diff --git a/packages/contracts-bedrock/test/invariants/CustomGasToken.t.sol b/packages/contracts-bedrock/test/invariants/CustomGasToken.t.sol
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+++ b/packages/contracts-bedrock/test/invariants/CustomGasToken.t.sol
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+// SPDX-License-Identifier: MIT
+pragma solidity 0.8.15;
+
+// Testing
+import { StdUtils } from "forge-std/Test.sol";
+import { Vm } from "forge-std/Vm.sol";
+import { CommonTest } from "test/setup/CommonTest.sol";
+
+// Libraries
+import { Predeploys } from "src/libraries/Predeploys.sol";
+
+// Contracts
+import { ILiquidityController } from "interfaces/L2/ILiquidityController.sol";
+import { INativeAssetLiquidity } from "interfaces/L2/INativeAssetLiquidity.sol";
+import { IProxyAdmin } from "interfaces/universal/IProxyAdmin.sol";
+
+/// @title CGT_Minter
+/// @notice An actor with the minter role (can mint and burn)
+contract LiquidityController_Minter is StdUtils {
+    /// @notice The Vm contract.
+    Vm internal vm;
+
+    /// @notice The LiquidityController contract.
+    ILiquidityController internal liquidityController;
+
+    /// @notice The RandomActor contract.
+    RandomActor internal randomActor;
+
+    /// @notice Ghost accounting
+    uint256 public totalAmountMinted;
+    uint256 public totalAmountBurned;
+    bool public deltaBalanceAndMint; // NativeAssetLiquidity balance change != amount minted?
+    bool public deltaBalanceAndBurn; // NativeAssetLiquidity balance change != amount burned?
+
+    /// @param _vm The Vm contract.
+    /// @param _liquidityController The LiquidityController contract.
+    /// @param _randomActor The RandomActor contract.
+    constructor(Vm _vm, ILiquidityController _liquidityController, RandomActor _randomActor) {
+        vm = _vm;
+        liquidityController = _liquidityController;
+        randomActor = _randomActor;
+    }
+
+    /// @notice Mint custom gas token to the random actor.
+    /// @param _amount The amount of CGT to mint.
+    /// @dev Accounting invariants are leveraging the balance difference between pre and post-condition
+    function mint(uint256 _amount) public {
+        // precondition: nil - update ghost variables
+        uint256 _preBalance = payable(Predeploys.NATIVE_ASSET_LIQUIDITY).balance;
+
+        // action: mint to the random actor
+        liquidityController.mint(address(randomActor), _amount);
+
+        // postcondition: is the NativeAssetLiquidity contract's balance changed by an amount different than minted?
+        deltaBalanceAndMint = _amount != (_preBalance - uint256(payable(Predeploys.NATIVE_ASSET_LIQUIDITY).balance));
+        totalAmountMinted += _amount;
+    }
+
+    /// @notice Burn custom gas token.
+    /// @param _amount The amount of CGT to burn, which is bounded to the actor's balance (avoid trivial revert)
+    /// @dev Accounting invariant are leveraging the balance difference between pre and post-condition
+    function burn(uint256 _amount) public {
+        // precondition: amount to burn has an upper bound (this contract's balance)
+        _amount = bound(_amount, 0, address(this).balance);
+        uint256 _preBalance = payable(Predeploys.NATIVE_ASSET_LIQUIDITY).balance;
+
+        // action: burn _amount
+        liquidityController.burn{ value: _amount }();
+
+        // postcondition: update ghost variables by tracking an accounting difference
+        deltaBalanceAndBurn = _preBalance + _amount != uint256(payable(Predeploys.NATIVE_ASSET_LIQUIDITY).balance);
+        totalAmountBurned += _amount;
+    }
+
+    /// @dev Receive needed to receive CGT from the random actor
+    receive() external payable { }
+}
+
+/// @notice An actor which funds the NativeAssetLiquidity contract
+/// @dev There is no underlying access control to this
+contract NativeAssetLiquidity_Fundooor is StdUtils {
+    /// @notice The Vm contract.
+    Vm internal vm;
+
+    /// @notice The NativeAssetLiquidity contract.
+    INativeAssetLiquidity internal nativeAssetLiquidity;
+
+    /// @notice Ghost accounting
+    uint256 public totalAmountFunded;
+
+    /// @param _vm The Vm contract.
+    constructor(Vm _vm) {
+        vm = _vm;
+        nativeAssetLiquidity = INativeAssetLiquidity(Predeploys.NATIVE_ASSET_LIQUIDITY);
+    }
+
+    /// @notice Wrap fund() calls on the NativeAssetLiquidity contract.
+    /// @param _amount The amount of CGT to fund.
+    /// @dev The amount is bounded to the actor's balance (avoid trivial revert)
+    function fund(uint256 _amount) public {
+        // precondition: amount to fund has an upper bound (this contract's balance) + ghost accounting
+        _amount = bound(_amount, 0, address(this).balance);
+
+        // action: fund _amount
+        nativeAssetLiquidity.fund{ value: _amount }();
+
+        // postcondition: nil here (in the invariant tests)
+        // update ghost variables
+        totalAmountFunded += _amount;
+    }
+
+    receive() external payable { }
+}
+
+/// @notice actor which receives fund and send them to either the minter or the funder actor,
+///         keeping a closed loop (no vm.deal). It receive() function always revert, to insure mint()/safeSend is
+///         always successfully sending the CGT.
+contract RandomActor is StdUtils {
+    address internal liquidityController_Minter;
+    address internal nativeAssetLiquidity_Fundooor;
+
+    /// @notice Flag to indicate if the actor has been called via receive()
+    bool public hasBeenCalled = false;
+
+    /// @notice Error thrown when sending CGT to minter fails.
+    error RandomActor_SendCGTToMinterFailed();
+
+    /// @notice Error thrown when sending CGT to funder fails.
+    error RandomActor_SendCGTtoFunderFailed();
+
+    /// @notice Initialize the addresses of the minter and funder actors.
+    /// @param _liquidityController_Minter The address of the minter actor.
+    /// @param _nativeAssetLiquidity_Fundooor The address of the funder actor.
+    /// @dev This function selector is excluded from the invariant tests
+    function initAddresses(address _liquidityController_Minter, address _nativeAssetLiquidity_Fundooor) public {
+        liquidityController_Minter = _liquidityController_Minter;
+        nativeAssetLiquidity_Fundooor = _nativeAssetLiquidity_Fundooor;
+    }
+
+    /// @notice Send CGT to the minter actor.
+    /// @param _amount The amount of CGT to send.
+    /// @dev The amount is bounded to the actor's balance (avoid trivial revert)
+    function sendCGTtoMinter(uint256 _amount) public {
+        // precondition: amount to send has an upper bound (this contract's balance)
+        uint256 _amountToSend = bound(_amount, 0, address(this).balance);
+
+        // action: send _amountToSend to the minter actor
+        (bool success,) = payable(address(liquidityController_Minter)).call{ value: _amountToSend }("");
+
+        // postcondition: the call must succeed (test suite sanity check)
+        if (!success) revert RandomActor_SendCGTToMinterFailed();
+    }
+
+    /// @notice Send CGT to the funder actor.
+    /// @param _amount The amount of CGT to send.
+    /// @dev The amount is bounded to the actor's balance (avoid trivial revert)
+    function sendCGTtoFunder(uint256 _amount) public {
+        // precondition: amount to send has an upper bound (this contract's balance)
+        uint256 _amountToSend = bound(_amount, 0, address(this).balance);
+
+        // action: send _amountToSend to the funder actor
+        (bool success,) = payable(address(nativeAssetLiquidity_Fundooor)).call{ value: _amountToSend }("");
+
+        // postcondition: the call must succeed (test suite sanity check)
+        if (!success) revert RandomActor_SendCGTtoFunderFailed();
+    }
+
+    /// @dev We track if the SafeSend triggers a logic on the receiver via a ghost variable
+    receive() external payable {
+        hasBeenCalled = true;
+    }
+
+    fallback() external payable {
+        hasBeenCalled = true;
+    }
+}
+
+/// @title ETHLiquidity_MintBurn_Invariant
+/// @notice Invariant that checks that the NativeAssetLiquidity contract's balance is always equal
+///         to the sum of the initial supply, the deposits, the funds, and minus the withdrawals.
+///         NAL Balance = Initial Supply + Deposits + Funds - Withdrawals
+contract CustomGasToken_Invariants_Test is CommonTest {
+    /// @notice Starting balance of the contract - arbitrary value (cf Config change)
+    uint256 internal constant STARTING_BALANCE = type(uint248).max / 5;
+
+    LiquidityController_Minter internal actor_minter;
+    NativeAssetLiquidity_Fundooor internal actor_funder;
+    RandomActor internal randomActor;
+
+    /// @notice Test setup.
+    function setUp() public override {
+        enableCustomGasToken();
+        super.setUp();
+
+        randomActor = new RandomActor();
+        actor_funder = new NativeAssetLiquidity_Fundooor(vm);
+        actor_minter = new LiquidityController_Minter(vm, liquidityController, randomActor);
+
+        // Initialize the addresses of the minter and funder actors
+        randomActor.initAddresses(address(actor_minter), address(actor_funder));
+
+        // Authorize the minter actor (simple access control in unit tests)
+        vm.prank(IProxyAdmin(Predeploys.PROXY_ADMIN).owner());
+        liquidityController.authorizeMinter(address(actor_minter));
+
+        // Create the initial supply
+        vm.deal(address(nativeAssetLiquidity), STARTING_BALANCE);
+
+        // Set the target contract.
+        targetContract(address(actor_minter));
+        targetContract(address(actor_funder));
+
+        // Set the target selectors (exclude the initAddresses function)
+        bytes4[] memory selectors = new bytes4[](2);
+        selectors[0] = RandomActor.sendCGTtoMinter.selector;
+        selectors[1] = RandomActor.sendCGTtoFunder.selector;
+        FuzzSelector memory selector = FuzzSelector({ addr: address(randomActor), selectors: selectors });
+        targetSelector(selector);
+    }
+
+    /// @notice Invariant that checks that the NativeAssetLiquidity contract's balance is always equal
+    ///         to the sum of the initial supply, the deposits, the funds, and minus the withdrawals.
+    ///         NAL Balance = Initial Supply + Deposits + Funds - Withdrawals
+    /// @dev liquidityController.burn() calls deposit, liquidityController.mint() calls withdraw
+    function invariant_supplyConservation() public view {
+        assertEq(
+            address(nativeAssetLiquidity).balance,
+            STARTING_BALANCE + actor_funder.totalAmountFunded() + actor_minter.totalAmountBurned()
+                - actor_minter.totalAmountMinted(),
+            "NativeAssetLiquidity balance is not equal to the sum of the initial supply, the deposits, the funds, and minus the withdrawals"
+        );
+    }
+
+    /// @notice Invariant that checks that the minted amount is equal to the withdrawn amount
+    /// @dev Checks if the amount minted equals the amount transferred *outside* the NativeAssetLiquidity contract
+    function invariant_mintedEqualsWithdrawn() public view {
+        assertFalse(actor_minter.deltaBalanceAndMint(), "Minted amount is not equal to the withdrawn amount");
+    }
+
+    /// @notice Invariant that checks that the burned amount is equal to the deposited amount
+    /// @dev Checks if the amount burned equals the amount transferred *to* the NativeAssetLiquidity contract
+    function invariant_burnedEqualsDeposited() public view {
+        assertFalse(actor_minter.deltaBalanceAndBurn(), "Burned amount is not equal to the deposited amount");
+    }
+
+    /// @notice Invariant that checks that the LiquidityController contract's balance is always 0
+    /// @dev Checks if the LiquidityController there is no CGT being trapped in the LiquidityController contract
+    function invariant_noDustLiquidityController() public view {
+        assertEq(address(liquidityController).balance, 0, "LiquidityController balance is not 0");
+    }
+
+    /// @notice Invariant that checks that the mint function never calls back to the RandomActor contract
+    /// @dev Checks if the mint function never calls back to the RandomActor contract (test SafeSend)
+    function invariant_mintNeverCallsBack() public view {
+        assertFalse(randomActor.hasBeenCalled(), "RandomActor receive() function has been triggered");
+    }
+}