturally supporting multi-asset pools.
Compared to Constant Product markets, LMSR offers:
1. Less slippage than Constant Product for small and medium trade sizes
2. N-asset pools for trading long-tail pairs in a single hop
3. Lower fees (smaller spread)
## Deeper Liquidity
According to game theory, the initial price slope of a Constant Product AMM is too steep, overcharging takers
with too much slippage at small and medium trade sizes. LMSR pools offer less slippage and cheaper
liquidity for the small and medium trade sizes used by real traders.
## Multi-asset
Naturally multi-asset, Liquidity Party altcoin pools provide direct, one-hop swaps on otherwise illiquid multi-hop pairs. Pools will quote any pair combination available in the pool:
| Assets | Pairs | Swap Gas | Mint Gas |
|-------:|------:|---------:|----------:|
| 2 | 1 | 131,000 | 143,000 |
| 2* | 1 | 118,000 | 143,000 |
| 10 | 45 | 142,000 | 412,000 |
| 20 | 190 | 157,000 | 749,000 |
| 50 | 1225 | 199,000 | 1,760,000 |
| 100 | 4950 | 269,000 | 2,684,000 |
\* Stablecoin pair pool optimization
Liquidity Party aggregates scarce, low market cap assets into a single pool, providing one-hop liquidity for exotic pairs without fragmenting LP assets. CP pools would need 190x the LP assets to provide the same pairwise liquidity as a single 20-asset Liquidity Party pool, due to asset fragmentation.
## Lower Fees
Since market makers offer the option to take either side of the market, they must receive a subsidy or charge a fee (spread) to compensate for adverse selection (impermanent loss). By protecting LP's against common value-extraction scenarios, LMSR pools have a reduced risk premium resulting in lower fees for takers.
### Minimized Impermanent Loss
All AMM's suffer from Impermanent Loss (IL), also known as adverse selection or toxic order flow. Liquidity
Party uses game theory to minimize IL for LPs, by charging lower fees to small legitimate traders and
higher fees to large adversarial traders during market dislocations. This means a higher effective rate
for LP's and cheaper swaps for legitimate small traders.
Liquidity Party swaps guarantee a bounded maximum loss to LP's of `κ\*S\*ln(N)` where `κ` is
the pool's liquidity parameter, `S` is the total size of the pool, and `N` is the
number of assets in the pool.
### No Intra-Pool Arbitrage
Other multi-asset systems can provide inconsistent price quotes, allowing arbitragers to
extract value from LP's by _trading assets inside the same pool against each other._ With Liquidity
Party, no intra-pool arbitrage is possible, because the mathematics guarantee fully consistent price
quotes on all pairs in the pool.
# Installation
1. Install [Foundry](https://getfoundry.sh/) development framework.
2. Update dependencies with `forge install`
3. Run `bin/mock` to launch a test environment running under `anvil` on `localhost:8545`. The mock environment will create several example pools along with mock ERC20 tokens that can be minted by anyone in any amount.
# Integration
Deployment addresses for each chain may be found in `deployment/liqp-deployments.json`, and the `solc` output including ABI information is stored under `deployment/{chain_id}/v1/...`
The primary entrypoint for all Liquidity Party actions is the [PartyPlanner](src/IPartyPlanner.sol) contract, which is a singleton per chain. The `PartyPlanner` contract not only deploys new pools but also indexes the pools and their tokens for easy metadata discovery. After a pool is created or discovered using the `PartyPlanner`, it can be used to perform swaps, minting, and other actions according to the [IPartyPool](src/IPartyPlanner.sol) interface. Due to contract size limitations, most view methods for prices and swaps are available from a separate singleton contract, [PartyInfo](src/IPartyInfo.sol).
# Implementation Notes
## Non-upgradable Proxy
Due to contract size constraints, the `PartyPool` contract uses `DELEGATECALL` to invoke implementations on the singleton [PartyPoolSwapImpl](src/PartyPoolSwapImpl.sol) and [PartyPoolMintImpl](src/PartyPoolMintImpl.sol) contracts. This proxy pattern is NOT upgradable and the implementation contract addresses used by the pool are immutable. Views implemented in `PartyInfo` have no delegation but simply accept the target pool as an argument, calculating prices etc. from public getters.
## Admin-Only Deployment
`PartyPlanner` allows only the admin to deploy new pools. This decision was made because Liquidity Party is a new protocol that does not support non-standard tokens such as fee-on-transfer tokens or rebasing tokens, and the selection of the `kappa` liquidity parameter is not straightforward for an average user. We hope to offer a version of Liquidity Party in the future that allows regular users to create their pools.
## Killable Contracts
PartyPools may be "killed" by their admin, in which case all swaps and mints are disabled, and the only modifying function allowed to be called is `burn()` to allow LP's to safely withdraw their funds. Killing is irreversible and intended to be used as a last-ditch safety measure in case a critical vulnerablility is discovered.
## Fee Mechanisms
Each asset in the pool has a fee associated with it, which is paid when that asset is involved in a swap.
The fee for a swap is the input asset fee plus the output asset fee, but this total fee percentage is taken only from the input amount, prior to the LMSR calculation. This results in more of the input asset being collected by the pool compared to the value of the output asset removed. In this way, the LP holders accumulate fee value implicitly in their prorata share of the pool's total assets.
For a swap-mint operation, only the input asset fee is charged on the input token. For a burn-swap, only the output asset fee is charged on the output token.
Flash loans are charged a single fee, the flash fee, no matter what asset is loaned.
Protocol fees are taken as a fraction of any LP fees earned, rounding down in favor of the LP stakers. Protocol fees accumulate in a separate account in the pool until the admin sends a collection transaction to sweep the fees. While protocol fees are waiting to be collected, those funds do not participate in liquidity operations or earn fees.

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#!/bin/bash
CODE_SIZE_LIMIT=65000
# Dev account #0
#PRIVATE_KEY=0xac0974bec39a17e36ba4a6b4d238ff944bacb478cbed5efcae784d7bf4f2ff80
# Dev account #4
PRIVATE_KEY=0x47e179ec197488593b187f80a00eb0da91f1b9d0b13f8733639f19c30a34926a
set -euo pipefail
# Function to cleanup processes
cleanup() {
kill $ANVIL_PID 2>/dev/null
if [[ -n "${ANVIL_PID:-}" ]] && kill -0 "$ANVIL_PID" 2>/dev/null; then
kill "$ANVIL_PID" 2>/dev/null || true
sleep 0.2
kill -9 "$ANVIL_PID" 2>/dev/null || true
fi
}
err() {
cleanup
exit $1
}
# Set up trap to handle script exit
# Ensure cleanup on any exit
trap cleanup EXIT
# On Ctrl-C or TERM: exit immediately (will trigger EXIT trap -> cleanup)
trap 'exit 130' INT
trap 'exit 143' TERM
# Create log directory if it doesn't exist
mkdir -p log
# Run anvil in background and redirect output to log file
anvil --code-size-limit ${CODE_SIZE_LIMIT} | tee log/anvil.txt &
# shellcheck disable=SC2086
anvil --disable-block-gas-limit | tee log/anvil.txt &
ANVIL_PID=$!
# Function to check if string exists in file
@@ -43,9 +47,13 @@ while ! check_string "Listening on" "log/anvil.txt"; do
fi
done
forge script --code-size-limit ${CODE_SIZE_LIMIT} --private-key ${PRIVATE_KEY} DeployMock --fork-url http://localhost:8545 --broadcast "$@" || err 1
forge script --private-key ${PRIVATE_KEY} DeployMock --fork-url http://localhost:8545 --broadcast "$@" || exit 1
if [ "${1:-}" = "slow" ]; then
echo "SLOW MODE: Setting mining mode to 12-second intervals."
cast rpc evm_setIntervalMining 12
fi
echo "Press Ctrl+C to exit..."
while true; do
sleep 1
done
# Wait for the anvil process; Ctrl-C will interrupt 'wait' and trigger cleanup via traps
wait "$ANVIL_PID"

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bin/sepolia-deploy Executable file
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#!/bin/bash
CHAINID=11155111
DEPLOY_SCRIPT=DeploySepolia
if [ -f ".env-secret" ]; then
echo "Reading environment from .env-secret"
set -a
source .env-secret
set +a
fi
if [ -z "$SEPOLIA_RPC_URL" ]; then
echo "Usage: SEPOLIA_RPC_URL environment variable must be set"
exit 1
fi
RPC=${SEPOLIA_RPC_URL}
if [ -z "$PRIVATE_KEY" ]; then
echo "Usage: PRIVATE_KEY environment variable must be set"
exit 1
fi
if [ -z "$ETHERSCAN_API_KEY" ]; then
echo "Usage: ETHERSCAN_API_KEY environment variable must be set"
exit 1
fi
if [ "$1" == "broadcast" ]; then
# BROADCAST=(--broadcast --verify --etherscan-api-key "$ETHERSCAN_API_KEY")
# use --slow to avoid triggering rate limits
BROADCAST=(--slow --broadcast --verify --etherscan-api-key "$ETHERSCAN_API_KEY")
else
BROADCAST=()
fi
if [ "$1" != "record" ]; then
forge clean
forge script --fork-url "$RPC" --private-key "$PRIVATE_KEY" "${BROADCAST[@]}" script/DeploySepolia.sol || exit 1
fi
# Update the liqp-deployments.json file if the contracts were broadcast or record was requested
if [ "$1" == "broadcast" ] || [ "$1" == "record" ]; then
METADATA_FILE=deployment/liqp-deployments.json
else
METADATA_FILE=./liqp-deployments.json
fi
address() {
if [ -z "$1" ]; then
echo ""
else
cast --to-checksum-address "$1"
fi
}
contract() {
address "$(jq -r ".transactions[] | select(.contractName == \"$1\" and .transactionType == \"CREATE\") | .contractAddress" broadcast/${DEPLOY_SCRIPT}.sol/${CHAINID}/run-latest.json)"
}
token() {
address "$(jq -r ".transactions[] | select(.contractName == \"MockERC20\" and .transactionType == \"CREATE\" and (.arguments | contains([\"$1\"]))) | .contractAddress" broadcast/${DEPLOY_SCRIPT}.sol/${CHAINID}/run-latest.json)"
}
PARTY_PLANNER=$(contract PartyPlanner)
PARTY_INFO=$(contract PartyInfo)
PARTY_POOL_MINT_IMPL=$(contract PartyPoolMintImpl)
PARTY_POOL_SWAP_IMPL=$(contract PartyPoolSwapImpl)
PARTY_POOL_DEPLOYER=$(contract PartyPoolDeployer)
PARTY_POOL_BP_DEPLOYER=$(contract PartyPoolBalancedPairDeployer)
USXD=$(token USXD)
FUSD=$(token FUSD)
DIVE=$(token DIVE)
BUTC=$(token BUTC)
WTETH=$(token WTETH)
OUT=deployment/$CHAINID/v1
mkdir -p $OUT
cp -r out $OUT/
# Build and insert the JSON object directly in jq
jq -n \
--arg chainId "$CHAINID" \
--arg partyPlanner "$PARTY_PLANNER" \
--arg partyInfo "$PARTY_INFO" \
--arg partyPoolMintImpl "$PARTY_POOL_MINT_IMPL" \
--arg partyPoolSwapImpl "$PARTY_POOL_SWAP_IMPL" \
--arg partyPoolDeployer "$PARTY_POOL_DEPLOYER" \
--arg partyPoolBPDeployer "$PARTY_POOL_BP_DEPLOYER" \
--arg usxd "$USXD" \
--arg fusd "$FUSD" \
--arg dive "$DIVE" \
--arg butc "$BUTC" \
--arg wteth "$WTETH" \
'
{
v1: {
PartyPlanner: $partyPlanner,
PartyInfo: $partyInfo,
PartyPoolMintImpl: $partyPoolMintImpl,
PartyPoolSwapImpl: $partyPoolSwapImpl,
PartyPoolDeployer: $partyPoolDeployer,
PartyPoolBalancedPairDeployer: $partyPoolBPDeployer,
USXD: $usxd,
FUSD: $fusd,
DIVE: $dive,
BUTC: $butc,
WTETH: $wteth
}
} as $entry |
(try (input | . + {($chainId): $entry}) catch {($chainId): $entry})
' "$METADATA_FILE" 2>/dev/null > "${METADATA_FILE}.tmp" && mv "${METADATA_FILE}.tmp" "$METADATA_FILE" || \
jq -n \
--arg chainId "$CHAINID" \
--arg partyPlanner "$PARTY_PLANNER" \
--arg partyInfo "$PARTY_INFO" \
--arg partyPoolMintImpl "$PARTY_POOL_MINT_IMPL" \
--arg partyPoolSwapImpl "$PARTY_POOL_SWAP_IMPL" \
--arg partyPoolDeployer "$PARTY_POOL_DEPLOYER" \
--arg partyPoolBPDeployer "$PARTY_POOL_BP_DEPLOYER" \
--arg usxd "$USXD" \
--arg fusd "$FUSD" \
--arg dive "$DIVE" \
--arg butc "$BUTC" \
--arg wteth "$WTETH" \
'{($chainId): {
v1: {
PartyPlanner: $partyPlanner,
PartyInfo.sol: $partyInfo,
PartyPoolMintImpl: $partyPoolMintImpl,
PartyPoolSwapImpl: $partyPoolSwapImpl,
PartyPoolDeployer: $partyPoolDeployer,
PartyPoolBalancedPairDeployer: $partyPoolBPDeployer,
USXD: $usxd,
FUSD: $fusd,
DIVE: $dive,
BUTC: $butc,
WTETH: $wteth
}
}}' > "$METADATA_FILE"
echo "Wrote $METADATA_FILE"

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bin/signature-upload Executable file
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#!/bin/bash
forge selectors upload --all

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{"abi":[],"bytecode":{"object":"0x6080806040523460175760399081601c823930815050f35b5f80fdfe5f80fdfea264697066735822122057dfc406d135bbbd662b6329b3654145fbb6deac545bf953b3306cd6af0898d864736f6c634300081e0033","sourceMap":"666:24871:0:-:0;;;;;;;;;;;;;;;;;;;;;","linkReferences":{}},"deployedBytecode":{"object":"0x5f80fdfea264697066735822122057dfc406d135bbbd662b6329b3654145fbb6deac545bf953b3306cd6af0898d864736f6c634300081e0033","sourceMap":"666:24871:0:-:0;;","linkReferences":{}},"methodIdentifiers":{},"rawMetadata":"{\"compiler\":{\"version\":\"0.8.30+commit.73712a01\"},\"language\":\"Solidity\",\"output\":{\"abi\":[],\"devdoc\":{\"kind\":\"dev\",\"methods\":{},\"version\":1},\"userdoc\":{\"kind\":\"user\",\"methods\":{},\"notice\":\"Smart contract library of mathematical functions operating with signed 64.64-bit fixed point numbers. Signed 64.64-bit fixed point number is basically a simple fraction whose numerator is signed 128-bit integer and denominator is 2^64. As long as denominator is always the same, there is no need to store it, thus in Solidity signed 64.64-bit fixed point numbers are represented by int128 type holding only the numerator.\",\"version\":1}},\"settings\":{\"compilationTarget\":{\"lib/abdk-libraries-solidity/ABDKMath64x64.sol\":\"ABDKMath64x64\"},\"evmVersion\":\"prague\",\"libraries\":{},\"metadata\":{\"bytecodeHash\":\"ipfs\"},\"optimizer\":{\"enabled\":true,\"runs\":100000000},\"remappings\":[\":@abdk/=lib/abdk-libraries-solidity/\",\":@openzeppelin/=lib/openzeppelin-contracts/\",\":abdk-libraries-solidity/=lib/abdk-libraries-solidity/\",\":erc4626-tests/=lib/openzeppelin-contracts/lib/erc4626-tests/\",\":forge-std/=lib/forge-std/src/\",\":halmos-cheatcodes/=lib/openzeppelin-contracts/lib/halmos-cheatcodes/src/\",\":openzeppelin-contracts/=lib/openzeppelin-contracts/\"],\"viaIR\":true},\"sources\":{\"lib/abdk-libraries-solidity/ABDKMath64x64.sol\":{\"keccak256\":\"0x1364fdc24192b982f647c7fc68dcb2f6fc1b5e201843e773144bd23a76cb3b97\",\"license\":\"BSD-4-Clause\",\"urls\":[\"bzz-raw://490712cc07db32f274899b17aade9c975f06010848c21500b8a5ead6898e09c7\",\"dweb:/ipfs/QmZMPKjDgwCFSGdLWJW6g5E7hDLByA9hNjXzAwJ4GKTZvN\"]}},\"version\":1}","metadata":{"compiler":{"version":"0.8.30+commit.73712a01"},"language":"Solidity","output":{"abi":[],"devdoc":{"kind":"dev","methods":{},"version":1},"userdoc":{"kind":"user","methods":{},"version":1}},"settings":{"remappings":["@abdk/=lib/abdk-libraries-solidity/","@openzeppelin/=lib/openzeppelin-contracts/","abdk-libraries-solidity/=lib/abdk-libraries-solidity/","erc4626-tests/=lib/openzeppelin-contracts/lib/erc4626-tests/","forge-std/=lib/forge-std/src/","halmos-cheatcodes/=lib/openzeppelin-contracts/lib/halmos-cheatcodes/src/","openzeppelin-contracts/=lib/openzeppelin-contracts/"],"optimizer":{"enabled":true,"runs":100000000},"metadata":{"bytecodeHash":"ipfs"},"compilationTarget":{"lib/abdk-libraries-solidity/ABDKMath64x64.sol":"ABDKMath64x64"},"evmVersion":"prague","libraries":{},"viaIR":true},"sources":{"lib/abdk-libraries-solidity/ABDKMath64x64.sol":{"keccak256":"0x1364fdc24192b982f647c7fc68dcb2f6fc1b5e201843e773144bd23a76cb3b97","urls":["bzz-raw://490712cc07db32f274899b17aade9c975f06010848c21500b8a5ead6898e09c7","dweb:/ipfs/QmZMPKjDgwCFSGdLWJW6g5E7hDLByA9hNjXzAwJ4GKTZvN"],"license":"BSD-4-Clause"}},"version":1},"id":0}

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{"abi":[{"type":"error","name":"ReentrancyGuardReentrantCall","inputs":[]}],"bytecode":{"object":"0x","sourceMap":"","linkReferences":{}},"deployedBytecode":{"object":"0x","sourceMap":"","linkReferences":{}},"methodIdentifiers":{},"rawMetadata":"{\"compiler\":{\"version\":\"0.8.30+commit.73712a01\"},\"language\":\"Solidity\",\"output\":{\"abi\":[{\"inputs\":[],\"name\":\"ReentrancyGuardReentrantCall\",\"type\":\"error\"}],\"devdoc\":{\"custom:stateless\":\"\",\"details\":\"Contract module that helps prevent reentrant calls to a function. Inheriting from `ReentrancyGuard` will make the {nonReentrant} modifier available, which can be applied to functions to make sure there are no nested (reentrant) calls to them. Note that because there is a single `nonReentrant` guard, functions marked as `nonReentrant` may not call one another. This can be worked around by making those functions `private`, and then adding `external` `nonReentrant` entry points to them. TIP: If EIP-1153 (transient storage) is available on the chain you're deploying at, consider using {ReentrancyGuardTransient} instead. TIP: If you would like to learn more about reentrancy and alternative ways to protect against it, check out our blog post https://blog.openzeppelin.com/reentrancy-after-istanbul/[Reentrancy After Istanbul]. IMPORTANT: Deprecated. This storage-based reentrancy guard will be removed and replaced by the {ReentrancyGuardTransient} variant in v6.0.\",\"errors\":{\"ReentrancyGuardReentrantCall()\":[{\"details\":\"Unauthorized reentrant call.\"}]},\"kind\":\"dev\",\"methods\":{},\"version\":1},\"userdoc\":{\"kind\":\"user\",\"methods\":{},\"version\":1}},\"settings\":{\"compilationTarget\":{\"lib/openzeppelin-contracts/contracts/utils/ReentrancyGuard.sol\":\"ReentrancyGuard\"},\"evmVersion\":\"prague\",\"libraries\":{},\"metadata\":{\"bytecodeHash\":\"ipfs\"},\"optimizer\":{\"enabled\":true,\"runs\":100000000},\"remappings\":[\":@abdk/=lib/abdk-libraries-solidity/\",\":@openzeppelin/=lib/openzeppelin-contracts/\",\":abdk-libraries-solidity/=lib/abdk-libraries-solidity/\",\":erc4626-tests/=lib/openzeppelin-contracts/lib/erc4626-tests/\",\":forge-std/=lib/forge-std/src/\",\":halmos-cheatcodes/=lib/openzeppelin-contracts/lib/halmos-cheatcodes/src/\",\":openzeppelin-contracts/=lib/openzeppelin-contracts/\"],\"viaIR\":true},\"sources\":{\"lib/openzeppelin-contracts/contracts/utils/ReentrancyGuard.sol\":{\"keccak256\":\"0x6f9ed073e3dab12233a79cd85153f72c9e0f99c1f5512f6d5b1ef09fb46abbb0\",\"license\":\"MIT\",\"urls\":[\"bzz-raw://093d2a804b792a0000883c2215585963ed98ec4341b45bc4224844623387d161\",\"dweb:/ipfs/QmR5shjVosAoxdmY3EfkUWgFNV4CVUcbRNS7tkvbipssPX\"]},\"lib/openzeppelin-contracts/contracts/utils/StorageSlot.sol\":{\"keccak256\":\"0xcf74f855663ce2ae00ed8352666b7935f6cddea2932fdf2c3ecd30a9b1cd0e97\",\"license\":\"MIT\",\"urls\":[\"bzz-raw://9f660b1f351b757dfe01438e59888f31f33ded3afcf5cb5b0d9bf9aa6f320a8b\",\"dweb:/ipfs/QmarDJ5hZEgBtCmmrVzEZWjub9769eD686jmzb2XpSU1cM\"]}},\"version\":1}","metadata":{"compiler":{"version":"0.8.30+commit.73712a01"},"language":"Solidity","output":{"abi":[{"inputs":[],"type":"error","name":"ReentrancyGuardReentrantCall"}],"devdoc":{"kind":"dev","methods":{},"version":1},"userdoc":{"kind":"user","methods":{},"version":1}},"settings":{"remappings":["@abdk/=lib/abdk-libraries-solidity/","@openzeppelin/=lib/openzeppelin-contracts/","abdk-libraries-solidity/=lib/abdk-libraries-solidity/","erc4626-tests/=lib/openzeppelin-contracts/lib/erc4626-tests/","forge-std/=lib/forge-std/src/","halmos-cheatcodes/=lib/openzeppelin-contracts/lib/halmos-cheatcodes/src/","openzeppelin-contracts/=lib/openzeppelin-contracts/"],"optimizer":{"enabled":true,"runs":100000000},"metadata":{"bytecodeHash":"ipfs"},"compilationTarget":{"lib/openzeppelin-contracts/contracts/utils/ReentrancyGuard.sol":"ReentrancyGuard"},"evmVersion":"prague","libraries":{},"viaIR":true},"sources":{"lib/openzeppelin-contracts/contracts/utils/ReentrancyGuard.sol":{"keccak256":"0x6f9ed073e3dab12233a79cd85153f72c9e0f99c1f5512f6d5b1ef09fb46abbb0","urls":["bzz-raw://093d2a804b792a0000883c2215585963ed98ec4341b45bc4224844623387d161","dweb:/ipfs/QmR5shjVosAoxdmY3EfkUWgFNV4CVUcbRNS7tkvbipssPX"],"license":"MIT"},"lib/openzeppelin-contracts/contracts/utils/StorageSlot.sol":{"keccak256":"0xcf74f855663ce2ae00ed8352666b7935f6cddea2932fdf2c3ecd30a9b1cd0e97","urls":["bzz-raw://9f660b1f351b757dfe01438e59888f31f33ded3afcf5cb5b0d9bf9aa6f320a8b","dweb:/ipfs/QmarDJ5hZEgBtCmmrVzEZWjub9769eD686jmzb2XpSU1cM"],"license":"MIT"}},"version":1},"id":31}

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{
"11155111": {
"v1": {
"PartyPlanner": "0x2954911231c44E49938b2FBd1e0cD2787FdF69AD",
"PartyPoolViewer": "0x71b04a353a77405a3217EAF3A24BA619B86cD5E9",
"PartyPoolMintImpl": "0x705272c50F905204187B3126701BeDEd82Dc2F9a",
"PartyPoolSwapImpl": "0xC9608aAaF772c1cAce83C863e88EC4FF54017CeB",
"PartyPoolDeployer": "0x6811C56804321F811eAFa3f7694b026d738Ba7a1",
"PartyPoolBalancedPairDeployer": "0xc321406Fc8e174Bb0D006C145D515b858b1b883d",
"USXD": "0x8E4D16886b8946dfE463fA172129eaBf4825fb09",
"FUSD": "0xdc225280216822CA956738390f589c794129bd53",
"DIVE": "0x7ba123e4e7395A361284d069bD0D545F3f820641",
"BUTC": "0x88125947BBF1A6dd0FeD4B257BB3f9E1FBdCb3Cc",
"WTETH": "0xC8dB65C0B9f4cf59097d4C5Bcb9e8E92B9e4e15F"
}
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}

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# Introduction
[Liquidity Party](https://liquidity.party) is a new game-theoretic multi-asset AMM based on this paper:
[Logarithmic Market Scoring Rules for Modular Combinatorial Information Aggregation](https://mason.gmu.edu/~rhanson/mktscore.pdf) (R. Hanson, 2002)
A Logarithmic Market Scoring Rule (LMSR) is a pricing formula for AMM's that know only their current asset inventories and no other information, naturally supporting multi-asset
Compared to Constant Product (CP) markets, LMSR offers:
1. Less slippage than CP for small and medium trade sizes
2. N-asset pools for trading long-tail pairs in a single hop
3. Lower fees (smaller spread)
## Deeper Liquidity
According to game theory, CP's slope at the current marginal price is too steep, overcharging takers with too much slippage at small and medium trade sizes. LMSR pools offer less slippage and cheaper liquidity for the small and medium trade sizes common for arbitrageurs and aggregators.
## Multi-asset
Naturally multi-asset, Liquidity Party altcoin pools provide direct, one-hop swaps on otherwise illiquid multi-hop pairs. Pools will quote any pair combination available in the pool:
| Assets | Pairs | Swap Gas | Mint Gas |
|-------:|------:|---------:|----------:|
| 2 | 1 | 146,000 | 149,000 |
| 10 | 45 | 157,000 | 426,000 |
| 20 | 190 | 171,000 | 772,000 |
| 50 | 1225 | 213,000 | 1,810,000 |
| 100 | 4950 | 283,000 | 3,542,000 |
Liquidity Party aggregates scarce, low market cap assets into a single pool, providing one-hop liquidity for exotic pairs without fragmenting LP assets. CP pools would need 190x the LP assets to provide the same pairwise liquidity as a single 20-asset Liquidity Party pool, due to asset fragmentation.
## Lower Fees
Since market makers offer the option to take either side of the market, they must receive a subsidy or charge a fee (spread) to compensate for adverse selection (impermanent loss). By protecting LP's against common value-extraction scenarios, LMSR pools have a reduced risk premium resulting in lower fees for takers.
### Minimized Impermanent Loss
### No Intra-Pool Arbitrage
LMSR
This leads to LP's of CP pools demanding higher fees than theoretically necessary. By minimizing impermanent loss for LP's, LMSR pools reduce the risk premium, providing lower fees and higher liquidity for takers.

24
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| Symbol | Address |
|-----------------|----------------------------------------------|
| **Stablecoins** | |
| USDT | `0xdAC17F958D2ee523a2206206994597C13D831ec7` |
| USDC | `0xA0b86991c6218b36c1d19D4a2e9Eb0cE3606eB48` |
| USDe | `0x4c9EDD5852cd905f086C759E8383e09bff1E68B3` |
| DAI | `0x6B175474E89094C44Da98b954EedeAC495271d0F` |
| **Chain Coins** | |
| WETH | `0xC02aaA39b223FE8D0A0e5C4F27eAD9083C756Cc2` |
| WBTC | `0x2260FAC5E5542a773Aa44fBCfeDf7C193bc2C599` |
| WSOL | `0xd1D82d3Ab815E0B47e38EC2d666c5b8AA05Ae501` |
| BNB | `0xB8c77482e45F1F44dE1745F52C74426C631bDD52` |
| TRX | `0x50327c6c5a14DCaDE707ABad2E27eB517df87AB5` |
| POL | `0x455e53CBB86018Ac2B8092FdCd39d8444aFFC3F6` |
| DOT | `0x21c2c96Dbfa137E23946143c71AC8330F9B44001` |
| NEAR | `0x85F17Cf997934a597031b2E18a9aB6ebD4B9f6a4` |
| **Others** | |
| WBETH | `0xa2E3356610840701BDf5611a53974510Ae27E2e1` |
| ARB | `0xB50721BCf8d664c30412Cfbc6cf7a15145234ad1` |
| UNI | `0x1f9840a85d5aF5bf1D1762F925BDADdC4201F984` |
| LINK | `0x514910771AF9Ca656af840dff83E8264EcF986CA` |
| AAVE | `0x7Fc66500c84A76Ad7e9c93437bFc5Ac33E2DDaE9` |
| PEPE | `0x6982508145454Ce325dDbE47a25d4ec3d2311933` |
| SHIB | `0x95aD61b0a150d79219dCF64E1E6Cc01f0B64C4cE` |

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# LMSR-based Multi-Asset AMM
## Abstract
We present a multi-asset automated market maker whose pricing kernel is the Logarithmic Market Scoring Rule (LMSR) ([R. Hanson, 2002](https://mason.gmu.edu/~rhanson/mktscore.pdf)). The pool maintains the convex potential $C(\mathbf{q}) = b(\mathbf{q}) \log\!\Big(\sum_i e^{q_i / b(\mathbf{q})}\Big)$ over normalized inventories $\mathbf{q}$, and sets the effective liquidity parameter proportional to pool size as $b(\mathbf{q}) = \kappa \, S(\mathbf{q})$ with $S(\mathbf{q}) = \sum_i q_i$ and fixed $\kappa>0$. This proportional parameterization preserves scale-invariant responsiveness while retaining softmax-derived pairwise price ratios under a quasi-static-$b$ view, enabling any-to-any swaps within a single potential. We derive and use closed-form expressions for two-asset reductions to compute exact-in, exact-out, limit-hitting (swap-to-limit), and capped-output trades. We discuss stability techniques such as log-sum-exp, ratio-once shortcuts, and domain guards for fixed-point arithmetic. Liquidity operations (proportional and single-asset joins/exits) follow directly from the same potential and admit monotone, invertible mappings. Parameters are immutable post-deployment for transparency and predictable depth calibration.
## Introduction and Motivation
Multi-asset liquidity typically trades off simplicity and expressivity. Classical CFMMs define multiplicative invariants over reserves, while LMSR specifies a convex cost function whose gradient yields prices. Our goal is a multi-asset AMM that uses LMSR to support any-to-any swaps, shares risk across many assets, and scales depth predictably with pool size. By setting $b(\mathbf{q})=\kappa S(\mathbf{q})$, we achieve scale invariance: proportional rescaling of all balances scales $b$ proportionally and preserves pairwise price ratios, so the markets responsiveness is consistent across liquidity regimes. The derivations below formulate instantaneous prices, closed-form swap mappings, limit logic, and liquidity operations tailored to this parameterization.
## System Model and Pricing Kernel
We consider $n\ge 2$ normalized assets with state vector $\mathbf{q}=(q_0,\dots,q_{n-1})\in\mathbb{R}_{\ge 0}^{\,n}$ and size metric $S(\mathbf{q})=\sum_i q_i$. The kernel is the LMSR cost function
$$
C(\mathbf{q}) = b(\mathbf{q}) \log\!\left(\sum_{i=0}^{n-1} e^{q_i / b(\mathbf{q})}\right), \qquad b(\mathbf{q})=\kappa\,S(\mathbf{q}),\quad \kappa>0.
$$
For numerical stability we evaluate $C$ with a log-sum-exp recentering. Let $y_i := q_i/b(\mathbf{q})$ and $M:=\max_i y_i$. Then
$$
C(\mathbf{q}) \;=\; b(\mathbf{q}) \left( M + \log \sum_{i=0}^{n-1} e^{\,y_i - M} \right),
$$
which prevents overflow/underflow when the $y_i$ are dispersed. Quantities are represented in fixed-point with explicit range and domain guards; equations are presented over the reals for clarity.
## Gradient, Price Shares, and Pairwise Prices
With $b$ treated as a constant parameter, the LMSR gradient recovers softmax shares
$$
\frac{\partial C}{\partial q_i} \;=\; \frac{e^{q_i/b}}{\sum_k e^{q_k/b}} \;=:\; \pi_i(\mathbf{q}),
$$
so that the ratio of marginal prices is $\pi_j/\pi_i = \exp\!\big((q_j-q_i)/b\big)$. When $b(\mathbf{q})=\kappa S(\mathbf{q})$ depends on state, $\frac{\partial C}{\partial q_i}$ acquires a common additive term across $i$ from $\partial b/\partial q_i$, but pairwise ratios remain governed by softmax differences. We therefore use a quasi-static-$b$ view for pricing steps, holding $b$ fixed at the pre-trade state for the infinitesimal move, and define the instantaneous pairwise marginal price ratio for exchanging $i$ into $j$ as
$$
P(i\to j \mid \mathbf{q}) \;=\; \exp\!\left(\frac{q_j - q_i}{b(\mathbf{q})}\right).
$$
This ratio drives swap computations and is invariant to proportional rescaling $\mathbf{q}\mapsto \lambda\mathbf{q}$ because $b$ scales by the same factor.
## Two-Asset Reduction and Exact Swap Mappings
Swaps are computed in the two-asset subspace spanned by the in-asset $i$ and out-asset $j$, with all other coordinates held fixed under a quasi-static-$b$ step. Let
$$
r_0 \;:=\; \exp\!\left(\frac{q_i - q_j}{b}\right), \qquad b \equiv b(\mathbf{q})\;\text{ held quasi-static}.
$$
Along the $i\!\to\! j$ path, the instantaneous ratio evolves multiplicatively as $r(t)=r_0\,e^{t/b}$ where $t$ denotes cumulative input of asset $i$. In the two-asset reduction the infinitesimal output satisfies
$$
\mathrm{d}y \;=\; \frac{r(t)}{1+r(t)}\,\mathrm{d}t.
$$
Integrating from $t=0$ to $t=a$ yields the exact-in closed form
$$
y(a) \;=\; b \,\ln\!\Big( 1 + r_0 \,\big(1 - e^{-a/b}\big) \Big).
$$
This mapping has $y(0)=0$, is strictly increasing and concave in $a$, and satisfies $y'(0)=\frac{r_0}{1+r_0}$ with asymptote $\lim_{a\to\infty} y = b\,\ln(1+r_0)$. The inverse exact-out mapping follows by solving for $a$ in terms of target $y$. Writing $E:=e^{y/b}$, we obtain
$$
a(y) \;=\; b \,\ln\!\left(\frac{r_0}{\,r_0 + 1 - E\,}\right),
$$
which is strictly increasing and convex for $y\in\big[0,\, b\ln(1+r_0)\big]$. These two expressions are the workhorses for exact-in and exact-out swaps in our kernel.
## Price Limits, Swap-to-Limit, and Capacity Caps
Users may provide a maximum acceptable marginal price ratio $\Lambda>0$ for $p_i/p_j$. The marginal ratio trajectory $r(t)=r_0 e^{t/b}$ first reaches the limit at the unique
$$
a_{\text{lim}} \;=\; b \,\ln\!\left(\frac{\Lambda}{r_0}\right),
$$
and the output realized at that truncation is
$$
y_{\text{lim}} \;=\; b \,\ln\!\Big( 1 + r_0 \,\big(1 - r_0/\Lambda\big) \Big).
$$
Outputs are further bounded by available inventory; if a computed $y$ would exceed $q_j$, we cap at $y=q_j$ and compute the implied input by inverting the exact-out formula,
$$
a_{\text{cap}} \;=\; b \,\ln\!\left(\frac{r_0}{\,r_0 + 1 - e^{\,q_j/b}\,}\right).
$$
These limit and capacity branches ensure monotone, conservative behavior near domain edges.
## Liquidity Operations from the Same Potential
Liquidity is accounted via pool shares $L$ taken proportional to the size metric, and we set $L=S(\mathbf{q})$ without loss of generality. At initialization with seed balances $\mathbf{q}^{(0)}$ the pool sets $L^{(0)}=S^{(0)}$ and $b^{(0)}=\kappa S^{(0)}$. A proportional deposit that scales balances to $\mathbf{q}'=(1+\alpha)\mathbf{q}$ mints $\Delta L = \alpha S(\mathbf{q})$ shares and scales liquidity to $b'=(1+\alpha)b$. Single-asset deposits target a proportional growth while rebalancing through kernel swaps: providing amount $a$ of asset $i$ induces a growth factor $\alpha\ge 0$ satisfying the monotone equation
$$
a \;=\; a_{\text{req}}(\alpha) \;=\; \alpha q_i \;+\; \sum_{j\ne i} b \,\ln\!\left(\frac{r_{0,j}}{\,r_{0,j} + 1 - e^{\,\alpha q_j/b}\,}\right), \quad r_{0,j}:=\exp\!\left(\frac{q_i-q_j}{b}\right),
$$
and mints $\Delta L=\alpha S(\mathbf{q})$ upon the unique solution. Proportional withdrawals burn $\Delta L$ and return $\alpha=\Delta L/S(\mathbf{q})$ of each asset, updating $b$ to $(1-\alpha)b$. Single-asset withdrawals redeem $\alpha q_i$ directly and swap each redeemed $\alpha q_j$ for $j\ne i$ into $i$ using the exact-in mapping evaluated on the local post-burn state; any capacity overrun is handled by a cap-and-invert branch as above. Because all operations reduce to the same two-asset closed forms, they inherit monotonicity and uniqueness.
### Single-Asset Mint and Redeem
#### Single-Asset Mint
Given a deposit of amount $a>0$ of asset $i$, the pool targets a proportional growth factor $\alpha \ge 0$ so that the post-mint state can be rebalanced to $(1+\alpha)\,\mathbf{q}$ using fee-free kernel swaps from $i$ into each $j\ne i$. For each $j\ne i$, let $y_j := \alpha\,q_j$ and define $r_{0,j} := \exp\!\big((q_i - q_j)/b\big)$. The input required to realize $y_j$ via the exact-out inverse is
$$
x_j(\alpha) \;=\; b \,\ln\!\left(\frac{r_{0,j}}{\,r_{0,j} + 1 - e^{\,y_j/b}\,}\right),
$$
so the total required input for growth $\alpha$ is
$$
a_{\text{req}}(\alpha) \;=\; \alpha\,q_i \;+\; \sum_{j\ne i} x_j(\alpha).
$$
Properties and solver:
- Monotonicity: $a_{\text{req}}(\alpha)$ is strictly increasing on its feasible domain, guaranteeing a unique solution.
- Solver: bracket $\alpha$ (e.g., start from $\alpha\sim a/S$ and double until $a_{\text{req}}(\alpha)\ge a$ or a safety cap), then bisection to a small tolerance $\varepsilon$ (e.g., $\sim10^{-6}$ in fixed-point units).
- Guards: enforce $b>0$, $e^{y_j/b}$ within range, and positivity of the denominator $r_{0,j}+1-e^{y_j/b}$; if a guard would be violated for some $j$, treat that path as infeasible and adjust the bracket.
- Outcome: the consumed input is $a_{\text{in}} = a_{\text{req}}(\alpha^\star) \le a$ and minted LP shares are $\Delta L = \alpha^\star S(\mathbf{q})$.
#### Single-Asset Redeem
Burning a proportional share $\alpha \in (0,1]$ returns a single asset $i$ by redeeming and rebalancing from other assets into $i$:
1) Form the local state after burn, $\mathbf{q}_{\text{local}}=(1-\alpha)\,\mathbf{q}$.
2) Start with the direct redemption $\alpha\,q_i$ in asset $i$.
3) For each $j\ne i$, withdraw $a_j := \alpha\,q_j$ and swap $j\to i$ using the exact-in form evaluated at $\mathbf{q}_{\text{local}}$:
$$
r_{0,j} \;=\; \exp\!\left(\frac{q^{\text{local}}_j - q^{\text{local}}_i}{b}\right),\qquad
y_{j\to i} \;=\; b \,\ln\!\Big(1 + r_{0,j}\,\big(1 - e^{-a_j/b}\big)\Big).
$$
4) Capacity cap and inverse: if $y_{j\to i} > q^{\text{local}}_i$, cap to $y=q^{\text{local}}_i$ and solve the implied input via
$$
a_{j,\text{used}} \;=\; b \,\ln\!\left(\frac{r_{0,j}}{\,r_{0,j} + 1 - e^{\,q^{\text{local}}_i/b}\,}\right),
$$
then update $\mathbf{q}_{\text{local}}$ accordingly.
5) The single-asset payout is
$$
Y_i \;=\; \alpha\,q_i \;+\; \sum_{j\ne i} y_{j\to i}, \qquad \text{with LP burned } L_{\text{in}} = \alpha \, S(\mathbf{q}).
$$
Guards and behavior:
- Enforce $b>0$, positivity of inner terms (e.g., $r_{0,j} + 1 - e^{y/b} > 0$), and safe exponent ranges; treat any per-asset numerical failure as zero contribution rather than aborting the whole redeem.
- The mapping is monotone in $\alpha$; the cap-and-invert branch preserves safety near capacity.
### LP Pricing vs. an Asset Token
With LP supply set to $L=S(\mathbf{q})$, the instantaneous price of one LP share in units of asset $k$ aggregates marginal exchange rates from each asset into $k$:
$$
P_L^{(k)}(\mathbf{q}) \;=\; \frac{1}{S(\mathbf{q})}\,\sum_{j=0}^{n-1} q_j \,\exp\!\left(\frac{q_j - q_k}{b(\mathbf{q})}\right).
$$
Interpretation: proportional deposits leave $P_L^{(k)}$ unchanged; swap fees retained in the pool increase $S$ relative to outstanding $L$, raising $P_L^{(k)}$ (implicit fee accrual). This expression helps LPs and integrators reason about share valuation and dilution across assets.
## Numerical Methods and Safety Guarantees
We evaluate log-sum-exp with recentring, compute ratios like $r_0=\exp((q_i-q_j)/b)$ directly rather than dividing exponentials, and guard all $\exp$ and $\ln$ calls to bounded domains with explicit checks on positivity of inner terms such as $r_0+1-e^{y/b}$. Fixed-point implementations precompute reciprocals like $1/b$ to reduce dispersion, clamp to capacity before inversion, and select cap-and-invert rather than extrapolating when inner terms approach zero. These measures ensure the swap maps remain strictly order-preserving and free of nonphysical outputs. Property-based and differential testing can confirm monotonicity of $y(a)$ and $a(y)$, uniqueness of limit hits when $\Lambda>r_0$, and adherence to predefined error budgets.
## Balanced Regime Optimization: Approximations, Dispatcher, and Stability
Since transcendental operations are gas-expensive on EVM chains, we use polynomial approximations in near-balanced regimes (e.g., stable-asset pairs) while preserving monotonicity and domain safety. Parameterize $\delta := (q_i - q_j)/b$ and $\tau := a/b$ for an $i\!\to\! j$ exact-in step. The exact mapping
$$
y(a) \;=\; b \,\ln\!\Big(1 + e^{\delta}\,\big(1 - e^{-\tau}\big)\Big)
$$
admits small-argument expansions for $|\delta|\ll 1$ and $|\tau|\ll 1$. Using $e^{\pm x}\approx 1\pm x+\tfrac{x^2}{2}$ and $\ln(1+u)\approx u - \tfrac{u^2}{2}$, we obtain
$$
y(a) \;\approx\; b \left[ r_0 \tau - \tfrac{1}{2} r_0 \tau^2 \right] + \mathcal{O}\!\left(\tau^3,\, |\delta|\,\tau^2\right), \qquad r_0=e^{\delta}\approx 1+\delta+\tfrac{\delta^2}{2},
$$
and at $\delta=0$ the symmetry reduces to $y(a)\approx \tfrac{a}{2} - \tfrac{a^2}{4b} + \cdots$.
### Dispatcher preconditions and thresholds (approx path):
- Scope: two-asset pools only; otherwise use the exact path.
- Magnitude bounds: $|\delta| \le 0.01$ and $\tau := a/b$ satisfies $0 < \tau \le 0.5$.
- Tiering: use the quadratic surrogate for $\tau \le 0.1$, and include a cubic correction for $0.1 < \tau \le 0.5$.
- Limit-price gate: approximate the limit truncation only when a positive limit is provided with $\Lambda>r_0$ and $|(\Lambda/r_0)-1| \le 0.1$; otherwise compute the limit exactly (or reject if $\Lambda \le r_0$).
- Capacity and positivity: require $b>0$ and $a>0$, and ensure the approximated output $\tilde{y}(a) \le q_j$; otherwise fall back to the exact cap-and-invert.
- Example thresholds: $\delta_\star=0.01$, $\tau_{\text{tier1}}=0.1$, $\tau_\star=0.5$, and an auxiliary limit-ratio gate $|x| \le 0.1$ where $x=(\Lambda/r_0)-1$ (for reference, $e^{\delta_\star}\approx 1.01005$).
### Approximation Path
- Replace $\exp$ on the bounded $\tau$ domain and $\ln(1+\cdot)$ with verified polynomials to meet a global error budget while maintaining $\tilde{y}'(a)>0$ on the domain.
- Cache common subexpressions (e.g., $r_0=e^\delta$, $\tau=a/b$) and guard inner terms to remain in $(0,\infty)$.
### Fallback Policy
- If any precondition fails (magnitude, domain, capacity, or limit binding), evaluate the exact closed forms for $y(a)$ or $a(y)$ (with cap and limit branches), preserving monotonicity and uniqueness.
- Prefer cap-and-invert near capacity or when the inner term of $\ln(\cdot)$ approaches zero.
### Error Shape
- The small-argument expansion above shows the leading behavior; when using polynomial surrogates, the composed relative error can be kept within a target $\epsilon$ with degrees chosen for the specified $(\delta_\star,\tau_\star,u_\star)$, yielding an error budget of the form $\epsilon \approx \epsilon_{\exp} + \epsilon_{\ln} + c_1 \tau_\star + c_2 |\delta_\star| \tau_\star$ for modest constants $c_1,c_2$.
- These bounds ensure the approximated path remains order-preserving and safely within domain; outside the domain, the dispatcher reverts to the exact path.
- Regardless of path, our policy prioritizes monotonicity, domain safety, and conservative decisions at boundaries.
## Fees and Economic Considerations
Fees are applied outside the fee-free LMSR kernel and are retained in the pool so that fee accrual increases the size metric $S(\mathbf{q})$ (and thereby raises LP share value under $L\propto S$). We extend the single global swap-fee to a per-token fee vector $f = (f_0, f_1, \dots, f_{n-1})$, where $f_i$ denotes the canonical fee rate associated with token $i$ (expressed as a fractional rate, e.g., ppm or bps). For a trade that takes token $i$ as input and token $j$ as output, the pool computes an effective pair fee and applies it to the user-submitted input before invoking the fee-free kernel.
Effective pair fee composition
- The effective fee for an asset-to-asset swap is an exact multiplicative composition:
$$
f_{\mathrm{eff}} \;=\; 1 - (1 - f_i)\,(1 - f_j),
$$
Asset-to-asset policy
- Charge on input: compute the kernel input as
$$
a_{\mathrm{eff}} \;=\; a_{\mathrm{user}}\,(1 - f_{\mathrm{eff}})
$$
and pass $a_{\mathrm{eff}}$ to the fee-free LMSR kernel; collect the retained fee in the input token. Charging on input keeps gas logic simple and makes effective price shifts monotone and predictable for takers.
- Protocol fees are taken as a fraction of LP fee earnings, and immediately moved to a separate account that does not participate in liquidity operations.
- Limit semantics: all limitPrice and cap computations refer to the fee-free kernel path (i.e., are evaluated against the kernel output computed from $a_{\mathrm{eff}}$). Aggregators should compute $f_{\mathrm{eff}}$ externally and present accurate expected outputs to users.
SwapMint and BurnSwap: single-asset fee policy
- Overview: swapMint (single-asset mint) and burnSwap (single-asset redeem) are single-asset-facing operations that interface the pool with one external token and the LP shares on the other side. To keep semantics simple and predictable, only the single assets fee is applied for these operations; there is no separate “LP token” fee ($f_{\mathrm{LP}} = 0$).
- swapMint (deposit one token to mint LP):
- Apply only the deposited tokens fee $f_i$. Compute the effective kernel input as
$$
a_{\mathrm{eff}} \;=\; a_{\mathrm{user}}\,(1 - f_i).
$$
The fee is collected in the deposited token and split by the protocol share $\phi$; the remainder increases the pool (raising $S$ and accruing value to LPs implicitly).
- burnSwap (burn LP to receive one token):
- Apply only the withdrawn tokens fee $f_j$. Compute the gross payout via the fee-free kernel for the burned LP fraction, and remit to the user:
$$
\text{payout}_{\mathrm{net}} \;=\; \text{payout}_{\mathrm{gross}}\,(1 - f_j).
$$
The collected fee is retained in the withdrawn token, the protocol takes $\phi$ of that fee, and the remainder increases pool-held balances (raising $S$ for remaining LPs).
Rationale and interactions with pair-fee rules
- Conceptual consistency: single-asset operations touch a single external token, so applying only that tokens fee is the most natural mapping from the per-token fee vector to operation-level economics. For asset-to-asset swaps the two-token multiplicative composition remains the canonical rule.
- $f_{\mathrm{LP}} = 0$: keeping LP-side fees at zero simplifies LP accounting and avoids double charging when LP shares are the other leg of a transaction. LPs still receive value via retained fees that increase $S$.
Rounding
Our policies aim to always protect the LPs value.
- Total fees are rounded up for the benefit of the pool and against takers.
- The Protocol fee is rounded down for the benefit of LPs and against the protocol developers.
## Risk Management and Bounded Loss
Under constant $b$, classical LMSR admits a worst-case loss bound of $b \ln n$ in the payoff numéraire. With $b(\mathbf{q})=\kappa S(\mathbf{q})$, the per-state bound scales with the current size metric, giving an instantaneous worst-case loss $b(\mathbf{q}) \ln n = \kappa\,S(\mathbf{q})\,\ln n$; per unit of size $S$ this is $\kappa \ln n$. Because $b$ varies with state, global worst-case loss along an arbitrary path depends on how $S$ evolves, but the proportionality clarifies how risk scales with liquidity. Operational mitigations include user price limits (swap-to-limit), capacity caps on outputs ($y \le q_j$), minimum bootstrap $S^{(0)}$ to avoid thin-liquidity regimes, and strict numerical guards (e.g., positivity of inner logarithm arguments) to prevent nonphysical states.
## Deployment and Parameter Fixity
The parameter tuple $(\kappa, f_{\text{swap}}, \phi)$ is set at deployment and remains immutable, with $\kappa>0$ defining $b(\mathbf{q})=\kappa S(\mathbf{q})$, $f_{\text{swap}}$ the swap fee rate, and $\phi$ the protocol share of fees. Given the initial state $\mathbf{q}^{(0)}$ with $S^{(0)}>0$, the induced pricing map is fully determined by
$$
C(\mathbf{q}) = b(\mathbf{q}) \log\!\left(\sum_i e^{q_i / b(\mathbf{q})}\right), \qquad b(\mathbf{q})=\kappa S(\mathbf{q}),
$$
and the two-asset closed forms above. Fixity eliminates governance risk, makes depth calibration transparent, and simplifies integration for external routers and valuation tools.
## Conclusion
By coupling LMSR with the proportional parameterization $b(\mathbf{q})=\kappa S(\mathbf{q})$, we obtain a multi-asset AMM that preserves softmax-driven price ratios under a quasi-static-b view and supports any-to-any swaps via a single convex potential. Exact two-asset reductions yield closed-form mappings for exact-in, exact-out, limit-hitting, and capped-output trades, and the same formulas underpin liquidity operations with monotonicity and uniqueness. Numerical stability follows from log-sum-exp evaluation, ratio-first derivations, guarded transcendental domains, and optional near-balance approximations, while fixed parameters provide predictable scaling and transparent economics.
## References
Hanson, R. (2002) [_Logarithmic Market Scoring Rules for Modular Combinatorial Information Aggregation_](https://mason.gmu.edu/~rhanson/mktscore.pdf)
Othman, Pennock, Reeves, Sandholm (2013) [_A Practical Liquidity-Sensitive Automated Market Maker_](https://www.cs.cmu.edu/~sandholm/liquidity-sensitive%20automated%20market%20maker.teac.pdf)
Xu, Paruch, Cousaert, Feng (2023) [SoK: Decentralized Exchanges (DEX) with Automated Market Maker (AMM) Protocols](https://arxiv.org/pdf/2103.12732)

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@@ -0,0 +1,11 @@
{
"lib/abdk-libraries-solidity": {
"rev": "5e1e7c11b35f8313d3f7ce11c1b86320d7c0b554"
},
"lib/forge-std": {
"rev": "8bbcf6e3f8f62f419e5429a0bd89331c85c37824"
},
"lib/openzeppelin-contracts": {
"rev": "c64a1edb67b6e3f4a15cca8909c9482ad33a02b0"
}
}

View File

@@ -7,10 +7,10 @@ remappings = [
'@abdk/=lib/abdk-libraries-solidity/',
]
optimizer=true
optimizer_runs=999999999
optimizer_runs=100000000 # maximum value allowed by etherscan's verifier XD. The max value is formally 2^32-1
viaIR=true
gas_reports = ['PartyPool', 'PartyPlanner', 'PartyPoolSwapMintImpl', 'PartyPoolMintImpl',]
fs_permissions = [{ access = "write", path = "chain.json"}]
gas_reports = ['PartyPool', 'PartyPoolBalancedPair', 'PartyPlanner', 'PartyPoolSwapImpl', 'PartyPoolMintImpl',]
fs_permissions = [{ access = "write", path = "liqp-deployments.json"}]
[lint]
lint_on_build=false # more annoying than helpful

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