failed attempt to save even more gas in balanced pair by interpolating from a lookup table

.gitignore

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

bin/mock

@@ -1,5 +1,4 @@
 #!/bin/bash
-CODE_SIZE_LIMIT=65000
 # Dev account #0
 #PRIVATE_KEY=0xac0974bec39a17e36ba4a6b4d238ff944bacb478cbed5efcae784d7bf4f2ff80
 # Dev account #4
@@ -22,7 +21,8 @@ trap cleanup EXIT
 mkdir -p log
 
 # Run anvil in background and redirect output to log file
-anvil --code-size-limit ${CODE_SIZE_LIMIT} | tee log/anvil.txt &
+# shellcheck disable=SC2086
+anvil | tee log/anvil.txt &
 ANVIL_PID=$!
 
 # Function to check if string exists in file
@@ -43,7 +43,12 @@ 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 ${PRIVATE_KEY} DeployMock --fork-url http://localhost:8545 --broadcast "$@"  || err 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

bin/sepolia-deploy

@@ -0,0 +1,138 @@
+#!/bin/bash
+
+CHAINID=11155111
+DEPLOY_SCRIPT=DeploySepolia
+
+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_POOL_VIEWER=$(contract PartyPoolViewer)
+PARTY_POOL_MINT_IMPL=$(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 "$PARTY_PLANNER" \
+  --arg partyPoolViewer "$PARTY_POOL_VIEWER" \
+  --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,
+      PartyPoolViewer: $partyPoolViewer,
+      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 "$PARTY_PLANNER" \
+    --arg partyPoolViewer "$PARTY_POOL_VIEWER" \
+    --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,
+        PartyPoolViewer: $partyPoolViewer,
+        PartyPoolMintImpl: $partyPoolMintImpl,
+        PartyPoolSwapImpl: $partyPoolSwapImpl,
+        PartyPoolDeployer: $partyPoolDeployer,
+        PartyPoolBalancedPairDeployer: $partyPoolBPDeployer,
+        USXD: $usxd,
+        FUSD: $fusd,
+        DIVE: $dive,
+        BUTC: $butc,
+        WTETH: $wteth
+      }
+    }}' > "$METADATA_FILE"
+
+echo "Wrote $METADATA_FILE"

bin/signature-upload

@@ -0,0 +1,2 @@
+#!/bin/bash
+forge selectors upload --all

deployment/11155111/v1/out/ABDKMath64x64.sol/ABDKMath64x64.json

@@ -0,0 +1 @@
+{"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}

deployment/11155111/v1/out/Address.sol/Address.json

@@ -0,0 +1 @@
+{"abi":[{"type":"error","name":"AddressEmptyCode","inputs":[{"name":"target","type":"address","internalType":"address"}]}],"bytecode":{"object":"0x6080806040523460175760399081601c823930815050f35b5f80fdfe5f80fdfea2646970667358221220eb0570070fec78251db3fa24b17454c9bec7df5e60c2499d03d66c5c28208ff764736f6c634300081e0033","sourceMap":"282:6520:33:-:0;;;;;;;;;;;;;;;;;;;;;","linkReferences":{}},"deployedBytecode":{"object":"0x5f80fdfea2646970667358221220eb0570070fec78251db3fa24b17454c9bec7df5e60c2499d03d66c5c28208ff764736f6c634300081e0033","sourceMap":"282:6520:33:-:0;;","linkReferences":{}},"methodIdentifiers":{},"rawMetadata":"{\"compiler\":{\"version\":\"0.8.30+commit.73712a01\"},\"language\":\"Solidity\",\"output\":{\"abi\":[{\"inputs\":[{\"internalType\":\"address\",\"name\":\"target\",\"type\":\"address\"}],\"name\":\"AddressEmptyCode\",\"type\":\"error\"}],\"devdoc\":{\"details\":\"Collection of functions related to the address type\",\"errors\":{\"AddressEmptyCode(address)\":[{\"details\":\"There's no code at `target` (it is not a contract).\"}]},\"kind\":\"dev\",\"methods\":{},\"version\":1},\"userdoc\":{\"kind\":\"user\",\"methods\":{},\"version\":1}},\"settings\":{\"compilationTarget\":{\"lib/openzeppelin-contracts/contracts/utils/Address.sol\":\"Address\"},\"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/Address.sol\":{\"keccak256\":\"0xd274645d15bb7e4fcb9c833e401b2c5837404f90057f11a49118f25e0af7c76f\",\"license\":\"MIT\",\"urls\":[\"bzz-raw://d38e0b997bb7aebae26d190b03d0991feb0d204c45f945e60014e1ca9175de69\",\"dweb:/ipfs/QmWzsUHHAZcjMyF8uMDEtNpMTkYZdQrfvdKPobXvwVHKo6\"]},\"lib/openzeppelin-contracts/contracts/utils/Errors.sol\":{\"keccak256\":\"0x6afa713bfd42cf0f7656efa91201007ac465e42049d7de1d50753a373648c123\",\"license\":\"MIT\",\"urls\":[\"bzz-raw://ba1d02f4847670a1b83dec9f7d37f0b0418d6043447b69f3a29a5f9efc547fcf\",\"dweb:/ipfs/QmQ7iH2keLNUKgq2xSWcRmuBE5eZ3F5whYAkAGzCNNoEWB\"]},\"lib/openzeppelin-contracts/contracts/utils/LowLevelCall.sol\":{\"keccak256\":\"0x50e81a8b089e3f382b6c915aa0166773de64ea4756e8f9479d9943a5f956ddf5\",\"license\":\"MIT\",\"urls\":[\"bzz-raw://bfeb96a150537222e2191c03887127499a4f21dfb5f9a7211da4d81749b52848\",\"dweb:/ipfs/QmYR75ECbsBuxSiXmGvGfNKJRLoK5MdLUZL1bd8SixzxL4\"]}},\"version\":1}","metadata":{"compiler":{"version":"0.8.30+commit.73712a01"},"language":"Solidity","output":{"abi":[{"inputs":[{"internalType":"address","name":"target","type":"address"}],"type":"error","name":"AddressEmptyCode"}],"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/Address.sol":"Address"},"evmVersion":"prague","libraries":{},"viaIR":true},"sources":{"lib/openzeppelin-contracts/contracts/utils/Address.sol":{"keccak256":"0xd274645d15bb7e4fcb9c833e401b2c5837404f90057f11a49118f25e0af7c76f","urls":["bzz-raw://d38e0b997bb7aebae26d190b03d0991feb0d204c45f945e60014e1ca9175de69","dweb:/ipfs/QmWzsUHHAZcjMyF8uMDEtNpMTkYZdQrfvdKPobXvwVHKo6"],"license":"MIT"},"lib/openzeppelin-contracts/contracts/utils/Errors.sol":{"keccak256":"0x6afa713bfd42cf0f7656efa91201007ac465e42049d7de1d50753a373648c123","urls":["bzz-raw://ba1d02f4847670a1b83dec9f7d37f0b0418d6043447b69f3a29a5f9efc547fcf","dweb:/ipfs/QmQ7iH2keLNUKgq2xSWcRmuBE5eZ3F5whYAkAGzCNNoEWB"],"license":"MIT"},"lib/openzeppelin-contracts/contracts/utils/LowLevelCall.sol":{"keccak256":"0x50e81a8b089e3f382b6c915aa0166773de64ea4756e8f9479d9943a5f956ddf5","urls":["bzz-raw://bfeb96a150537222e2191c03887127499a4f21dfb5f9a7211da4d81749b52848","dweb:/ipfs/QmYR75ECbsBuxSiXmGvGfNKJRLoK5MdLUZL1bd8SixzxL4"],"license":"MIT"}},"version":1},"id":33}

deployment/11155111/v1/out/Base.sol/CommonBase.json

@@ -0,0 +1 @@
+{"abi":[],"bytecode":{"object":"0x","sourceMap":"","linkReferences":{}},"deployedBytecode":{"object":"0x","sourceMap":"","linkReferences":{}},"methodIdentifiers":{},"rawMetadata":"{\"compiler\":{\"version\":\"0.8.30+commit.73712a01\"},\"language\":\"Solidity\",\"output\":{\"abi\":[],\"devdoc\":{\"kind\":\"dev\",\"methods\":{},\"stateVariables\":{\"CONSOLE\":{\"details\":\"console.sol and console2.sol work by executing a staticcall to this address. Calculated as `address(uint160(uint88(bytes11(\\\"console.log\\\"))))`.\"},\"CREATE2_FACTORY\":{\"details\":\"Used when deploying with create2. Taken from https://github.com/Arachnid/deterministic-deployment-proxy.\"},\"DEFAULT_SENDER\":{\"details\":\"The default address for tx.origin and msg.sender. Calculated as `address(uint160(uint256(keccak256(\\\"foundry default caller\\\"))))`.\"},\"DEFAULT_TEST_CONTRACT\":{\"details\":\"The address of the first contract `CREATE`d by a running test contract. When running tests, each test contract is `CREATE`d by `DEFAULT_SENDER` with nonce 1. Calculated as `VM.computeCreateAddress(VM.computeCreateAddress(DEFAULT_SENDER, 1), 1)`.\"},\"MULTICALL3_ADDRESS\":{\"details\":\"Deterministic deployment address of the Multicall3 contract. Taken from https://www.multicall3.com.\"},\"SECP256K1_ORDER\":{\"details\":\"The order of the secp256k1 curve.\"},\"VM_ADDRESS\":{\"details\":\"Cheat code address. Calculated as `address(uint160(uint256(keccak256(\\\"hevm cheat code\\\"))))`.\"}},\"version\":1},\"userdoc\":{\"kind\":\"user\",\"methods\":{},\"version\":1}},\"settings\":{\"compilationTarget\":{\"lib/forge-std/src/Base.sol\":\"CommonBase\"},\"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/forge-std/src/Base.sol\":{\"keccak256\":\"0x4b2a5a85e045dcf6a082700c7252e43854c2eed88f860aaa18ec1e85218ae2bf\",\"license\":\"MIT\",\"urls\":[\"bzz-raw://98d060ed5be569a92d908fc358149039dc8f833d61973aa1b9d1d8235676bf6d\",\"dweb:/ipfs/QmaWQpn5dJmbMS5skwmPPMeUWZG35BLkignPpcA3zyagEs\"]},\"lib/forge-std/src/StdStorage.sol\":{\"keccak256\":\"0x04102de0a79398e4bdea57b7a4818655b4cc66d6f81d1cff08bf428cd0b384cd\",\"license\":\"MIT\",\"urls\":[\"bzz-raw://53edc6c8f7f67cafc0129f039637c77d979880f7f1947defea31e8f0c05095bc\",\"dweb:/ipfs/QmUKXJd1vFCkxxrkXNLURdXrx2apoyWQFrFb5UqNkjdHVi\"]},\"lib/forge-std/src/Vm.sol\":{\"keccak256\":\"0x9b4df44a3b748593a58be7ba64fa5f420e5dcd7927bfa5173186228bfe61782f\",\"license\":\"MIT OR Apache-2.0\",\"urls\":[\"bzz-raw://b89fcf92ee1d14237cfb0dd949341053389d5b6a043ad77349b65bef80b1d59f\",\"dweb:/ipfs/QmPkia3aNHrqvE4tqxG2AyrdB4W91jTAvcbchgs2wAo6NL\"]}},\"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/forge-std/src/Base.sol":"CommonBase"},"evmVersion":"prague","libraries":{},"viaIR":true},"sources":{"lib/forge-std/src/Base.sol":{"keccak256":"0x4b2a5a85e045dcf6a082700c7252e43854c2eed88f860aaa18ec1e85218ae2bf","urls":["bzz-raw://98d060ed5be569a92d908fc358149039dc8f833d61973aa1b9d1d8235676bf6d","dweb:/ipfs/QmaWQpn5dJmbMS5skwmPPMeUWZG35BLkignPpcA3zyagEs"],"license":"MIT"},"lib/forge-std/src/StdStorage.sol":{"keccak256":"0x04102de0a79398e4bdea57b7a4818655b4cc66d6f81d1cff08bf428cd0b384cd","urls":["bzz-raw://53edc6c8f7f67cafc0129f039637c77d979880f7f1947defea31e8f0c05095bc","dweb:/ipfs/QmUKXJd1vFCkxxrkXNLURdXrx2apoyWQFrFb5UqNkjdHVi"],"license":"MIT"},"lib/forge-std/src/Vm.sol":{"keccak256":"0x9b4df44a3b748593a58be7ba64fa5f420e5dcd7927bfa5173186228bfe61782f","urls":["bzz-raw://b89fcf92ee1d14237cfb0dd949341053389d5b6a043ad77349b65bef80b1d59f","dweb:/ipfs/QmPkia3aNHrqvE4tqxG2AyrdB4W91jTAvcbchgs2wAo6NL"],"license":"MIT OR Apache-2.0"}},"version":1},"id":1}

deployment/11155111/v1/out/Base.sol/ScriptBase.json

@@ -0,0 +1 @@
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deployment/11155111/v1/out/Base.sol/TestBase.json

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deployment/11155111/v1/out/Context.sol/Context.json

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+{"abi":[],"bytecode":{"object":"0x","sourceMap":"","linkReferences":{}},"deployedBytecode":{"object":"0x","sourceMap":"","linkReferences":{}},"methodIdentifiers":{},"rawMetadata":"{\"compiler\":{\"version\":\"0.8.30+commit.73712a01\"},\"language\":\"Solidity\",\"output\":{\"abi\":[],\"devdoc\":{\"details\":\"Provides information about the current execution context, including the sender of the transaction and its data. While these are generally available via msg.sender and msg.data, they should not be accessed in such a direct manner, since when dealing with meta-transactions the account sending and paying for execution may not be the actual sender (as far as an application is concerned). This contract is only required for intermediate, library-like contracts.\",\"kind\":\"dev\",\"methods\":{},\"version\":1},\"userdoc\":{\"kind\":\"user\",\"methods\":{},\"version\":1}},\"settings\":{\"compilationTarget\":{\"lib/openzeppelin-contracts/contracts/utils/Context.sol\":\"Context\"},\"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/Context.sol\":{\"keccak256\":\"0x493033a8d1b176a037b2cc6a04dad01a5c157722049bbecf632ca876224dd4b2\",\"license\":\"MIT\",\"urls\":[\"bzz-raw://6a708e8a5bdb1011c2c381c9a5cfd8a9a956d7d0a9dc1bd8bcdaf52f76ef2f12\",\"dweb:/ipfs/Qmax9WHBnVsZP46ZxEMNRQpLQnrdE4dK8LehML1Py8FowF\"]}},\"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/openzeppelin-contracts/contracts/utils/Context.sol":"Context"},"evmVersion":"prague","libraries":{},"viaIR":true},"sources":{"lib/openzeppelin-contracts/contracts/utils/Context.sol":{"keccak256":"0x493033a8d1b176a037b2cc6a04dad01a5c157722049bbecf632ca876224dd4b2","urls":["bzz-raw://6a708e8a5bdb1011c2c381c9a5cfd8a9a956d7d0a9dc1bd8bcdaf52f76ef2f12","dweb:/ipfs/Qmax9WHBnVsZP46ZxEMNRQpLQnrdE4dK8LehML1Py8FowF"],"license":"MIT"}},"version":1},"id":34}

deployment/11155111/v1/out/Errors.sol/Errors.json

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deployment/11155111/v1/out/IERC165.sol/IERC165.json

@@ -0,0 +1 @@
+{"abi":[{"type":"function","name":"supportsInterface","inputs":[{"name":"interfaceId","type":"bytes4","internalType":"bytes4"}],"outputs":[{"name":"","type":"bool","internalType":"bool"}],"stateMutability":"view"}],"bytecode":{"object":"0x","sourceMap":"","linkReferences":{}},"deployedBytecode":{"object":"0x","sourceMap":"","linkReferences":{}},"methodIdentifiers":{"supportsInterface(bytes4)":"01ffc9a7"},"rawMetadata":"{\"compiler\":{\"version\":\"0.8.30+commit.73712a01\"},\"language\":\"Solidity\",\"output\":{\"abi\":[{\"inputs\":[{\"internalType\":\"bytes4\",\"name\":\"interfaceId\",\"type\":\"bytes4\"}],\"name\":\"supportsInterface\",\"outputs\":[{\"internalType\":\"bool\",\"name\":\"\",\"type\":\"bool\"}],\"stateMutability\":\"view\",\"type\":\"function\"}],\"devdoc\":{\"details\":\"Interface of the ERC-165 standard, as defined in the https://eips.ethereum.org/EIPS/eip-165[ERC]. Implementers can declare support of contract interfaces, which can then be queried by others ({ERC165Checker}). For an implementation, see {ERC165}.\",\"kind\":\"dev\",\"methods\":{\"supportsInterface(bytes4)\":{\"details\":\"Returns true if this contract implements the interface defined by `interfaceId`. See the corresponding https://eips.ethereum.org/EIPS/eip-165#how-interfaces-are-identified[ERC section] to learn more about how these ids are created. This function call must use less than 30 000 gas.\"}},\"version\":1},\"userdoc\":{\"kind\":\"user\",\"methods\":{},\"version\":1}},\"settings\":{\"compilationTarget\":{\"lib/openzeppelin-contracts/contracts/utils/introspection/IERC165.sol\":\"IERC165\"},\"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/introspection/IERC165.sol\":{\"keccak256\":\"0x8891738ffe910f0cf2da09566928589bf5d63f4524dd734fd9cedbac3274dd5c\",\"license\":\"MIT\",\"urls\":[\"bzz-raw://971f954442df5c2ef5b5ebf1eb245d7105d9fbacc7386ee5c796df1d45b21617\",\"dweb:/ipfs/QmadRjHbkicwqwwh61raUEapaVEtaLMcYbQZWs9gUkgj3u\"]}},\"version\":1}","metadata":{"compiler":{"version":"0.8.30+commit.73712a01"},"language":"Solidity","output":{"abi":[{"inputs":[{"internalType":"bytes4","name":"interfaceId","type":"bytes4"}],"stateMutability":"view","type":"function","name":"supportsInterface","outputs":[{"internalType":"bool","name":"","type":"bool"}]}],"devdoc":{"kind":"dev","methods":{"supportsInterface(bytes4)":{"details":"Returns true if this contract implements the interface defined by `interfaceId`. See the corresponding https://eips.ethereum.org/EIPS/eip-165#how-interfaces-are-identified[ERC section] to learn more about how these ids are created. This function call must use less than 30 000 gas."}},"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/introspection/IERC165.sol":"IERC165"},"evmVersion":"prague","libraries":{},"viaIR":true},"sources":{"lib/openzeppelin-contracts/contracts/utils/introspection/IERC165.sol":{"keccak256":"0x8891738ffe910f0cf2da09566928589bf5d63f4524dd734fd9cedbac3274dd5c","urls":["bzz-raw://971f954442df5c2ef5b5ebf1eb245d7105d9fbacc7386ee5c796df1d45b21617","dweb:/ipfs/QmadRjHbkicwqwwh61raUEapaVEtaLMcYbQZWs9gUkgj3u"],"license":"MIT"}},"version":1},"id":39}

deployment/11155111/v1/out/IPartyFlashCallback.sol/IPartyFlashCallback.json

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+{"abi":[{"type":"function","name":"partyFlashCallback","inputs":[{"name":"loanAmounts","type":"uint256[]","internalType":"uint256[]"},{"name":"repaymentAmounts","type":"uint256[]","internalType":"uint256[]"},{"name":"data","type":"bytes","internalType":"bytes"}],"outputs":[],"stateMutability":"nonpayable"}],"bytecode":{"object":"0x","sourceMap":"","linkReferences":{}},"deployedBytecode":{"object":"0x","sourceMap":"","linkReferences":{}},"methodIdentifiers":{"partyFlashCallback(uint256[],uint256[],bytes)":"f6c10706"},"rawMetadata":"{\"compiler\":{\"version\":\"0.8.30+commit.73712a01\"},\"language\":\"Solidity\",\"output\":{\"abi\":[{\"inputs\":[{\"internalType\":\"uint256[]\",\"name\":\"loanAmounts\",\"type\":\"uint256[]\"},{\"internalType\":\"uint256[]\",\"name\":\"repaymentAmounts\",\"type\":\"uint256[]\"},{\"internalType\":\"bytes\",\"name\":\"data\",\"type\":\"bytes\"}],\"name\":\"partyFlashCallback\",\"outputs\":[],\"stateMutability\":\"nonpayable\",\"type\":\"function\"}],\"devdoc\":{\"kind\":\"dev\",\"methods\":{},\"version\":1},\"userdoc\":{\"kind\":\"user\",\"methods\":{},\"version\":1}},\"settings\":{\"compilationTarget\":{\"src/IPartyFlashCallback.sol\":\"IPartyFlashCallback\"},\"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\":{\"src/IPartyFlashCallback.sol\":{\"keccak256\":\"0xff1d473d27c4dc75441a5f0db2d761916cce4a702f660e998467791efd1d9b2e\",\"license\":\"UNLICENSED\",\"urls\":[\"bzz-raw://3220d69c62ed8c8106762c92857f24011284e8ddcfa5db4210e506b112fa1870\",\"dweb:/ipfs/QmYoZiGsVwoJvyPMcsSste4tq93wVBgDqCZkwPY7dvyLBJ\"]}},\"version\":1}","metadata":{"compiler":{"version":"0.8.30+commit.73712a01"},"language":"Solidity","output":{"abi":[{"inputs":[{"internalType":"uint256[]","name":"loanAmounts","type":"uint256[]"},{"internalType":"uint256[]","name":"repaymentAmounts","type":"uint256[]"},{"internalType":"bytes","name":"data","type":"bytes"}],"stateMutability":"nonpayable","type":"function","name":"partyFlashCallback"}],"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":{"src/IPartyFlashCallback.sol":"IPartyFlashCallback"},"evmVersion":"prague","libraries":{},"viaIR":true},"sources":{"src/IPartyFlashCallback.sol":{"keccak256":"0xff1d473d27c4dc75441a5f0db2d761916cce4a702f660e998467791efd1d9b2e","urls":["bzz-raw://3220d69c62ed8c8106762c92857f24011284e8ddcfa5db4210e506b112fa1870","dweb:/ipfs/QmYoZiGsVwoJvyPMcsSste4tq93wVBgDqCZkwPY7dvyLBJ"],"license":"UNLICENSED"}},"version":1},"id":45}

deployment/11155111/v1/out/LMSRStabilized.sol/LMSRStabilized.json

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deployment/11155111/v1/out/LMSRStabilizedBalancedPair.sol/LMSRStabilizedBalancedPair.json

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deployment/11155111/v1/out/LowLevelCall.sol/LowLevelCall.json

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deployment/11155111/v1/out/OwnableInternal.sol/OwnableInternal.json

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deployment/11155111/v1/out/PartyPoolHelpers.sol/PartyPoolHelpers.json

@@ -0,0 +1 @@
+{"abi":[],"bytecode":{"object":"0x","sourceMap":"","linkReferences":{}},"deployedBytecode":{"object":"0x","sourceMap":"","linkReferences":{}},"methodIdentifiers":{},"rawMetadata":"{\"compiler\":{\"version\":\"0.8.30+commit.73712a01\"},\"language\":\"Solidity\",\"output\":{\"abi\":[],\"devdoc\":{\"kind\":\"dev\",\"methods\":{},\"version\":1},\"userdoc\":{\"kind\":\"user\",\"methods\":{},\"version\":1}},\"settings\":{\"compilationTarget\":{\"src/PartyPoolHelpers.sol\":\"PartyPoolHelpers\"},\"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\"]},\"src/PartyPoolHelpers.sol\":{\"keccak256\":\"0xd43b635d12b6684ae38a685eea4bc5783cebb3696514d8aafe3f4ce34f5e759c\",\"license\":\"UNLICENSED\",\"urls\":[\"bzz-raw://832046b365d443c4c1c715f98fe3de224e3ba82c67960053d51e6a79847c4af5\",\"dweb:/ipfs/QmZ4nWMwyYQzaBGF7rBE73GYTs4z3DRNYL1ZrGAsxN6RfP\"]}},\"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":{"src/PartyPoolHelpers.sol":"PartyPoolHelpers"},"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"},"src/PartyPoolHelpers.sol":{"keccak256":"0xd43b635d12b6684ae38a685eea4bc5783cebb3696514d8aafe3f4ce34f5e759c","urls":["bzz-raw://832046b365d443c4c1c715f98fe3de224e3ba82c67960053d51e6a79847c4af5","dweb:/ipfs/QmZ4nWMwyYQzaBGF7rBE73GYTs4z3DRNYL1ZrGAsxN6RfP"],"license":"UNLICENSED"}},"version":1},"id":59}

deployment/11155111/v1/out/Proxy.sol/Proxy.json

@@ -0,0 +1 @@
+{"abi":[{"type":"fallback","stateMutability":"payable"}],"bytecode":{"object":"0x","sourceMap":"","linkReferences":{}},"deployedBytecode":{"object":"0x","sourceMap":"","linkReferences":{}},"methodIdentifiers":{},"rawMetadata":"{\"compiler\":{\"version\":\"0.8.30+commit.73712a01\"},\"language\":\"Solidity\",\"output\":{\"abi\":[{\"stateMutability\":\"payable\",\"type\":\"fallback\"}],\"devdoc\":{\"details\":\"This abstract contract provides a fallback function that delegates all calls to another contract using the EVM instruction `delegatecall`. We refer to the second contract as the _implementation_ behind the proxy, and it has to be specified by overriding the virtual {_implementation} function. Additionally, delegation to the implementation can be triggered manually through the {_fallback} function, or to a different contract through the {_delegate} function. The success and return data of the delegated call will be returned back to the caller of the proxy.\",\"kind\":\"dev\",\"methods\":{},\"version\":1},\"userdoc\":{\"kind\":\"user\",\"methods\":{},\"version\":1}},\"settings\":{\"compilationTarget\":{\"lib/openzeppelin-contracts/contracts/proxy/Proxy.sol\":\"Proxy\"},\"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/proxy/Proxy.sol\":{\"keccak256\":\"0x25f9b099413f805b4c4bbad8cc179326c10be237aec00349caf91524f8db0bbc\",\"license\":\"MIT\",\"urls\":[\"bzz-raw://dcfb75af07ad33b1f8e966f793db3df8fbcfb14103ed3644c0c634658a8fd099\",\"dweb:/ipfs/QmPWamdkbcKwG3ah2G9TZtKHzQmjnunsWoPWr5KKfbrKNb\"]}},\"version\":1}","metadata":{"compiler":{"version":"0.8.30+commit.73712a01"},"language":"Solidity","output":{"abi":[{"inputs":[],"stateMutability":"payable","type":"fallback"}],"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/proxy/Proxy.sol":"Proxy"},"evmVersion":"prague","libraries":{},"viaIR":true},"sources":{"lib/openzeppelin-contracts/contracts/proxy/Proxy.sol":{"keccak256":"0x25f9b099413f805b4c4bbad8cc179326c10be237aec00349caf91524f8db0bbc","urls":["bzz-raw://dcfb75af07ad33b1f8e966f793db3df8fbcfb14103ed3644c0c634658a8fd099","dweb:/ipfs/QmPWamdkbcKwG3ah2G9TZtKHzQmjnunsWoPWr5KKfbrKNb"],"license":"MIT"}},"version":1},"id":28}

deployment/11155111/v1/out/ReentrancyGuard.sol/ReentrancyGuard.json

@@ -0,0 +1 @@
+{"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":37}

deployment/11155111/v1/out/StdChains.sol/StdChains.json

@@ -0,0 +1 @@
+{"abi":[],"bytecode":{"object":"0x","sourceMap":"","linkReferences":{}},"deployedBytecode":{"object":"0x","sourceMap":"","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\":\"StdChains provides information about EVM compatible chains that can be used in scripts/tests. For each chain, the chain's name, chain ID, and a default RPC URL are provided. Chains are identified by their alias, which is the same as the alias in the `[rpc_endpoints]` section of the `foundry.toml` file. For best UX, ensure the alias in the `foundry.toml` file match the alias used in this contract, which can be found as the first argument to the `setChainWithDefaultRpcUrl` call in the `initializeStdChains` function. There are two main ways to use this contract:   1. Set a chain with `setChain(string memory chainAlias, ChainData memory chain)` or      `setChain(string memory chainAlias, Chain memory chain)`   2. Get a chain with `getChain(string memory chainAlias)` or `getChain(uint256 chainId)`. The first time either of those are used, chains are initialized with the default set of RPC URLs. This is done in `initializeStdChains`, which uses `setChainWithDefaultRpcUrl`. Defaults are recorded in `defaultRpcUrls`. The `setChain` function is straightforward, and it simply saves off the given chain data. The `getChain` methods use `getChainWithUpdatedRpcUrl` to return a chain. For example, let's say we want to retrieve the RPC URL for `mainnet`:   - If you have specified data with `setChain`, it will return that.   - If you have configured a mainnet RPC URL in `foundry.toml`, it will return the URL, provided it     is valid (e.g. a URL is specified, or an environment variable is given and exists).   - If neither of the above conditions is met, the default data is returned. Summarizing the above, the prioritization hierarchy is `setChain` -> `foundry.toml` -> environment variable -> defaults.\",\"version\":1}},\"settings\":{\"compilationTarget\":{\"lib/forge-std/src/StdChains.sol\":\"StdChains\"},\"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/forge-std/src/StdChains.sol\":{\"keccak256\":\"0xb2cbca1a6ffa19926c31bad47393a070305c809fe5d88c52214d5c51ce0733c6\",\"license\":\"MIT\",\"urls\":[\"bzz-raw://cf20975cfd9733910305fc8e746c7631c2ab210289aab036cec32f3c530335c7\",\"dweb:/ipfs/QmYYvVzvAN1uCt8XtDmWo5x2inSVJBYajFexe92rVWEuMf\"]},\"lib/forge-std/src/Vm.sol\":{\"keccak256\":\"0x9b4df44a3b748593a58be7ba64fa5f420e5dcd7927bfa5173186228bfe61782f\",\"license\":\"MIT OR Apache-2.0\",\"urls\":[\"bzz-raw://b89fcf92ee1d14237cfb0dd949341053389d5b6a043ad77349b65bef80b1d59f\",\"dweb:/ipfs/QmPkia3aNHrqvE4tqxG2AyrdB4W91jTAvcbchgs2wAo6NL\"]}},\"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/forge-std/src/StdChains.sol":"StdChains"},"evmVersion":"prague","libraries":{},"viaIR":true},"sources":{"lib/forge-std/src/StdChains.sol":{"keccak256":"0xb2cbca1a6ffa19926c31bad47393a070305c809fe5d88c52214d5c51ce0733c6","urls":["bzz-raw://cf20975cfd9733910305fc8e746c7631c2ab210289aab036cec32f3c530335c7","dweb:/ipfs/QmYYvVzvAN1uCt8XtDmWo5x2inSVJBYajFexe92rVWEuMf"],"license":"MIT"},"lib/forge-std/src/Vm.sol":{"keccak256":"0x9b4df44a3b748593a58be7ba64fa5f420e5dcd7927bfa5173186228bfe61782f","urls":["bzz-raw://b89fcf92ee1d14237cfb0dd949341053389d5b6a043ad77349b65bef80b1d59f","dweb:/ipfs/QmPkia3aNHrqvE4tqxG2AyrdB4W91jTAvcbchgs2wAo6NL"],"license":"MIT OR Apache-2.0"}},"version":1},"id":4}

deployment/11155111/v1/out/StdCheats.sol/StdCheats.json

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deployment/11155111/v1/out/StdCheats.sol/StdCheatsSafe.json

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deployment/11155111/v1/out/StdJson.sol/stdJson.json

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deployment/11155111/v1/out/StdMath.sol/stdMath.json

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deployment/11155111/v1/out/StdStorage.sol/stdStorage.json

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deployment/11155111/v1/out/StdStyle.sol/StdStyle.json

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deployment/11155111/v1/out/StdToml.sol/stdToml.json

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deployment/11155111/v1/out/StdUtils.sol/StdUtils.json

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deployment/11155111/v1/out/StorageSlot.sol/StorageSlot.json

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deployment/11155111/v1/out/build-info/425098d9ecb6b837.json

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deployment/11155111/v1/out/build-info/94d187b8ff52264a.json

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deployment/11155111/v1/out/build-info/bc3908669ec8c50f.json

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deployment/11155111/v1/out/build-info/c5529240b2dab858.json

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deployment/11155111/v1/out/console.sol/console.json

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deployment/11155111/v1/out/safeconsole.sol/safeconsole.json

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deployment/liqp-deployments.json

@@ -0,0 +1,17 @@
+{
+  "11155111": {
+    "v1": {
+      "PartyPlanner": "0x0ad06C08ab5049e6Fd4d7f5AF457115A1475326b",
+      "PartyPoolViewer": "0x750d63a39a4ccfCfB69D2f5aFDa065909C717cAB",
+      "PartyPoolMintImpl": "0x25bb10BA84944F8aAEf1fD247C3B7Fe7271C23F9",
+      "PartyPoolSwapImpl": "0x69b4F102e0747f61F8529b3bbFf2FC4b27438d0F",
+      "PartyPoolDeployer": "0x0939F93BAa3c96226853F9F39A95beF48eA8fF04",
+      "PartyPoolBalancedPairDeployer": "0xfda454fF7876aad9408517Ed2F0d11AA229Ad0a4",
+      "USXD": "0x8E4D16886b8946dfE463fA172129eaBf4825fb09",
+      "FUSD": "0xdc225280216822CA956738390f589c794129bd53",
+      "DIVE": "0x7ba123e4e7395A361284d069bD0D545F3f820641",
+      "BUTC": "0x88125947BBF1A6dd0FeD4B257BB3f9E1FBdCb3Cc",
+      "WTETH": "0xC8dB65C0B9f4cf59097d4C5Bcb9e8E92B9e4e15F"
+    }
+  }
+}

doc/introduction.md

@@ -24,11 +24,14 @@ Naturally multi-asset, Liquidity Party altcoin pools provide direct, one-hop swa
 
 | Assets | Pairs | Swap Gas |  Mint Gas |
 |-------:|------:|---------:|----------:|
-|      2 |     1 |  146,000 |   149,000 |
+|      2 |     1 |  131,000 |   143,000 |
-|     10 |    45 |  157,000 |   426,000 |
+|     2* |     1 |  118,000 |   143,000 |
-|     20 |   190 |  171,000 |   772,000 |
+|     10 |    45 |  142,000 |   412,000 |
-|     50 |  1225 |  213,000 | 1,810,000 |
+|     20 |   190 |  157,000 |   749,000 |
-|    100 |  4950 |  283,000 | 3,542,000 |
+|     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.
 

doc/whitepaper.md

@@ -1,551 +1,170 @@
 # LMSR-based Multi-Asset AMM
 
-Abstract
+## Abstract
-We propose a multi-asset automated market maker (AMM) whose pricing kernel is the Logarithmic Market Scoring Rule (LMSR) (Hanson, 2002.) The AMM maintains a 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, $b(\mathbf{q}) = \kappa \, S(\mathbf{q})$ with $S(\mathbf{q}) = \sum_i q_i$ and fixed $\kappa>0$. This choice preserves scale-invariant responsiveness while retaining LMSR’s softmax pricing structure under a quasi-static-$b$ view. We derive closed-form expressions for asset-to-asset swaps in the induced two-asset subspace, including exact-in, exact-out, limit-hitting (swap-to-limit), and capped-output variants. We discuss numerical stability techniques (e.g., log-sum-exp reformulations, guarded domains) and a balanced two-asset specialization that enables polynomial approximations with provable error bounds. The protocol is parameter-fixed at deployment (no governance over $\kappa$ or fees), yielding reproducible behavior and transparent depth calibration. Analytical and numerical evidence suggest that this LMSR AMM combines desirable theoretical properties (convexity, path-independent cost differences at constant $b$, multi-asset support) with practical robustness (monotonicity preservation and conservative fallbacks). We outline liquidity operations (proportional and single-asset joins/exits), fee accrual to LPs via state appreciation, and risk considerations.
+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.
-
+
-Keywords
+## Introduction and Motivation
-AMM; LMSR; cost-function market maker; multi-asset liquidity; bounded loss; convex optimization; fixed-point arithmetic; numerical stability.
+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 market’s 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.
-
+
-2) Executive Summary
+## 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
-Motivation and problem
+$$
-- Multi-asset liquidity often faces a trade-off between simplicity (CFMM invariants) and expressivity (risk sharing across many assets). We pursue an AMM that natively supports many assets while delivering predictable depth and strong theoretical guarantees.
+C(\mathbf{q}) = b(\mathbf{q}) \log\!\left(\sum_{i=0}^{n-1} e^{q_i / b(\mathbf{q})}\right), \qquad b(\mathbf{q})=\kappa\,S(\mathbf{q}),\quad \kappa>0.
-
+$$
-Mechanism overview
+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
-- The AMM’s kernel is the LMSR cost function
+$$
-  $$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}),\;\; S(\mathbf{q})=\sum_i q_i.$$
+C(\mathbf{q}) \;=\; b(\mathbf{q}) \left( M + \log \sum_{i=0}^{n-1} e^{\,y_i - M} \right),
-- Instantaneous marginal price ratios follow the softmax structure under quasi-static $b$:
+$$
-  $$P(\text{base}\to\text{quote}\mid \mathbf{q})=\exp\!\left(\frac{q_{\text{quote}}-q_{\text{base}}}{b(\mathbf{q})}\right).$$
+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.
-
+
-Key properties
+## Gradient, Price Shares, and Pairwise Prices
-- Convex potential and softmax gradient (at constant $b$), multi-asset support via a single potential.
+With $b$ treated as a constant parameter, the LMSR gradient recovers softmax shares
-- Path independence of cost differences under constant $b$; pairwise price ratios preserved under $b=\kappa S$ via a common additive gradient term.
+$$
-- Bounded-loss intuition from LMSR extends proportionally with $b$; scale invariance via $b=\kappa S$.
+\frac{\partial C}{\partial q_i} \;=\; \frac{e^{q_i/b}}{\sum_k e^{q_k/b}} \;=:\; \pi_i(\mathbf{q}),
-- Closed forms for two-asset reductions enable exact-in/exact-out and limit-hitting swaps with monotonicity.
+$$
-
+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
-Main contributions
+$$
-- Fixed-parameter LMSR AMM: $b=\kappa S$ with immutable $\kappa$ and fees post-deployment.
+P(i\to j \mid \mathbf{q}) \;=\; \exp\!\left(\frac{q_j - q_i}{b(\mathbf{q})}\right).
-- Stability techniques: log-sum-exp evaluation, domain guards, ratio shortcuts, and conservative fallbacks.
+$$
-- Balanced two-asset optimization: polynomial approximations with error bounds and dispatcher preconditions.
+This ratio drives swap computations and is invariant to proportional rescaling $\mathbf{q}\mapsto \lambda\mathbf{q}$ because $b$ scales by the same factor.
-- Evaluation plan: analytical depth comparisons, numerical accuracy, monotonicity/no-negative-arbitrage checks, and gas microbenchmarks.
+
-
+## Two-Asset Reduction and Exact Swap Mappings
-3) Background and Related Work
+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
-
+$$
-AMM landscape
+r_0 \;:=\; \exp\!\left(\frac{q_i - q_j}{b}\right), \qquad b \equiv b(\mathbf{q})\;\text{ held quasi-static}.
-- CFMMs define implicit invariants over reserves. Examples include:
+$$
-  - Constant product (e.g., Uniswap): $x y = k$, offering simple two-asset liquidity and predictable slippage profiles.
+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
-  - Constant mean (e.g., Balancer): $\prod_i q_i^{w_i} = \text{const}$, generalizing to many assets with weights.
+$$
-  - Stableswap (e.g., Curve): combines constant sum and constant product to target low-slippage near parity.
+\mathrm{d}y \;=\; \frac{r(t)}{1+r(t)}\,\mathrm{d}t.
-- LMSR differs by specifying a convex cost function $C(\mathbf{q})$; prices are given by its gradient (or ratios thereof), rather than from a multiplicative invariant.
+$$
-
+Integrating from $t=0$ to $t=a$ yields the exact-in closed form
-LMSR primer and adaptation to AMMs
+$$
-- The classical LMSR potential with constant $b$ is
+y(a) \;=\; b \,\ln\!\Big( 1 + r_0 \,\big(1 - e^{-a/b}\big) \Big).
-  $$C(\mathbf{q}) = b \log\!\left(\sum_i e^{q_i/b}\right),\qquad \frac{\partial C}{\partial q_i} = \frac{e^{q_i/b}}{\sum_k e^{q_k/b}}.$$
+$$
-- In our AMM setting, we parameterize $b(\mathbf{q})=\kappa S(\mathbf{q})$ for scale-invariant responsiveness, and use a quasi-static-$b$ view to compute instantaneous price ratios:
+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
-  $$P(\text{base}\to\text{quote})=\frac{e^{q_{\text{quote}}/b}}{e^{q_{\text{base}}/b}}=\exp\!\left(\frac{q_{\text{quote}}-q_{\text{base}}}{b}\right).$$
+$$
-- Two-asset reduction yields closed forms for exact-in and exact-out trades (see Sections 5–6 and Appendix A).
+a(y) \;=\; b \,\ln\!\left(\frac{r_0}{\,r_0 + 1 - E\,}\right),
-
+$$
-Related LMSR applications and prior DeFi adaptations
+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.
-- LMSR originates from scoring-rule-based market making in information markets. Subsequent adaptations explored cost-function AMMs and variants that tailor $b$ to achieve targeted responsiveness. We adopt a proportional $b$ tied to total pool size for transparency and predictable scaling across liquidity regimes.
+
-
+## Price Limits, Swap-to-Limit, and Capacity Caps
-When LMSR is preferable and limitations
+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
-- Preferable when:
+$$
-  - Multi-asset exposure and cross-asset risk sharing are primary goals.
+a_{\text{lim}} \;=\; b \,\ln\!\left(\frac{\Lambda}{r_0}\right),
-  - A convex potential with softmax-driven pricing is desired for analytical tractability and monotonic behavior.
+$$
-- Limitations and design choices:
+and the output realized at that truncation is
-  - With $b=\kappa S$, gradient components include a common additive term; we rely on pairwise ratios for pricing.
+$$
-  - Extreme imbalances can induce steep price moves; capacity caps and domain guards mitigate numerical and economic edge cases.
+y_{\text{lim}} \;=\; b \,\ln\!\Big( 1 + r_0 \,\big(1 - r_0/\Lambda\big) \Big).
-
+$$
-4) System Model and Notation
+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,
-
+$$
-4.1 State, assets, and units
+a_{\text{cap}} \;=\; b \,\ln\!\left(\frac{r_0}{\,r_0 + 1 - e^{\,q_j/b}\,}\right).
-- Assets and indices: We consider $n \ge 2$ assets indexed by $i \in \{0,\dots,n-1\}$.
+$$
-- State vector: $\mathbf{q} = (q_0,\dots,q_{n-1}) \in \mathbb{R}_{\ge 0}^{\,n}$ denotes normalized internal quantities held by the pool. Each $q_i$ is in common “internal units” so cross-asset operations are comparable. In practice, token amounts are scaled to a common unit (e.g., $10^{-\text{decimals}}$ normalization) and represented with fixed-point arithmetic; equations here are stated over reals for clarity.
+These limit and capacity branches ensure monotone, conservative behavior near domain edges.
-- Size metric: $S(\mathbf{q}) := \sum_i q_i$. This is the aggregate pool size used both to summarize liquidity and to set the effective liquidity parameter.
+
-- Liquidity parameterization: The effective LMSR liquidity parameter is $b(\mathbf{q}) := \kappa \cdot S(\mathbf{q})$, where $\kappa > 0$ is a fixed, deployment-time constant. Intuitively, $b$ scales linearly with the pool’s total size, preserving responsiveness under proportional rescaling of $\mathbf{q}$.
+## Liquidity Operations from the Same Potential
-- Fees: Let $f_{\text{swap}} \in [0,1)$ denote the swap fee applied at the token layer (separate from the fee-free pricing kernel). Optionally a protocol fee $f_{\text{proto}}$ can be taken as a fraction of the swap fee. All derivations of kernel prices below are fee-free; fees are applied as multiplicative factors to input/output amounts outside the kernel.
+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
-
+$$
-4.2 Cost function and prices
+a \;=\; a_{\text{req}}(\alpha) \;=\; \alpha q_i \;+\; \sum_{j\ne i} b \,\ln\!\left(\frac{r_{0,j}}{\,r_{0,j} + 1 - e^{\,\alpha q_j/b}\,}\right), \quad r_{0,j}:=\exp\!\left(\frac{q_i-q_j}{b}\right),
-- Cost function: We use the LMSR cost function
+$$
-  $$C(\mathbf{q}) \;=\; b(\mathbf{q}) \,\log\!\left(\sum_{i} e^{\,q_i / b(\mathbf{q})}\right).$$
+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.
-  For numerical stability we compute it via a log-sum-exp formulation. Define $y_i := q_i / b(\mathbf{q})$ and $M := \max_i y_i$; then
+
-  $$C(\mathbf{q}) \;=\; b(\mathbf{q}) \left( M + \log \sum_{i} e^{\,y_i - M} \right).$$
+### Single-Asset Mint and Redeem
-- Price shares (softmax): Define the unnormalized weights $w_i := e^{q_i / b(\mathbf{q})}$ and $W := \sum_i w_i$. The price share of asset $i$ is
+
-  $$\pi_i(\mathbf{q}) := \frac{w_i}{W} \;=\; \frac{e^{q_i / b(\mathbf{q})}}{\sum_j e^{q_j / b(\mathbf{q})}}.$$
+#### Single-Asset Mint
-  Note: With $b$ constant, the gradient satisfies $\partial C/\partial q_i = \pi_i$. With $b = \kappa \, S(\mathbf{q})$, $\partial C/\partial q_i$ includes an additive term common across $i$; differences in marginal prices still track $\pi_i$ up to an additive constant, and the pairwise ratios below remain unchanged.
+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
-- Pairwise marginal price ratio: The instantaneous marginal price of “base” in units of “quote” is
+$$
-  $$P(\text{base}\to\text{quote}\mid \mathbf{q}) \;=\; \exp\!\left(\frac{q_{\text{quote}} - q_{\text{base}}}{b(\mathbf{q})}\right).$$
+x_j(\alpha) \;=\; b \,\ln\!\left(\frac{r_{0,j}}{\,r_{0,j} + 1 - e^{\,y_j/b}\,}\right),
-  This equals $w_{\text{quote}}/w_{\text{base}}$ and is invariant to the common softmax denominator, and remains valid under the quasi-static-$b$ swap model (holding $b$ constant over an infinitesimal trade or a single pricing step; see Appendix A).
+$$
-
+so the total required input for growth $\alpha$ is
-4.3 Swap quantities and conventions
+$$
-- Exact-in: Given an input amount $a \ge 0$ of asset $i$, the fee-free kernel determines the output amount $y \ge 0$ of asset $j$ by integrating the marginal price along the $i\to j$ path with $b$ held quasi-static at its pre-trade value (see Appendix A).
+a_{\text{req}}(\alpha) \;=\; \alpha\,q_i \;+\; \sum_{j\ne i} x_j(\alpha).
-- Exact-out: Given a desired output $y \ge 0$ of asset $j$, the fee-free kernel solves for the required input $a \ge 0$ of asset $i$ (inverse of exact-in).
+$$
-- Price limits (swap-to-limit): A user can provide a maximum acceptable marginal price ratio $\Lambda > 0$ for $p_i/p_j$. If the marginal price trajectory would exceed $\Lambda$ before consuming the full $a$, the swap truncates at the unique $a_{\text{lim}}$ that reaches $\Lambda$ (see Appendix A).
+Properties and solver:
-- Capacity caps: Outputs cannot exceed the available balance of the out-asset; if a formula would produce $y > q_j$, we cap to $q_j$ and solve inversely for the corresponding input.
+- 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).
-4.4 Units, scaling, and normalization
+- 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.
-- Token decimals: For each token $i$ with decimals $d_i$, on-chain amounts are normalized to a common internal unit so that arithmetic over $\mathbf{q}$ is coherent. Let $s_i$ be the scale factor implied by $d_i$; normalized internal balances are proportional to on-chain token balances via $s_i$.
+- Outcome: the consumed input is $a_{\text{in}} = a_{\text{req}}(\alpha^\star) \le a$ and minted LP shares are $\Delta L = \alpha^\star S(\mathbf{q})$.
-- Scale invariance: If $\mathbf{q}$ is scaled by $\lambda > 0$ (all assets multiplied by the same $\lambda$), then $S$ scales by $\lambda$ and $b = \kappa S$ scales by $\lambda$; prices as pairwise ratios, $P(\text{base}\to\text{quote})$, are invariant to this rescaling.
+
-
+#### Single-Asset Redeem
-4.5 Assumptions
+Burning a proportional share $\alpha \in (0,1]$ returns a single asset $i$ by redeeming and rebalancing from other assets into $i$:
-- Tokens are standard fungible assets with deterministic, non-rebasing balances; no transfer fees are embedded at the kernel level.
+1) Form the local state after burn, $\mathbf{q}_{\text{local}}=(1-\alpha)\,\mathbf{q}$.
-- Swaps and liquidity operations are atomic; the mechanism is permissionless (subject to access rules at the wrapper layer).
+2) Start with the direct redemption $\alpha\,q_i$ in asset $i$.
-- No external price oracles are required by the kernel; price discovery is endogenous via the cost function.
+3) For each $j\ne i$, withdraw $a_j := \alpha\,q_j$ and swap $j\to i$ using the exact-in form evaluated at $\mathbf{q}_{\text{local}}$:
-- Numerical computations are performed in fixed-point with explicit domain guards (see Appendix B).
+$$
-
+r_{0,j} \;=\; \exp\!\left(\frac{q^{\text{local}}_j - q^{\text{local}}_i}{b}\right),\qquad
-5) AMM Design and LMSR Formulation
+y_{j\to i} \;=\; b \,\ln\!\Big(1 + r_{0,j}\,\big(1 - e^{-a_j/b}\big)\Big).
-
+$$
-5.1 Convex potential and invariant view
+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
-- We model the pool by the LMSR potential
+$$
-  $$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}),\;\; S(\mathbf{q})=\sum_i q_i,$$
+a_{j,\text{used}} \;=\; b \,\ln\!\left(\frac{r_{0,j}}{\,r_{0,j} + 1 - e^{\,q^{\text{local}}_i/b}\,}\right),
-  which induces a softmax over coordinates of $\mathbf{q}$. For pricing, we operate under a quasi-static-$b$ view for an infinitesimal step, recovering the usual LMSR gradient structure (see Section 6 and Appendix A).
+$$
-- Intuition: $C$ is a convex potential in $\mathbf{q}$ when $b$ is treated as a constant parameter; gradient components are softmax probabilities. This convexity underpins path independence of cost differences and no-arbitrage properties in the constant-$b$ setting. With $b=\kappa S(\mathbf{q})$, the gradient picks up a common additive term across coordinates; pairwise price ratios, which drive swaps, remain governed by softmax differences (Appendix A).
+then update $\mathbf{q}_{\text{local}}$ accordingly.
-
+5) The single-asset payout is
-5.2 Kappa parameterization: $b=\kappa \cdot S$
+$$
-- Rationale: Choosing $b$ proportional to pool size preserves responsiveness under proportional rescalings of inventory. If all $q_i$ are multiplied by $\lambda>0$, then $S$ and $b$ scale by $\lambda$, while price ratios
+Y_i \;=\; \alpha\,q_i \;+\; \sum_{j\ne i} y_{j\to i}, \qquad \text{with LP burned } L_{\text{in}} = \alpha \, S(\mathbf{q}).
-  $$P(\text{base}\to\text{quote}\mid \mathbf{q}) \;=\; \exp\!\left(\frac{q_{\text{quote}}-q_{\text{base}}}{b(\mathbf{q})}\right)$$
+$$
-  remain invariant.
+Guards and behavior:
-- Responsiveness: Smaller $\kappa$ yields smaller $b$ for a given $S$, producing steeper price impact (more responsive market); larger $\kappa$ produces deeper liquidity and gentler impact.
+- 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.
-- Conformance: The induced prices coincide with the classic LMSR softmax ratios under quasi-static-$b$, ensuring consistency with LMSR’s scoring-rule interpretation for marginal moves.
+- The mapping is monotone in $\alpha$; the cap-and-invert branch preserves safety near capacity.
-
+
-5.3 Choice of $S$ and alternatives
+### LP Pricing vs. an Asset Token
-- Default choice: $S(\mathbf{q})=\sum_i q_i$ (the $\ell_1$ size metric) is transparent, easy to compute, and scale-consistent across assets in normalized units.
+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 $k$:
-- Alternatives:
+$$
-  - Weighted sum: $S_w(\mathbf{q})=\sum_i w_i q_i$ for exogenous weights $w_i>0$; may bias depth across assets.
+P_L^{(k)}(\mathbf{q}) \;=\; \frac{1}{S(\mathbf{q})}\,\sum_{j=0}^{n-1} q_j \,\exp\!\left(\frac{q_j - q_k}{b(\mathbf{q})}\right).
-  - Quadratic norm: $S_2(\mathbf{q})=(\sum_i q_i^2)^{1/2}$; increases $b$ more when inventory is concentrated, potentially dampening extreme price moves.
+$$
-- Trade-offs: Simplicity, composability, and transparency argue for $S=\sum_i q_i$. Alternatives can tailor depth but complicate interpretation and comparability.
+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.
-
+
-5.4 Fixed-parameter policy
+## Numerical Methods and Safety Guarantees
-- The proportionality constant $\kappa$ and fee parameters are set at deployment and remain immutable. This yields reproducible behavior, eliminates governance risk, and allows users to evaluate depth and price impact ex-ante for a given $S$.
+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.
-
+
-5.5 Bounded-loss and capital efficiency implications
+## Balanced Regime Optimization: Approximations, Dispatcher, and Stability
-- Classical LMSR with constant $b$ admits a bounded-loss guarantee of $b\ln n$ in appropriate units. With $b=\kappa S(\mathbf{q})$, scale invariance implies an instantaneous bound per unit of $S$ that is proportional to $\kappa \ln n$; as liquidity scales, so does absolute depth and the notional bound.
+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
-- Capital efficiency: For fixed $\kappa$, larger $S$ linearly increases price depth while preserving price ratios; for fixed $S$, tuning $\kappa$ linearly trades off depth versus responsiveness. The two-asset closed forms in Section 6 quantify this via $y(a)$ and its slope at the origin $y'(0)=\frac{r_0}{1+r_0}$.
+$$
-
+y(a) \;=\; b \,\ln\!\Big(1 + e^{\delta}\,\big(1 - e^{-\tau}\big)\Big)
-6) Pricing and Swap Mechanics
+$$
-
+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
-6.1 Instantaneous pricing from the gradient
+$$
-- Define unnormalized weights $w_i = e^{q_i/b}$ and $W=\sum_k w_k$. Under quasi-static $b$,
+y(a) \;\approx\; b \left[ r_0 \tau - \tfrac{1}{2} r_0 \tau^2 \right] + \mathcal{O}\!\left(\tau^3,\, |\delta|\,\tau^2\right), \qquad r_0=e^{\delta}\approx 1+\delta+\tfrac{\delta^2}{2},
-  $$\pi_i(\mathbf{q})=\frac{\partial C}{\partial q_i}=\frac{w_i}{W},\qquad
+$$
-  \frac{\pi_{\text{quote}}}{\pi_{\text{base}}}=\frac{w_{\text{quote}}}{w_{\text{base}}}=\exp\!\left(\frac{q_{\text{quote}}-q_{\text{base}}}{b}\right).$$
+and at $\delta=0$ the symmetry reduces to $y(a)\approx \tfrac{a}{2} - \tfrac{a^2}{4b} + \cdots$.
-  We interpret $P(\text{base}\to\text{quote}) := \pi_{\text{quote}}/\pi_{\text{base}}$ as the instantaneous marginal price ratio.
+
-
+### Dispatcher preconditions and thresholds (approx path):
-6.2 Cost differences and asset-to-asset swaps
+- Scope: two-asset pools only; otherwise use the exact path.
-- Conceptually, an asset-to-asset trade from $i$ to $j$ of sizes $(+a,-y)$ satisfies
+- Magnitude bounds: $|\delta| \le 0.01$ and $\tau := a/b$ satisfies $0 < \tau \le 0.5$.
-  $$\Delta C \;=\; C(\mathbf{q} + a\,\mathbf{e}_i - y\,\mathbf{e}_j) - C(\mathbf{q}),$$
+- Tiering: use the quadratic surrogate for $\tau \le 0.1$, and include a cubic correction for $0.1 < \tau \le 0.5$.
-  and the two-asset reduction with quasi-static $b$ yields a closed-form relation between $a$ and $y$ (Appendix A):
+- 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 $\Lambda \le r_0$).
-  $$y(a) \;=\; b \,\ln\!\Big( 1 + r_0 \,\big(1 - e^{-a/b}\big) \Big),\qquad r_0 := \exp\!\left(\frac{q_i - q_j}{b}\right).$$
+- 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.
-- The inverse exact-out mapping for a target $y$ is
+- 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, $e^{\delta_\star}\approx 1.01005$).
-  $$a(y) \;=\; b \,\ln\!\left(\frac{r_0}{\,r_0 + 1 - e^{\,y/b}\,}\right).$$
+
-
+### Approximation Path
-6.3 Limit-hitting swaps and swap-to-limit
+- 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.
-- For a user-specified price limit $\Lambda > 0$ on $p_i/p_j$, the marginal price trajectory $r(t)=r_0 e^{t/b}$ hits the limit at
+- Cache common subexpressions (e.g., $r_0=e^\delta$, $\tau=a/b$) and guard inner terms to remain in $(0,\infty)$.
-  $$a_{\text{lim}} \;=\; b \,\ln\!\left(\frac{\Lambda}{r_0}\right),\qquad
+
-    y_{\text{lim}} \;=\; b \,\ln\!\Big( 1 + r_0 \,\big(1 - r_0/\Lambda\big) \Big).$$
+### Fallback Policy
-- Capacity cap: If $y_{\text{lim}} > q_j$, cap to $y=q_j$ and use the inverse mapping to compute the implied input
+- 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.
-  $$a_{\text{cap}} \;=\; b \,\ln\!\left(\frac{r_0}{\,r_0 + 1 - e^{\,q_j/b}\,}\right).$$
+- Prefer cap-and-invert near capacity or when the inner term of $\ln(\cdot)$ approaches zero.
-
+
-6.4 Properties: monotonicity, uniqueness, and stability
+### Error Shape
-- Monotonicity and uniqueness: For feasible states, $y(a)$ is strictly increasing and concave in $a$; the inverse $a(y)$ is strictly increasing and convex in $y$. The limit-hitting $a_{\text{lim}}$ is unique when $\Lambda>r_0$.
+- 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 $c_1,c_2$.
-- Numerical stability: Evaluations use log-sum-exp style reformulations, direct ratio formation for $r_0$, and argument guards for $\exp$ and $\ln$. Domain checks ensure denominators (e.g., $r_0 + 1 - e^{y/b}$) remain positive. See Appendix B for details.
+- 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.
-7) Liquidity Operations
+
-
+## Fees and Economic Considerations
-7.1 Pool initialization and bootstrap
+Swap fees are applied outside the fee-free kernel. For an exact-in submission $a$ on asset $i$, the effective kernel input is $a_{\text{eff}}=(1-f_{\text{swap}})a$. The kernel computes output using $a_{\text{eff}}$, while the retained fee remains in the pool, increasing $S(\mathbf{q})$ relative to outstanding $L$ and thereby accruing value to LPs implicitly. Scale invariance under $b=\kappa S$ implies that proportional growth of inventories preserves price ratios while deepening notional liquidity linearly. The classical LMSR bounded-loss intuition for constant $b$ gives $b\ln n$ in appropriate units; under our proportional $b$, this scales with $S$, so the instantaneous bound per unit of $S$ is proportional to $\kappa\ln n$.
-- Let the seed inventory be $\mathbf{q}^{(0)} \in \mathbb{R}_{\ge 0}^{\,n}$ with $S^{(0)} := \sum_i q_i^{(0)} > 0$. The effective liquidity is $b^{(0)} = \kappa\,S^{(0)}$.
+
-- LP supply: We take LP supply proportional to the size metric, $L := \eta\,S(\mathbf{q})$, with a fixed conversion $\eta>0$. Without loss of generality we set $\eta=1$ so that
+## Risk Management and Bounded Loss
-  $$L \;=\; S(\mathbf{q}) \;=\; \sum_i q_i.$$
+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.
-  At bootstrap, the seeder mints $L^{(0)} = S^{(0)}$ LP shares against $\mathbf{q}^{(0)}$.
+
-- LP price in units of asset $k$: Define the marginal value of one unit of $S$ in asset $k$ as
+## Deployment and Parameter Fixity
-  $$P_L^{(k)}(\mathbf{q}) \;=\; \frac{1}{S(\mathbf{q})}\,\sum_{j=0}^{n-1} q_j \,\exp\!\left(\frac{q_j - q_k}{b(\mathbf{q})}\right),$$
+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
-  which aggregates the marginal exchange rates from each asset into $k$ (cf. Section 6).
+$$
-
+C(\mathbf{q}) = b(\mathbf{q}) \log\!\left(\sum_i e^{q_i / b(\mathbf{q})}\right), \qquad b(\mathbf{q})=\kappa S(\mathbf{q}),
-7.2 Proportional deposit (mint)
+$$
-- A proportional deposit scales all coordinates by $(1+\alpha)$ for some $\alpha \ge 0$:
+and the two-asset closed forms above. Fixity eliminates governance risk, makes depth calibration transparent, and simplifies integration for external routers and valuation tools.
-  $$\mathbf{q}' \;=\; (1+\alpha)\,\mathbf{q},\qquad \Delta q_i \;=\; \alpha\,q_i.$$
+
-- Minted LP shares are linear in the size-metric increase:
+## Conclusion
-  $$\Delta L \;=\; L' - L \;=\; S(\mathbf{q}') - S(\mathbf{q}) \;=\; \alpha\,S(\mathbf{q}).$$
+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.
-- The post-deposit liquidity is $b'=\kappa\,S(\mathbf{q}')=(1+\alpha)\,b$.
+
-
+## References
-7.3 Single-asset deposit (exact-in)
+Hanson, R. (2002) [_Logarithmic Market Scoring Rules for Modular Combinatorial Information Aggregation_](https://mason.gmu.edu/~rhanson/mktscore.pdf)
-- A contributor provides amount $a$ of asset $i$ and receives a proportional growth $\alpha \ge 0$ such that the system state can be rebalanced to $(1+\alpha)\,\mathbf{q}$ by swapping from $i$ into $j\ne i$ along the fee-free kernel. For each $j \ne i$, target out-amount $y_j := \alpha\,q_j$ requires input
-  $$x_j(\alpha) \;=\; b \,\ln\!\left(\frac{r_{0,j}}{\,r_{0,j} + 1 - e^{\,y_j/b}\,}\right),\qquad
-    r_{0,j} \;:=\; \exp\!\left(\frac{q_i - q_j}{b}\right).$$
-- The total input required to realize proportional growth $\alpha$ is
-  $$a_{\text{req}}(\alpha) \;=\; \alpha\,q_i \;+\; \sum_{j\ne i} x_j(\alpha).$$
-- The minted shares are
-  $$\Delta L \;=\; \alpha\,S(\mathbf{q}),$$
-  where $\alpha$ is the unique solution to $a_{\text{req}}(\alpha)=a$ on its feasible domain (see Appendix A.5).
-
-7.4 Multi-asset deposit (arbitrary vector)
-- Given a deposit vector $\mathbf{a} \in \mathbb{R}_{\ge 0}^{\,n}$, decompose it into:
-  - a proportional component $\bar{\alpha} := \min_i \{ a_i / q_i \}$ (with convention $a_i/q_i=+\infty$ if $q_i=0$ and $a_i>0$), which mints $\bar{\alpha}\,S(\mathbf{q})$ shares and updates $\mathbf{q}$ proportionally, and
-  - residuals $\tilde{\mathbf{a}} := \mathbf{a} - \bar{\alpha}\,\mathbf{q}$ that can be contributed via single-asset deposit(s) using 7.3 (sequence or batching).
-- The total minted shares are additive in the realized proportional growths:
-  $$\Delta L \;=\; \left(\bar{\alpha} + \sum_{m} \alpha_m\right)\,S(\mathbf{q})$$
-  where each $\alpha_m$ solves $a_{\text{req}}(\alpha_m)$ for a residual leg.
-
-7.5 Proportional withdrawal (burn)
-- Burning $\Delta L$ LP shares effects a proportional redemption with factor
-  $$\alpha \;=\; \frac{\Delta L}{S(\mathbf{q})} \in (0,1],\qquad \mathbf{q}' \;=\; (1-\alpha)\,\mathbf{q}.$$
-- The holder receives $\alpha\,q_i$ units of each asset $i$; equivalently, $L' = L - \Delta L = S(\mathbf{q}')$ and $b'=(1-\alpha)\,b$.
-
-7.6 Single-asset withdrawal (exact-out)
-- A holder burns $\Delta L$ shares (i.e., $\alpha=\Delta L/S(\mathbf{q})$) and requests payout exclusively in asset $i$. Starting from $\mathbf{q}_\text{local}=(1-\alpha)\,\mathbf{q}$, for each $j\ne i$:
-  - withdraw $\alpha\,q_j$ units of $j$, and
-  - swap $j \to i$ along the fee-free kernel using the two-asset closed form. The candidate out-amount is
-    $$y_{j\to i} \;=\; b \,\ln\!\Big( 1 + r_{0,j}\,\big(1 - e^{-a_j/b}\big) \Big),\quad
-      a_j := \alpha\,q_j,\quad r_{0,j} := \exp\!\left(\frac{q^{\text{local}}_j - q^{\text{local}}_i}{b}\right),$$
-    with $b=\kappa\,S(\mathbf{q})$ evaluated at pre-burn or quasi-static local state.
-- If the computed $y_{j\to i}$ would exceed $q^{\text{local}}_i$, cap to capacity and invert to solve the implied input (Appendix A.6). The total single-asset payout is
-  $$Y_i \;=\; \alpha\,q_i \;+\; \sum_{j\ne i} y_{j\to i}.$$
-
-7.7 Share issuance, pricing, and dilution
-- With $L=S$, share issuance is linear in the size-metric; proportional joins/exits preserve relative ownership. The instantaneous LP price in units of asset $k$ is $P_L^{(k)}(\mathbf{q})$ from 7.1. Under joins, $P_L^{(k)}$ remains unchanged for proportional deposits; under single-asset joins, it adjusts according to the realized rebalancing path.
-
-7.8 Fee accrual to LPs and value capture
-- Swap fees are taken at the token layer and retained in the pool balances, increasing $S(\mathbf{q})$ relative to $L$ and thereby raising $P_L^{(k)}$ for all $k$. This constitutes implicit fee accrual to LPs via state appreciation rather than explicit distributions.
-
-7.9 Edge cases and operational notes
-- Tiny liquidity: When $S$ is small, $b=\kappa S$ is small and price impact is steep; deployments SHOULD enforce a minimum bootstrap $S^{(0)}$ and/or minimum minted $L^{(0)}$.
-- Extreme imbalances: As some $q_j \to 0$, price ratios $\exp((q_{\text{quote}}-q_{\text{base}})/b)$ can become large; capacity caps ($y \le q_j$) and positivity checks on logarithm arguments ensure safe evaluation.
-- Asset additions/removals: Changing the asset set alters $n$ and the pricing manifold. Deployments typically fix the asset universe; adding/removing assets is best handled via new pool instances with fresh initialization.
-
-8) Fees and Incentives (Static Parameters)
-
-8.1 Fee model and placement
-- Let the swap fee rate be $f_{\text{swap}} \in [0,1)$, and let the protocol capture a fraction $\phi \in [0,1]$ of that fee (so LPs receive the remaining $1-\phi$ share via state appreciation).
-- We apply fees outside the fee-free pricing kernel. For an exact-in trade with submitted input $a$ on asset $i$, the effective kernel input is
-  $$a_{\text{eff}} \;=\; (1 - f_{\text{swap}})\,a.$$
-  The fee amount is $a - a_{\text{eff}}$, of which $\phi\,(a - a_{\text{eff}})$ accrues to the protocol and $(1-\phi)\,(a - a_{\text{eff}})$ to LPs (retained in the pool state).
-- The fee-free kernel computes the out-amount $y_{\text{ker}}$ using $a_{\text{eff}}$; the user receives $y_{\text{user}} = y_{\text{ker}}$ (or a fee-adjusted variant if fees are taken from output instead). The invariant and closed forms remain unaffected because pricing is computed on $a_{\text{eff}}$.
-
-8.2 Economic impact
-- Effective price and slippage: With input-side fees, the user’s effective marginal price scales by $(1 - f_{\text{swap}})^{-1}$ for small trades; total slippage decomposes into kernel slippage (from the LMSR curve) plus a constant offset due to fees.
-- LP returns: Fees retained in the pool increase $S(\mathbf{q})$ relative to outstanding $L$ and thus raise LP share value. Protocol revenue scales with $\phi$ and trade flow; LP revenue scales with $(1-\phi)$.
-
-8.3 Static-parameter policy (immutability)
-- Parameters $\kappa$, $f_{\text{swap}}$, and $\phi$ are set at deployment and are immutable thereafter. Benefits include:
-  - Predictability: depth and fee impact are ex-ante auditable for a given $S$.
-  - Governance minimization: no discretionary levers to be toggled post-deployment.
-  - Composability: integrators can rely on stable behavior across time.
-
-9) Risk Analysis and Theoretical Properties
-
-9.1 Convexity and path independence
-- With constant $b$, $C(\mathbf{q}) = b\log\!\big(\sum_i e^{q_i/b}\big)$ is convex and cost differences are path independent:
-  $$\Delta C \;=\; C(\mathbf{q}+\Delta\mathbf{q}) - C(\mathbf{q}) \quad \text{depends only on the endpoints}.$$
-- With $b=\kappa S(\mathbf{q})$, $\partial C/\partial q_i$ includes a common additive term (Section 4); pairwise ratios
-  $$P(\text{base}\to\text{quote}\mid \mathbf{q}) \;=\; \exp\!\left(\frac{q_{\text{quote}}-q_{\text{base}}}{b(\mathbf{q})}\right)$$
-  remain valid under a quasi-static-$b$ view, which is the pricing lens used for infinitesimal (or discretized) steps.
-
-9.2 Bounded loss (intuition) and capital efficiency
-- For constant $b$, the classic LMSR worst-case loss is $b\ln n$ in the payout numéraire. Under $b=\kappa S$, this scales proportionally with $S$, giving an instantaneous per-unit-$S$ bound proportional to $\kappa \ln n$.
-- Capital efficiency follows from linear scaling: increasing $S$ (or $\kappa$) linearly deepens liquidity. The two-asset exact-in form
-  $$y(a) \;=\; b\,\ln\!\Big(1 + r_0(1 - e^{-a/b})\Big)$$
-  exhibits $y'(0)=\frac{r_0}{1+r_0}$ and curvature $\frac{\mathrm{d}^2 y}{\mathrm{d}a^2}<0$, quantifying the marginal depth and diminishing returns for larger $a$.
-
-9.3 Sensitivity to $b$ and reserve scales
-- Scale invariance: If $\mathbf{q}\mapsto \lambda \mathbf{q}$, then $S\mapsto \lambda S$, $b\mapsto \lambda b$, and $P(\text{base}\to\text{quote})$ is unchanged. Thus depth in notional terms scales linearly with $\lambda$.
-- As $b$ increases (via larger $S$ or $\kappa$), the function $y(a)$ becomes less curved (greater depth), reducing slippage for a given input size $a$.
-
-9.4 Failure modes and mitigations
-- Thin liquidity: Small $S$ implies small $b$, steep impact, and sensitivity to large orders. Mitigations: enforce minimum bootstrap $S^{(0)}$, external routing safeguards, and user-specified price limits $\Lambda$.
-- Extreme concentration: As some $q_j \to 0$, prices can become very large; capacity caps ($y\le q_j$) and limit-hitting logic prevent pathological outputs.
-- Numerical edge cases: Guard $\exp$/$\ln$ domains, ensure denominators like $r_0 + 1 - e^{y/b} > 0$, and prefer ratio-based computations (Appendix B).
-- No-arbitrage hygiene: Maintain monotonicity of $y(a)$ and its inverse $a(y)$; avoid rounding that could create free lunches (see Section 12).
-
-10) Numerical Methods and Implementation Considerations
-
-10.1 Fixed-point arithmetic and precision policy
-- Representation: Quantities are computed in fixed-point; equations are presented over reals for clarity. Let $F$ denote the fractional precision (bits or decimal places).
-- Range limits: For stability of exponentials and logarithms, enforce
-  $$|x| \le X_{\max} \quad \text{when evaluating } \exp(x),\qquad u > 0 \quad \text{when evaluating } \ln(u).$$
-  Practical choices take $X_{\max}$ large enough to cover the operating envelope while preventing overflow.
-- Rounding: Use round-toward-zero or round-to-nearest consistently, prioritizing order-preservation (see 10.6). Avoid mixed rounding modes within a single expression.
-
-10.2 Stable exp/log evaluation (log-sum-exp)
-- Cost and shares are evaluated via a log-sum-exp recentering. Define $y_i := q_i/b$, $M := \max_i y_i$, then
-  $$C(\mathbf{q}) \;=\; b\left(M + \log \sum_i e^{\,y_i - M}\right),\qquad
-    \pi_i \;=\; \frac{e^{\,y_i - M}}{\sum_k e^{\,y_k - M}}.$$
-  Centering at $M$ prevents overflow/underflow when $y_i$ are far apart.
-- Ratio formation: Compute ratios directly to avoid extra $\exp$/$\ln$ where possible, e.g.
-  $$r_0 \;=\; \exp\!\left(\frac{q_i - q_j}{b}\right)$$
-  rather than $e^{q_i/b}/e^{q_j/b}$.
-
-10.3 Reformulations for numerical stability
-- Use $\ln(1+u)$ and $e^x-1$ style identities for small arguments:
-  $$\ln(1+u) \approx u - \frac{u^2}{2} \quad (|u|\ll 1),\qquad e^{x}-1 \approx x + \frac{x^2}{2} \quad (|x|\ll 1),$$
-  switching to series forms when $|u|$ or $|x|$ are below thresholds to reduce cancellation.
-- Inverse mapping stability: For exact-out inversion
-  $$a(y) \;=\; b \,\ln\!\left(\frac{r_0}{\,r_0 + 1 - e^{\,y/b}\,}\right),$$
-  compute $E:=e^{y/b}$ once; if $E\approx 1$, use series for $E-1$ to avoid subtractive cancellation.
-- Precompute reciprocals: Cache $b^{-1}$ to replace divisions by multiplications and reduce dispersion.
-
-10.4 Algorithm selection, termination, and convergence
-- Closed forms: Prefer the exact two-asset formulas for exact-in and exact-out when applicable (Sections 6 and A.2–A.3).
-- Root-finding for proportional joins: Solve $a_{\text{req}}(\alpha)=a$ via bracketing and bisection on a monotone map:
-  $$a_{\text{req}}(\alpha) \;=\; \alpha q_i + \sum_{j\ne i} b \ln\!\left(\frac{r_{0,j}}{\,r_{0,j} + 1 - e^{\,\alpha q_j/b}\,}\right).$$
-  Terminate when the interval width is below $\varepsilon$ or the function gap is within tolerance. Monotonicity guarantees uniqueness.
-- Limit-hitting: Compute $a_{\text{lim}}=b\ln(\Lambda/r_0)$ directly; validate $\Lambda>r_0$ and that intermediate expressions stay in-range.
-
-10.5 Performance vs precision trade-offs
-- Caching: Reuse common subexpressions (e.g., $b$, $b^{-1}$, $r_{0,j}$) across loops and iterative steps.
-- Operation count: Prefer fused operations and single-pass accumulations (e.g., recentered $\sum e^{\cdot}$ with on-the-fly rescaling).
-- Approximation regions: In designated near-balanced regimes (Section 11), switch to polynomial approximations to avoid transcendental calls, respecting global error budgets.
-
-10.6 Error analysis, monotonicity, and arbitrage-safety
-- Error budgeting: Allocate a maximum relative error $\epsilon_{\text{rel}}$ to each primitive ($\exp$, $\ln$, polynomials), ensuring the composed map (e.g., $y(a)$) meets end-to-end bounds.
-- Monotonicity preservation: Ensure numerical implementations of $y(a)$ are strictly increasing and of $a(y)$ are strictly increasing by:
-  - enforcing positive denominators (e.g., $r_0 + 1 - e^{y/b} > 0$),
-  - clamping intermediate “inner” terms to $(0,\infty)$,
-  - preferring formulations without subtractive cancellation near boundaries.
-- Arbitrage hygiene: Use conservative branches (cap-and-invert) when near capacity or domain boundaries to avoid nonphysical outputs (negative or exceeding balances).
-
-11) BalancedPair Optimization (Dedicated Section)
-
-11.1 Applicability conditions
-- Define $\delta := (q_i - q_j)/b$ and $\tau := a/b$. The balanced regime is characterized by
-  $$|\delta| \le \delta_\star,\qquad |\tau| \le \tau_\star,$$
-  with design thresholds $(\delta_\star,\tau_\star)$ chosen so that polynomial approximations meet the global error budget while preserving monotonicity.
-
-11.2 Balanced 2-asset closed form and small-argument expansions
-- The exact two-asset mapping is
-  $$y(a) \;=\; b \,\ln\!\Big(1 + r_0 (1 - e^{-a/b})\Big),\qquad r_0=e^{\delta}.$$
-- For $|\delta|\ll 1$ and $|\tau|\ll 1$, use expansions
-  $$e^{\pm x} \approx 1 \pm x + \frac{x^2}{2},\qquad \ln(1+u) \approx u - \frac{u^2}{2},$$
-  yielding
-  $$y(a) \;\approx\; b \left[ r_0 \tau - \frac{1}{2} r_0 \tau^2 \right] + \mathcal{O}\!\left(\tau^3,\, |\delta|\,\tau^2\right),\quad r_0 \approx 1 + \delta + \frac{\delta^2}{2}.$$
-- Symmetry: At $\delta=0$, the mapping satisfies $y(a)\approx \tfrac{a}{2} - \tfrac{a^2}{4b} + \cdots$, reflecting equal liquidity on both sides.
-
-11.3 Polynomial approximations without $\exp/\ln$
-- Construct minimax polynomials $P_d(x)\approx e^{x}$ on $[-\tau_\star,0]$ and $Q_d(u)\approx \ln(1+u)$ on $[0,u_\star]$, where $u_\star$ is induced by the range of $r_0(1-e^{-\tau})$ in the regime.
-- Compose
-  $$\tilde{y}(a) \;=\; b \, Q_d\!\Big( r_0 \,\big(1 - P_d(-\tau)\big) \Big),\qquad \tau=\frac{a}{b},$$
-  with $r_0$ optionally approximated by a low-degree polynomial in $\delta$ when $|\delta|\le \delta_\star$.
-- Error bounds:
-  $$\big|e^{x}-P_d(x)\big| \le e^{\tau_\star}\,\frac{\tau_\star^{\,d+1}}{(d+1)!},\qquad
-    \big|\ln(1+u)-Q_d(u)\big| \le \frac{u^{\,d+1}}{(d+1)\,(1-u)^{\,d+1}},$$
-  ensuring $\big|y(a)-\tilde{y}(a)\big| \le \epsilon$ for a target $\epsilon$ via appropriate $d$, $\delta_\star$, $\tau_\star$, $u_\star$.
-
-11.4 Dispatcher logic and safe fallback
-- Preconditions:
-  - check $|\delta|\le \delta_\star$, $|a|/b \le \tau_\star$, and positivity of intermediate “inner” terms,
-  - ensure capacity is respected ($\tilde{y}(a)\le q_j$) or switch to cap-and-invert branch.
-- If any precondition fails, fall back to the general closed-form path with full transcendental evaluations.
-- Price-limit compatibility: When a price limit $\Lambda$ is set, verify that the approximated trajectory respects $r(t)\le \Lambda$; otherwise, revert to exact limit-hitting computation $a_{\text{lim}}=b\ln(\Lambda/r_0)$.
-
-11.5 Invariant preservation and monotonicity guarantees
-- Enforce $\tilde{y}'(a) > 0$ on the approximation domain by design (choose $P_d$, $Q_d$ that are monotonically increasing on their intervals and validate numerically).
-- Guard inner arguments to keep them in $(0,\infty)$, preventing nonphysical outputs or $\ln$ domain violations.
-- Capacity and nonnegativity: Clamp to $[0, q_j]$ and use inverse mapping to reconcile inputs in cap branches.
-
-11.6 Gas and performance analysis
-- Eliminating transcendental calls in the balanced regime reduces cost to a small fixed number of polynomial evaluations and multiplications.
-- Dispatcher overhead is minimal (few comparisons and a couple of scaled differences). Overall, the optimization provides substantial speedups in near-parity trades while maintaining accuracy guarantees.
-- The fallback ensures worst-case performance is bounded by the general path.
-
-12) Protocol Safety: Numerical and Invariant Guarantees
-
-12.1 Invariant checks and fail-fast conditions
-- Domain guards:
-  - Size metric: $S(\mathbf{q}) = \sum_i q_i > 0$, hence $b=\kappa S > 0$.
-  - Valid indices and nonnegative inputs/outputs for user-facing operations.
-  - Exponential and logarithm arguments within bounded, valid domains; prefer log-sum-exp recentering.
-- Capacity and limit checks:
-  - Out-amounts are capped by available balances ($y \le q_j$).
-  - Price-limit trades enforce $\Lambda > r_0$ and truncate at $a_{\text{lim}}=b\ln(\Lambda/r_0)$.
-- Consistency guards:
-  - Denominators (e.g., $r_0 + 1 - e^{y/b}$) must be positive.
-  - Reciprocal quantities (e.g., $1/b$) are computed once and reused to avoid drift.
-
-12.2 Precision-induced error handling and rounding
-- Monotonicity-first policy: Prefer formulations that preserve order (e.g., log-sum-exp, ratio formation for $r_0$).
-- Conservative rounding: When a decision boundary is approached (e.g., inner argument of $\ln$ near zero), choose the conservative branch (cap-and-invert) rather than extrapolating.
-- Bounded evaluations: Enforce $|x| \le X_{\max}$ for $\exp(x)$ to prevent overflow; clamp inputs that would violate this bound and surface clear errors to callers.
-
-12.3 Verification targets
-- Structural properties:
-  - Convexity under constant $b$; gradient softmax identities.
-  - Pairwise price ratios consistent with $P(\text{base}\to\text{quote})$ under quasi-static $b$.
-- Numerical properties:
-  - Monotonicity of $y(a)$ and $a(y)$, uniqueness of $a_{\text{lim}}$ when $\Lambda>r_0$.
-  - Path-independence of $\Delta C$ in constant-$b$ tests; bounded relative error within predefined budgets.
-
-12.4 Testing approach
-- Property-based tests across randomized states $\mathbf{q}$, input sizes, and asset pairs, including adversarial edge cases (tiny $S$, extreme $r_0$, near-capacity).
-- Boundary tests for domain guards (e.g., $S\downarrow 0$, $\Lambda \downarrow r_0$, inner argument of $\ln$ near zero).
-- Differential tests against high-precision reference implementations for $y(a)$, $a(y)$, and price ratios.
-- No-negative-arbitrage checks under rounding: ensure discrete effects cannot be exploited for profit with zero risk.
-
-13) Deployment Model and Parameter Fixity
-
-13.1 Immutable parameters and non-upgradability
-- The pool is deployed with a fixed asset set and immutable parameters $(\kappa, f_{\text{swap}}, \phi)$, where $\kappa>0$ determines $b(\mathbf{q})=\kappa S(\mathbf{q})$, $f_{\text{swap}}$ is the swap fee rate, and $\phi$ is the protocol share of fees.
-- Contracts are deployed in a non-upgradable, ownerless configuration. No governance can modify $\kappa$, fees, or the asset universe after deployment.
-
-13.2 Deployment inputs and initialization
-- Deployment specifies: the asset list, normalization conventions, and parameter tuple $(\kappa, f_{\text{swap}}, \phi)$. Initialization requires a seed inventory $\mathbf{q}^{(0)}$ with $S^{(0)}=\sum_i q_i^{(0)}>0$, yielding initial liquidity
-  $$b^{(0)} \;=\; \kappa \, S^{(0)}.$$
-- A minimum bootstrap size $S^{(0)}$ SHOULD be enforced to avoid thin-liquidity regimes at genesis.
-
-13.3 Reproducibility and transparency
-- Given $(\kappa, f_{\text{swap}}, \phi)$ and the initial state $\mathbf{q}^{(0)}$, the AMM’s pricing map is fully determined for all subsequent states via
-  $$C(\mathbf{q}) \;=\; b(\mathbf{q}) \,\log\!\left(\sum_i e^{q_i / b(\mathbf{q})}\right),\qquad b(\mathbf{q})=\kappa\,S(\mathbf{q}).$$
-- Observability: Public views expose instantaneous price ratios $P(\text{base}\to\text{quote})$, price shares $\pi_i$, LP price $P_L^{(k)}$, and size metric $S(\mathbf{q})$.
-
-13.4 Operational implications
-- Asset changes: To add or remove assets, deploy a new pool instance and migrate liquidity; existing pools remain immutable.
-- Ecosystem integration: The fixed-parameter model simplifies routing and valuation, enabling integrators to precompute depth profiles for anticipated $S$ regimes.
-- Risk discipline: The absence of admin levers eliminates governance risk but requires careful parameter selection at deployment.
-
-15) Limitations and Future Work
-
-15.1 Limitations
-- Quasi-static $b$ assumption: Pricing steps treat $b$ as locally constant. While pairwise ratios are exact for infinitesimal moves, finite trades are evaluated with closed forms derived from the two-asset reduction; model fidelity remains high but is not a full global-gradient integration under state-dependent $b$.
-- Thin-liquidity vulnerability: For small $S$, $b=\kappa S$ is small and price impact is steep; users should rely on price limits $\Lambda$ and integrators should enforce minimum bootstrap sizes.
-- Extreme concentration and domain edges: As some $q_j \to 0$, ratios $\exp((q_{\text{quote}}-q_{\text{base}})/b)$ become large; capacity caps and domain guards prevent nonphysical outcomes but can truncate trades.
-- Expressivity: The mechanism is not tuned for pegged pairs like stableswap, nor does it encode cross-asset correlations by default.
-- Numerical constraints: Fixed-point range/precision, exponential/log bounds, and approximation regimes impose domain restrictions for safe operation.
-- Static parameters: Immutability removes governance agility; mis-specified $\kappa$ or fees require new deployments.
-
-15.2 Future work
-- Adaptive proportionality: Explore principled adaptive $\kappa$ while preserving LMSR properties (e.g., bounded-loss analogues) and avoiding governance risk (e.g., rule-based or oracle-free triggers).
-- Correlated or basket-targeted variants: Incorporate weighted size metrics $S_w(\mathbf{q})$ or correlation-aware formulations, with rigorous analysis of price and risk implications.
-- Enhanced approximations: Extend polynomial or rational approximations with verified remainder bounds, larger safe domains, and automatic dispatchers with certified monotonicity.
-- Off-chain assists and proofs: Use off-chain computation for heavy numerical routines with on-chain verification (e.g., succinct proofs) while maintaining transparency.
-- MEV-aware design: Integrate user-settled price limits, batch auctions, or commit-reveal to mitigate adverse selection and sandwich risk.
-- Layer-2 deployment: Leverage lower fees and faster settlement to widen the safe domain for numerical precision and to support more assets.
-
-16) Conclusion
-
-- We presented a multi-asset AMM whose pricing kernel is the LMSR cost function with an effective liquidity parameter proportional to pool size, $b(\mathbf{q})=\kappa S(\mathbf{q})$. This delivers scale-invariant responsiveness, preserves softmax-derived pairwise price ratios, and supports any-to-any swaps via a single convex potential.
-- Closed-form two-asset reductions provide exact-in, exact-out, and limit-hitting formulas with strong monotonicity and uniqueness properties, while capacity caps and conservative inverses ensure safety at domain boundaries. Liquidity operations (proportional and single-asset joins/exits) follow directly from the same potential framework.
-- A fixed-parameter policy eliminates governance risk and makes depth calibration transparent. Numerical stability is achieved through log-sum-exp reformulations, guarded transcendental domains, and optional balanced-regime polynomial approximations with error bounds.
-- Outlook: This LMSR AMM complements CFMMs by offering multi-asset price discovery under a convex potential with predictable scaling. Future work includes adaptive yet governance-minimized responsiveness, correlation-aware variants, and verifiable off-chain assists—aimed at retaining theoretical guarantees while broadening applicability.
-
-
-
-
-
-
-
-
-
-17) Appendices
-
-A. Full derivations and proofs
-
-A.1 Gradient, price shares, and pairwise prices
-- With $b$ treated as a constant parameter, the LMSR cost $C(\mathbf{q}) = b \log\!\big(\sum_k e^{q_k/b}\big)$ yields
-  $$\frac{\partial C}{\partial q_i} \;=\; \frac{e^{q_i/b}}{\sum_k e^{q_k/b}} \;=\; \pi_i(\mathbf{q}).$$
-- With $b = \kappa \, S(\mathbf{q})$, the total derivative becomes
-  $$\frac{\partial C}{\partial q_i} \;=\; A(\mathbf{q}) \;+\; \frac{e^{q_i/b}}{\sum_k e^{q_k/b}},$$
-  where $A(\mathbf{q})$ is an additive term common to all $i$ that arises from $\partial b/\partial q_i$. Consequently, differences between marginal prices are preserved, and the pairwise marginal price ratio reduces to
-  $$P(\text{base}\to\text{quote}\mid \mathbf{q}) \;=\; \exp\!\left(\frac{q_{\text{quote}} - q_{\text{base}}}{b(\mathbf{q})}\right).$$
-  This is the exchange rate used by the kernel, under the quasi-static-$b$ assumption.
-
-A.2 Two-asset closed form: exact-in
-- Consider a swap from $i$ (in) to $j$ (out) with quasi-static $b$. Let $r_0 := \exp\!\big((q_i - q_j)/b\big)$. Along the trade path, the instantaneous marginal price ratio evolves as $r(t) = r_0 \, e^{t/b}$, where $t$ is the cumulative input of asset $i$.
-- The infinitesimal output satisfies
-  $$\mathrm{d}y \;=\; \frac{r(t)}{1 + r(t)} \,\mathrm{d}t,$$
-  in the two-asset reduction induced by the LMSR gradient. Integrating from $0$ to $a$ yields the closed form
-  $$y(a) \;=\; b \,\ln\!\Big( 1 + r_0 \,\big(1 - e^{-a/b}\big) \Big).$$
-- Properties: $y(0) = 0$, $y'(0) = \frac{r_0}{1 + r_0}$, $y$ is increasing and concave in $a$, and $\lim_{a\to\infty} y = b \,\ln(1 + r_0)$.
-
-A.3 Two-asset closed form: exact-out (inverse)
-- Given $y \ge 0$, invert the relation in A.2. Let $E := e^{y/b}$. Then
-  $$1 + r_0 \,\big(1 - e^{-a/b}\big) \;=\; E
-  \;\Rightarrow\; e^{-a/b} \;=\; 1 - \frac{E - 1}{r_0} \;=\; \frac{r_0 + 1 - E}{r_0}$$
-  $$\Rightarrow\quad a(y) \;=\; -\,b \,\ln\!\left(\frac{r_0 + 1 - E}{r_0}\right) \;=\; b \,\ln\!\left(\frac{r_0}{\,r_0 + 1 - E\,}\right).$$
-- This inverse exists and is unique for $y \in \big[0,\, b \ln(1 + r_0)\big]$.
-
-A.4 Limit-hitting and swap-to-limit
-- Let $\Lambda > 0$ be a maximum acceptable marginal price ratio for $p_i/p_j$. With $r(t) = r_0 \, e^{t/b}$, the limit is reached when $r(t) = \Lambda$, giving the unique truncated input
-  $$a_{\text{lim}} \;=\; b \,\ln\!\left(\frac{\Lambda}{r_0}\right).$$
-- The corresponding output at the limit is
-  $$y_{\text{lim}} \;=\; b \,\ln\!\Big( 1 + r_0 \,\big(1 - e^{-a_{\text{lim}}/b}\big) \Big)
-  \;=\; b \,\ln\!\Big( 1 + r_0 \,\big(1 - r_0/\Lambda\big) \Big).$$
-- If $y_{\text{lim}}$ exceeds the available out-asset balance $q_j$, cap output to $q_j$ and solve for the input required to realize $y = q_j$ using the inverse formula of A.3:
-  $$a_{\text{cap}} \;=\; b \,\ln\!\left(\frac{r_0}{\,r_0 + 1 - e^{\,q_j / b}\,}\right).$$
-
-A.5 Single-asset mint via proportional growth (exact-in to many)
-- Suppose a user contributes amount $a$ of asset $i$ and wishes to increase the pool proportionally by factor $1 + \alpha$ (with $\alpha \ge 0$). For each $j \ne i$, let $y_j := \alpha \, q_j$ be the target out-amount in $j$ when swapping from $i$. Define $r_{0,j} := \exp\!\big((q_i - q_j)/b\big)$. From A.3, the input required to realize $y_j$ is
-  $$x_j(\alpha) \;=\; b \,\ln\!\left(\frac{r_{0,j}}{\,r_{0,j} + 1 - e^{\,y_j / b}\,}\right).$$
-- The self-asset contribution is $\alpha \, q_i$. The total input required is
-  $$a_{\text{req}}(\alpha) \;=\; \alpha \, q_i \;+\; \sum_{j \ne i} x_j(\alpha).$$
-- Solve for $\alpha$ via a monotone root-find on $a_{\text{req}}(\alpha) = a$. The function is increasing in $\alpha$ on its domain, with unique solution when feasible.
-
-A.6 Single-asset burn via proportional redemption
-- Burning a proportional share $\alpha \in (0, 1]$ reduces the pool balances to $(1 - \alpha)\,\mathbf{q}$. A single-asset payout in asset $i$ aggregates (i) the direct $\alpha \, q_i$ redemption and (ii) the swaps from each asset $j \ne i$ of their redeemed $\alpha \, q_j$ portions into $i$ using A.2 with the local (post-burn) state. If a computed out-amount would exceed the local $q_i$, cap to capacity and solve the inverse for the input used.
-
-A.7 Balanced 2-asset special case and polynomial approximations
-- Near balance, define $\delta := (q_i - q_j)/b$ with $|\delta| \ll 1$ and let $a/b$ be small. Using second-order expansions:
-  $$e^{\pm x} \approx 1 \pm x + \frac{x^2}{2},\qquad \ln(1 + u) \approx u - \frac{u^2}{2},$$
-  we obtain for small $a/b$ and $\delta$:
-  $$r_0 = e^{\delta} \approx 1 + \delta + \frac{\delta^2}{2},$$
-  $$y(a) = b \,\ln\!\big(1 + r_0(1 - e^{-a/b})\big)
-       \approx b \left[ r_0 \left(\frac{a}{b}\right) - \frac{1}{2} r_0 \left(\frac{a}{b}\right)^2 \right]
-       + \mathcal{O}\!\left(\left(\frac{a}{b}\right)^3,\, \delta \left(\frac{a}{b}\right)^2\right).$$
-- In particular, when $\delta \approx 0$,
-  $$y(a) \approx \frac{a}{2} - \frac{a^2}{4b} + \cdots,$$
-  which admits efficient evaluation via fixed low-degree polynomials. This motivates a “balanced pair” dispatcher that, under explicit near-balance preconditions ($|\delta| \le \delta_\star$ and $a/b \le \tau_\star$), uses minimax Chebyshev polynomials for $\exp$ and $\ln$ on compact intervals to meet a specified error budget, and otherwise falls back to the general path.
-
-B. Error bounds and approximation details
-
-B.1 Fixed-point arithmetic and stability policy
-- Representation: All quantities are computed in fixed-point with a wide fractional field; equations are written over reals for exposition. Overflow/underflow and domain errors are prevented with explicit guards.
-- Log-sum-exp: The cost is evaluated as $C = b \left(M + \log \sum_i e^{\,y_i - M}\right)$ with $y_i := q_i/b$ and $M := \max_i y_i$. This ensures stable accumulation even when some $y_i$ are far apart.
-- Exponential guard: The arguments to $\exp(\cdot)$ are restricted to a bounded interval to ensure finite, monotone outputs. A practical bound is $|x| \le 32$ (in internal fixed-point units), which comfortably covers operational regimes while preventing overflow.
-- Ratio shortcuts: Where possible, we form ratios such as $r_0 = \exp\!\big((q_i - q_j)/b\big)$ directly, avoiding separate exponentials and a division, improving both precision and cost.
-
-B.2 Monotonicity and error budgets
-- Kernel monotonicity: The closed forms in A.2–A.4 are strictly increasing in input and satisfy $y'(a) \in (0,1)$ for feasible states. Numerical implementations preserve monotonicity by:
-  - using log-sum-exp,
-  - guarding denominators (e.g., $r_0 + 1 - e^{\,y/b} > 0$),
-  - clamping to capacity when necessary and solving inverses in the capped branch.
-- Error targets: Prices, shares, and swap amounts are computed to within small relative error (e.g., $\le 10^{-9}$ for typical ranges). Guards reject or cap inputs that would violate error or domain constraints.
-
-B.3 Polynomial approximations in balanced 2-asset mode
-- Domains: For $|\delta| \le \delta_\star$ and $\big|a/b\big| \le \tau_\star$, $\exp$ and $\ln$ are approximated by minimax polynomials on compact intervals $[-\tau_\star, \tau_\star]$ and $[\,1 - u_\star,\, 1 + u_\star\,]$, respectively, with $u_\star$ induced by the $\exp$ range.
-- Construction: Coefficients are obtained offline (e.g., via Remez) to minimize the maximum relative error over the domain.
-- Remainder bounds: Standard analytic bounds apply:
-  $$\big|e^{x} - P_d(x)\big| \;\le\; e^{\tau_\star}\,\frac{\tau_\star^{\,d+1}}{(d+1)!},$$
-  $$\big|\ln(1 + u) - Q_d(u)\big| \;\le\; \frac{|u|^{\,d+1}}{(d+1)\,(1 - |u|)^{\,d+1}},\qquad |u| < 1.$$
-  Degree $d$ and domain parameters $(\delta_\star, \tau_\star, u_\star)$ are chosen to meet the global error budget while maintaining monotonicity of the composed swap mapping.
-
-B.4 Implementation notes for stability
-- Prefer single-pass accumulations with on-the-fly recentering for $\sum \exp(\cdot)$.
-- Maintain consistent reciprocals (e.g., precompute $1/b$) to reduce rounding dispersion.
-- Use explicit positivity checks (e.g., size metric $S > 0$, $\exp$ arguments within bounds, denominators $> 0$).
-- When a computed “inner” argument to $\ln(\cdot)$ is $\le 0$ due to rounding, switch to a conservative branch (cap-and-invert) rather than continuing.
-
-C. Additional figures and tables (to be included)
-- Price impact curves vs. constant-product and constant-mean baselines across $\kappa$.
-- Parameter sweeps for $\kappa$ and $S$ showing depth and slippage profiles.
-- Numerical accuracy: worst-case relative error heatmaps for prices and swap amounts; monotonicity checks.
-- Gas microbenchmarks: general path vs. balanced 2-asset approximations; cache effects.
-
-D. Glossary and notation
-- $n$: number of assets.
-- $i, j$: asset indices in $\{0,\dots,n-1\}$.
-- $\mathbf{q}\in \mathbb{R}_{\ge 0}^{\,n}$: vector of normalized internal quantities; $q_i$ is the $i$-th component.
-- $S(\mathbf{q}) = \sum_i q_i$: size metric (aggregate pool size).
-- $\kappa > 0$: fixed liquidity proportionality constant.
-- $b(\mathbf{q}) = \kappa \cdot S(\mathbf{q})$: effective LMSR liquidity parameter.
-- $w_i = e^{q_i / b}$; $W = \sum_i w_i$.
-- $\pi_i = w_i / W$: price share (softmax probability).
-- $P(\text{base}\to\text{quote}) = \exp\!\big((q_{\text{quote}} - q_{\text{base}})/b\big)$: pairwise marginal price ratio.
-- $a$: exact-in input amount for asset $i$ (fee-free kernel).
-- $y$: exact-out output amount for asset $j$ (fee-free kernel).
-- $r_0 = \exp\!\big((q_i - q_j)/b\big)$: initial ratio for an $i\to j$ swap.
-- $\Lambda$: user-specified price limit (maximum acceptable $p_i/p_j$).
-- $\alpha$: proportional growth/redeem factor for liquidity operations.
-
-E. References
-- Hanson, R. (2002). [Logarithmic Market Scoring Rules for Modular Combinatorial Information Aggregation.](https://mason.gmu.edu/~rhanson/mktscore.pdf)
-- Abernethy, J., Chen, Y., & Waggoner, B. (2013). Low-Regret Learning in Prediction Markets.
-- Uniswap (Hayden Adams et al.). Constant product market maker design docs and whitepapers.
-- Balancer. Constant mean market makers and multi-asset pool design notes.
-- Curve Finance. StableSwap invariant design notes.
-- Fixed-point arithmetic references and standard libraries for 64.64 computations.

foundry.lock

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

foundry.toml

@@ -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', 'PartyPoolSwapImpl', 'PartyPoolMintImpl',]
+gas_reports = ['PartyPool', 'PartyPoolBalancedPair', 'PartyPlanner', 'PartyPoolSwapImpl', 'PartyPoolMintImpl',]
-fs_permissions = [{ access = "write", path = "chain.json"}]
+fs_permissions = [{ access = "write", path = "liqp-deployments.json"}]
 
 [lint]
 lint_on_build=false  # more annoying than helpful

research/gas_data.csv

@@ -0,0 +1,117 @@
+gas
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research/get_quotes.js

@@ -0,0 +1,459 @@
+const { ethers } = require('ethers');
+const { Token } = require('@uniswap/sdk-core');
+const fs = require('fs');
+
+// Token definitions
+const ChainId = {
+    MAINNET: 1
+};
+
+const USDC_TOKEN = new Token(
+    ChainId.MAINNET,
+    '0xa0b86991c6218b36c1d19d4a2e9eb0ce3606eb48',
+    6,
+    'USDC',
+    'USDC'
+);
+
+const USDT_TOKEN = new Token(
+    ChainId.MAINNET,
+    '0xdAC17F958D2ee523a2206206994597C13D831ec7',
+    6,
+    'USDT',
+    'USDT'
+);
+
+// Configuration
+const QUOTER_ADDRESS = '0x52f0e24d1c21c8a0cb1e5a5dd6198556bd9e1203';
+const POSITION_MANAGER_ADDRESS = '0xbD216513d74C8cf14cf4747E6AaA6420FF64ee9e';
+
+// Pool ID to fetch pool key from
+const POOL_ID = '0x8aa4e11cbdf30eedc92100f4c8a31ff748e201d44712cc8c90d189edaa8e4e47';
+
+// Providers
+const anvilProvider = new ethers.providers.JsonRpcProvider('http://127.0.0.1:8545');
+
+// Quoter contract ABI
+const QUOTER_ABI = [
+    {
+        inputs: [
+            {
+                components: [
+                    {
+                        components: [
+                            { name: 'currency0', type: 'address' },
+                            { name: 'currency1', type: 'address' },
+                            { name: 'fee', type: 'uint24' },
+                            { name: 'tickSpacing', type: 'int24' },
+                            { name: 'hooks', type: 'address' }
+                        ],
+                        name: 'poolKey',
+                        type: 'tuple'
+                    },
+                    { name: 'zeroForOne', type: 'bool' },
+                    { name: 'exactAmount', type: 'uint128' },
+                    { name: 'hookData', type: 'bytes' }
+                ],
+                name: 'params',
+                type: 'tuple'
+            }
+        ],
+        name: 'quoteExactInputSingle',
+        outputs: [
+            {
+                components: [
+                    { name: 'amountOut', type: 'uint256' }
+                ],
+                name: 'result',
+                type: 'tuple'
+            }
+        ],
+        stateMutability: 'view',
+        type: 'function'
+    }
+];
+// StateView ABI for getSlot0 and getLiquidity
+const STATE_VIEW_ABI = [
+    {
+        inputs: [
+            // { name: 'manager', type: 'address' },
+            { name: 'poolId', type: 'bytes32' }
+        ],
+        name: 'getSlot0',
+        outputs: [
+            { name: 'sqrtPriceX96', type: 'uint160' },
+            { name: 'tick', type: 'int24' },
+            { name: 'protocolFee', type: 'uint24' },
+            { name: 'lpFee', type: 'uint24' }
+        ],
+        stateMutability: 'view',
+        type: 'function'
+    },
+];
+
+// StateView contract address for reading pool state
+const STATE_VIEW_ADDRESS = '0x7ffe42c4a5deea5b0fec41c94c136cf115597227';
+
+// Position Manager ABI
+const POSITION_MANAGER_ABI = [
+    {
+        inputs: [{ name: 'poolId', type: 'bytes25' }],
+        name: 'poolKeys',
+        outputs: [
+            {
+                components: [
+                    { name: 'currency0', type: 'address' },
+                    { name: 'currency1', type: 'address' },
+                    { name: 'fee', type: 'uint24' },
+                    { name: 'tickSpacing', type: 'int24' },
+                    { name: 'hooks', type: 'address' }
+                ],
+                name: 'poolKey',
+                type: 'tuple'
+            }
+        ],
+        stateMutability: 'view',
+        type: 'function'
+    }
+];
+
+// Function to get pool key from Position Manager (uses mainnet)
+async function getPoolKey() {
+    try {
+        const positionManager = new ethers.Contract(
+            POSITION_MANAGER_ADDRESS,
+            POSITION_MANAGER_ABI,
+            anvilProvider
+        );
+
+        // Extract first 25 bytes (50 hex chars + 0x prefix = 52 chars)
+        const poolIdBytes25 = POOL_ID.slice(0, 52);
+
+        const poolKey = await positionManager.poolKeys(poolIdBytes25);
+
+        return {
+            currency0: poolKey.currency0,
+            currency1: poolKey.currency1,
+            fee: poolKey.fee,
+            tickSpacing: poolKey.tickSpacing,
+            hooks: poolKey.hooks
+        };
+    } catch (error) {
+        console.error('Error fetching pool key:', error.message);
+        throw error;
+    }
+}
+
+// Convert sqrtPriceX96 to human-readable price
+function sqrtPriceX96ToPrice(sqrtPriceX96, decimals0, decimals1) {
+    const Q96 = ethers.BigNumber.from(2).pow(96);
+    const sqrtPrice = ethers.BigNumber.from(sqrtPriceX96);
+
+    // Calculate price = (sqrtPriceX96 / 2^96)^2
+    const numerator = sqrtPrice.mul(sqrtPrice);
+    const denominator = Q96.mul(Q96);
+
+    // Adjust for token decimals
+    const decimalAdjustment = ethers.BigNumber.from(10).pow(decimals0 - decimals1);
+
+    // Convert to float for readability
+    return parseFloat(numerator.toString()) / parseFloat(denominator.toString()) * parseFloat(decimalAdjustment.toString());
+}
+
+// Get pool price using StateView
+async function getPoolPriceWithSDK(blockNumber) {
+    try {
+        // Create StateView contract with ethers
+        const stateViewContract = new ethers.Contract(
+            STATE_VIEW_ADDRESS,
+            STATE_VIEW_ABI,
+            anvilProvider
+        );
+
+        // Get slot0 data
+        const slot0 = await stateViewContract.getSlot0(POOL_ID, {
+            blockTag: blockNumber
+        });
+
+        // Convert sqrtPriceX96 to human-readable price
+        const price = sqrtPriceX96ToPrice(slot0.sqrtPriceX96, 6, 6); // USDC=6, USDT=6
+        const inversePrice = 1 / price;
+
+        console.log('\n=== Pool State ===');
+        console.log('Block:', blockNumber);
+        console.log('sqrtPriceX96:', slot0.sqrtPriceX96.toString());
+        console.log('Tick:', slot0.tick.toString());
+        console.log('Price (USDT per USDC):', price.toFixed(8));
+        console.log('Price (USDC per USDT):', inversePrice.toFixed(8));
+        console.log('LP Fee:', slot0.lpFee, `(${(slot0.lpFee / 10000).toFixed(2)}%)`);
+
+        return {
+            sqrtPriceX96: slot0.sqrtPriceX96.toString(),
+            tick: slot0.tick.toString(),
+            price: price,              // Human-readable price
+            inversePrice: inversePrice,
+            protocolFee: slot0.protocolFee,
+            lpFee: slot0.lpFee
+        };
+    } catch (error) {
+        console.error('Error getting pool price:', error.message);
+        throw error;
+    }
+}
+
+
+// Get quote from historical block (10 blocks back) with multiple amount testing
+async function getQuoteFromHistoricalBlock(poolKey, targetBlock) {
+    try {
+        
+        // Get starting pool price using SDK
+        try {
+            await getPoolPriceWithSDK(targetBlock);
+        } catch (error) {
+            console.error('Error getting pool price with SDK:', error.message);
+        }
+        
+        console.log('\n=== Testing Multiple Input Amounts ===');
+        console.log('Testing amounts from 1 USDC, increasing by 30% each iteration (limited to 5 iterations)');
+        console.log('Testing both directions: USDC→USDT and USDT→USDC\n');
+        
+        // Create a new provider instance that queries at specific block
+        const quoterContract = new ethers.Contract(QUOTER_ADDRESS, QUOTER_ABI, anvilProvider);
+        
+        const resultsForward = [];  // USDC→USDT
+        const resultsReverse = [];  // USDT→USDC
+        let currentAmount = 1; // Start with 1 token
+        const multiplier = 1.3; // 30% increase
+        const maxIterations = 200; // Limit to 5 iterations for testing
+        
+        // Test USDC→USDT (forward direction)
+        console.log('\n=== USDC → USDT (Forward Direction) ===');
+        for (let i = 0; i < maxIterations; i++) {
+            // Check if currentAmount exceeds 10 million
+            if (currentAmount > 10000000) {
+                console.log(`\nReached maximum amount limit of 1 million USDC. Stopping iterations.`);
+                break;
+            }
+            
+            console.log(`\n--- Iteration ${i + 1}: ${currentAmount.toFixed(6)} USDC ---`);
+            
+            const amountIn = ethers.utils.parseUnits(currentAmount.toFixed(6), USDC_TOKEN.decimals);
+
+            // Make the call at the specific block using overrides
+            const quotedAmountOut = await quoterContract.callStatic.quoteExactInputSingle({
+                poolKey: poolKey,
+                zeroForOne: true,
+                exactAmount: amountIn.toString(),
+                hookData: '0x00',
+            }, {
+                blockTag: targetBlock // Query at specific historical block
+            });
+
+            const actualAmountOut = ethers.BigNumber.from(quotedAmountOut.amountOut);
+            
+            // Calculate ideal amount out (1:1 ratio for stablecoins)
+            const idealAmountOut = amountIn; // Since both USDC and USDT have 6 decimals
+            
+            // Calculate the difference from ideal
+            const difference = actualAmountOut.sub(idealAmountOut);
+            const isPositive = difference.gte(0);
+            
+            // Calculate slippage in basis points and percentage
+            const slippageBasisPoints = difference.mul(10000).div(idealAmountOut);
+            const slippagePercentage = parseFloat(slippageBasisPoints.toString()) / 100;
+            
+            // Calculate effective exchange rate
+            const effectiveRate = parseFloat(ethers.utils.formatUnits(actualAmountOut, USDT_TOKEN.decimals)) / currentAmount;
+            
+            // Log results for this amount
+            console.log(`Amount In: ${currentAmount.toFixed(6)} USDC`);
+            console.log(`Amount Out: ${ethers.utils.formatUnits(actualAmountOut, USDT_TOKEN.decimals)} USDT`);
+            console.log(`Effective Rate: ${effectiveRate.toFixed(6)} USDT/USDC`);
+            console.log(`Ideal Rate (1:1): ${currentAmount.toFixed(6)} USDT`);
+            console.log(`Difference: ${isPositive ? '+' : ''}${ethers.utils.formatUnits(difference, USDT_TOKEN.decimals)} USDT`);
+            console.log(`Slippage: ${isPositive ? '+' : ''}${slippagePercentage.toFixed(4)}% (${isPositive ? '+' : ''}${slippageBasisPoints.toString()} basis points)`);
+            
+            // Store result
+            resultsForward.push({
+                iteration: i + 1,
+                amountIn: currentAmount,
+                amountInFormatted: currentAmount.toFixed(6) + ' USDC',
+                amountOut: ethers.utils.formatUnits(actualAmountOut, USDT_TOKEN.decimals) + ' USDT',
+                effectiveRate: effectiveRate,
+                slippagePercentage: slippagePercentage,
+                slippageBasisPoints: parseInt(slippageBasisPoints.toString()),
+                isPositive: isPositive
+            });
+            
+            // Increase amount by 30% for next iteration
+            currentAmount *= multiplier;
+        }
+        
+        // Reset current amount for reverse direction
+        currentAmount = 1;
+        
+        // Test USDT→USDC (reverse direction)
+        console.log('\n\n=== USDT → USDC (Reverse Direction) ===');
+        for (let i = 0; i < maxIterations; i++) {
+            // Check if currentAmount exceeds 1 million
+            if (currentAmount > 10000000) {
+                console.log(`\nReached maximum amount limit of 1 million USDT. Stopping iterations.`);
+                break;
+            }
+            
+            console.log(`\n--- Iteration ${i + 1}: ${currentAmount.toFixed(6)} USDT ---`);
+            
+            const amountIn = ethers.utils.parseUnits(currentAmount.toFixed(6), USDT_TOKEN.decimals);
+
+            // Make the call at the specific block using overrides with zeroForOne: false
+            const quotedAmountOut = await quoterContract.callStatic.quoteExactInputSingle({
+                poolKey: poolKey,
+                zeroForOne: false,  // false for USDT→USDC
+                exactAmount: amountIn.toString(),
+                hookData: '0x00',
+            }, {
+                blockTag: targetBlock // Query at specific historical block
+            });
+
+            const actualAmountOut = ethers.BigNumber.from(quotedAmountOut.amountOut);
+            
+            // Calculate ideal amount out (1:1 ratio for stablecoins)
+            const idealAmountOut = amountIn; // Since both USDC and USDT have 6 decimals
+            
+            // Calculate the difference from ideal
+            const difference = actualAmountOut.sub(idealAmountOut);
+            const isPositive = difference.gte(0);
+            
+            // Calculate slippage in basis points and percentage
+            const slippageBasisPoints = difference.mul(10000).div(idealAmountOut);
+            const slippagePercentage = parseFloat(slippageBasisPoints.toString()) / 100;
+            
+            // Calculate effective exchange rate
+            const effectiveRate = parseFloat(ethers.utils.formatUnits(actualAmountOut, USDC_TOKEN.decimals)) / currentAmount;
+            
+            // Log results for this amount
+            console.log(`Amount In: ${currentAmount.toFixed(6)} USDT`);
+            console.log(`Amount Out: ${ethers.utils.formatUnits(actualAmountOut, USDC_TOKEN.decimals)} USDC`);
+            console.log(`Effective Rate: ${effectiveRate.toFixed(6)} USDC/USDT`);
+            console.log(`Ideal Rate (1:1): ${currentAmount.toFixed(6)} USDC`);
+            console.log(`Difference: ${isPositive ? '+' : ''}${ethers.utils.formatUnits(difference, USDC_TOKEN.decimals)} USDC`);
+            console.log(`Slippage: ${isPositive ? '+' : ''}${slippagePercentage.toFixed(4)}% (${isPositive ? '+' : ''}${slippageBasisPoints.toString()} basis points)`);
+            
+            // Store result
+            resultsReverse.push({
+                iteration: i + 1,
+                amountIn: currentAmount,
+                amountInFormatted: currentAmount.toFixed(6) + ' USDT',
+                amountOut: ethers.utils.formatUnits(actualAmountOut, USDC_TOKEN.decimals) + ' USDC',
+                effectiveRate: effectiveRate,
+                slippagePercentage: slippagePercentage,
+                slippageBasisPoints: parseInt(slippageBasisPoints.toString()),
+                isPositive: isPositive
+            });
+            
+            // Increase amount by 30% for next iteration
+            currentAmount *= multiplier;
+        }
+        
+        // Summary
+        console.log('\n\n=== Summary of Results ===');
+        
+        console.log('\n--- Forward Direction (USDC → USDT) ---');
+        console.log('\nAmount In → Amount Out (Rate) [Slippage]');
+        resultsForward.forEach(r => {
+            console.log(`${r.amountInFormatted} → ${r.amountOut} (${r.effectiveRate.toFixed(6)}) [${r.isPositive ? '+' : ''}${r.slippagePercentage.toFixed(4)}%]`);
+        });
+        
+        console.log('\n--- Reverse Direction (USDT → USDC) ---');
+        console.log('\nAmount In → Amount Out (Rate) [Slippage]');
+        resultsReverse.forEach(r => {
+            console.log(`${r.amountInFormatted} → ${r.amountOut} (${r.effectiveRate.toFixed(6)}) [${r.isPositive ? '+' : ''}${r.slippagePercentage.toFixed(4)}%]`);
+        });
+        
+        return {
+            blockNumber: targetBlock,
+            forward: resultsForward,
+            reverse: resultsReverse
+        };
+    } catch (error) {
+        console.error('Error getting historical quote:', error.message);
+        throw error;
+    }
+}
+
+// Function to write results to CSV
+function writeResultsToCSV(blockNumber, priceData, quoteResults) {
+    const filename = `swap_results_block_${blockNumber}.csv`;
+    
+    // Create CSV header
+    let csvContent = 'Block Number,USDT per USDC,USDC per USDT,Forward Direction Amount In,Forward Direction Amount Out,Reverse Direction Amount In,Reverse Direction Amount Out\n';
+    
+    // Get max number of iterations
+    const maxIterations = Math.max(quoteResults.forward.length, quoteResults.reverse.length);
+    
+    // Add data rows
+    for (let i = 0; i < maxIterations; i++) {
+        const forwardResult = quoteResults.forward[i] || { amountIn: '', amountOut: '' };
+        const reverseResult = quoteResults.reverse[i] || { amountIn: '', amountOut: '' };
+        
+        // Only include block number and prices in first row
+        if (i === 0) {
+            csvContent += `${blockNumber},${priceData.price.toFixed(8)},${priceData.inversePrice.toFixed(8)},`;
+        } else {
+            csvContent += `,,,`;
+        }
+        
+        // Extract just the numbers from the formatted strings
+        const forwardAmountIn = forwardResult.amountIn ? forwardResult.amountIn.toFixed(6) : '';
+        const forwardAmountOut = forwardResult.amountOut ? forwardResult.amountOut.split(' ')[0] : '';
+        const reverseAmountIn = reverseResult.amountIn ? reverseResult.amountIn.toFixed(6) : '';
+        const reverseAmountOut = reverseResult.amountOut ? reverseResult.amountOut.split(' ')[0] : '';
+        
+        csvContent += `${forwardAmountIn},${forwardAmountOut},${reverseAmountIn},${reverseAmountOut}\n`;
+    }
+    
+    // Write to file
+    fs.writeFileSync(filename, csvContent);
+    console.log(`\n✅ Results written to ${filename}`);
+}
+
+// Main function
+async function main() {
+    console.log('=== Uniswap V4 Quote and Gas Estimation ===\n');
+    // Get current block
+    const currentBlock = await anvilProvider.getBlockNumber();
+    const targetBlock = currentBlock - 10;
+
+
+    // Fetch pool key from Position Manager
+    let poolKey;
+    try {
+        poolKey = await getPoolKey();
+    } catch (error) {
+        console.error('Failed to fetch pool key. Exiting.');
+        return;
+    }
+
+    // Get pool price data
+    let poolPriceData;
+    try {
+        poolPriceData = await getPoolPriceWithSDK(targetBlock);
+    } catch (error) {
+        console.error('Failed to get pool price data:', error.message);
+        return;
+    }
+
+    // Get quotes for both directions
+    try {
+        const quoteResults = await getQuoteFromHistoricalBlock(poolKey, targetBlock);
+        console.log('✅ Historical quote successful!');
+        
+        // Write results to CSV
+        writeResultsToCSV(targetBlock, poolPriceData, quoteResults);
+    } catch (error) {
+        console.error('❌ Failed to get historical quote:', error.message);
+    }
+}
+
+// Run the main function
+main().catch(console.error);