Liveness Fixes

contracts/src/external/Hyperdrive.sol

@@ -236,7 +236,7 @@ abstract contract Hyperdrive is
 
     /// @inheritdoc IHyperdriveCore
     function checkpoint(uint256) external {
-        _delegate(target2);
+        _delegate(target4);
     }
 
     /// Admin ///

contracts/src/external/HyperdriveTarget2.sol

@@ -71,12 +71,4 @@ abstract contract HyperdriveTarget2 is
     ) external returns (uint256) {
         return _closeShort(_maturityTime, _bondAmount, _minOutput, _options);
     }
-
-    /// Checkpoints ///
-
-    /// @notice Allows anyone to mint a new checkpoint.
-    /// @param _checkpointTime The time of the checkpoint to create.
-    function checkpoint(uint256 _checkpointTime) external {
-        _checkpoint(_checkpointTime);
-    }
 }

contracts/src/external/HyperdriveTarget4.sol

@@ -55,4 +55,12 @@ abstract contract HyperdriveTarget4 is
         return
             _openShort(_bondAmount, _maxDeposit, _minVaultSharePrice, _options);
     }
+
+    /// Checkpoints ///
+
+    /// @notice Allows anyone to mint a new checkpoint.
+    /// @param _checkpointTime The time of the checkpoint to create.
+    function checkpoint(uint256 _checkpointTime) external {
+        _checkpoint(_checkpointTime);
+    }
 }

contracts/src/interfaces/IHyperdrive.sol

@@ -250,10 +250,6 @@ interface IHyperdrive is
     /// @notice Thrown when the present value calculation fails.
     error InvalidPresentValue();
 
-    /// @notice Thrown when update liquidity brings the share reserves below
-    ///         the minimum share reserves.
-    error InvalidShareReserves();
-
     /// @notice Thrown when an invalid signature is used provide permit access
     ///         to the MultiToken. A signature is considered to be invalid if
     ///         it fails to recover to the owner's address.
@@ -352,6 +348,9 @@ interface IHyperdrive is
     ///         targets that are supported vary between instances.
     error UnsupportedToken();
 
+    /// @notice Thrown when `LPMath.calculateUpdateLiquidity` fails.
+    error UpdateLiquidityFailed();
+
     /// Getters ///
 
     /// @notice Gets the target0 address.

contracts/src/libraries/HyperdriveMath.sol

@@ -135,21 +135,45 @@ library HyperdriveMath {
     ///      flat+curve trades.
     /// @param _shareReserves The pool's share reserves.
     /// @param _shareAdjustment The pool's share adjustment.
-    /// @return The effective share reserves.
+    /// @return effectiveShareReserves The effective share reserves.
     function calculateEffectiveShareReserves(
         uint256 _shareReserves,
         int256 _shareAdjustment
-    ) internal pure returns (uint256) {
-        int256 effectiveShareReserves = _shareReserves.toInt256() -
-            _shareAdjustment;
-        if (effectiveShareReserves < 0) {
+    ) internal pure returns (uint256 effectiveShareReserves) {
+        bool success;
+        (effectiveShareReserves, success) = calculateEffectiveShareReservesSafe(
+            _shareReserves,
+            _shareAdjustment
+        );
+        if (!success) {
             Errors.throwInsufficientLiquidityError(
                 IHyperdrive
                     .InsufficientLiquidityReason
                     .InvalidEffectiveShareReserves
             );
         }
-        return uint256(effectiveShareReserves);
+    }
+
+    /// @dev Calculates the effective share reserves. The effective share
+    ///      reserves are the share reserves minus the share adjustment or
+    ///      z - zeta. We use the effective share reserves as the z-parameter
+    ///      to the YieldSpace pricing model. The share adjustment is used to
+    ///      hold the pricing mechanism invariant under the flat component of
+    ///      flat+curve trades.
+    /// @param _shareReserves The pool's share reserves.
+    /// @param _shareAdjustment The pool's share adjustment.
+    /// @return The effective share reserves.
+    /// @return A flag indicating if the calculation succeeded.
+    function calculateEffectiveShareReservesSafe(
+        uint256 _shareReserves,
+        int256 _shareAdjustment
+    ) internal pure returns (uint256, bool) {
+        int256 effectiveShareReserves = _shareReserves.toInt256() -
+            _shareAdjustment;
+        if (effectiveShareReserves < 0) {
+            return (0, false);
+        }
+        return (uint256(effectiveShareReserves), true);
     }
 
     /// @dev Calculates the initial bond reserves assuming that the initial LP