diff --git a/.github/workflows/invariants.yml b/.github/workflows/invariants.yml
new file mode 100644
index 0000000..091925f
--- /dev/null
+++ b/.github/workflows/invariants.yml
@@ -0,0 +1,19 @@
+# Value-conservation invariant suite for the constant-sum hook.
+# Runs `CounterHunterInvariant.t.sol` (hand-configured to mirror Counter.t.sol's setUp,
+# since the constant-sum design intentionally rejects native v4 liquidity).
+# Optional. Delete this file to remove the gate; no other deps.
+name: invariants
+on:
+  pull_request:
+permissions:
+  contents: read
+jobs:
+  invariants:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+        with:
+          submodules: recursive
+      - uses: foundry-rs/foundry-toolchain@v1
+      - name: Run constant-sum value-conservation invariants
+        run: forge test --mc CounterHunterInvariant -vvv
diff --git a/test/CounterHunterInvariant.t.sol b/test/CounterHunterInvariant.t.sol
new file mode 100644
index 0000000..41ad889
--- /dev/null
+++ b/test/CounterHunterInvariant.t.sol
@@ -0,0 +1,113 @@
+// SPDX-License-Identifier: MIT
+// Value-conservation invariant suite -- hand-configured for the constant-sum hook.
+// Mirrors Counter.t.sol's setUp (Fixtures.deployAndApprovePosm + hook.addLiquidity), NOT
+// Deployers.initPoolAndAddLiquidity which the hook intentionally reverts with
+// "No v4 Liquidity allowed" -- the constant-sum design is a hook-managed liquidity model.
+pragma solidity ^0.8.24;
+
+import "forge-std/Test.sol";
+import {IERC20} from "forge-std/interfaces/IERC20.sol";
+import {IHooks} from "v4-core/src/interfaces/IHooks.sol";
+import {Hooks} from "v4-core/src/libraries/Hooks.sol";
+import {PoolKey} from "v4-core/src/types/PoolKey.sol";
+import {Currency} from "v4-core/src/types/Currency.sol";
+import {IERC20Minimal} from "v4-core/src/interfaces/external/IERC20Minimal.sol";
+import {BalanceDelta} from "v4-core/src/types/BalanceDelta.sol";
+import {IPoolManager} from "v4-core/src/interfaces/IPoolManager.sol";
+import {Counter} from "../src/Counter.sol";
+import {Fixtures} from "./utils/Fixtures.sol";
+
+/// forge-config: default.invariant.fail-on-revert = false
+contract CounterHunterInvariant is Test, Fixtures {
+    Counter hook;
+    bool public swapRoundTripProfit;    // set true iff any 0->1->0 round-trip returned > spent
+    bool public callbackUnguarded;      // set true iff any callback ran for a non-PoolManager caller
+    int256 public maxSwapRtDelta = type(int256).min;  // largest round-trip currency0 delta seen
+
+    function setUp() public {
+        deployFreshManagerAndRouters();
+        deployMintAndApprove2Currencies();
+        deployAndApprovePosm(manager);
+
+        // Mine an address whose low 14 bits match the hook's declared permissions.
+        address flagsAddr = address(
+            uint160(Hooks.BEFORE_SWAP_FLAG | Hooks.BEFORE_SWAP_RETURNS_DELTA_FLAG | Hooks.BEFORE_ADD_LIQUIDITY_FLAG)
+                ^ (0x4444 << 144)
+        );
+        deployCodeTo("src/Counter.sol:Counter", abi.encode(manager), flagsAddr);
+        hook = Counter(flagsAddr);
+
+        // Pool init: raw manager.initialize (NOT Deployers' initPoolAndAddLiquidity -- the hook
+        // rejects native v4 liquidity by design).
+        key = PoolKey(currency0, currency1, 3000, 60, IHooks(hook));
+        manager.initialize(key, SQRT_PRICE_1_1);
+
+        // Seed liquidity through the hook itself (the constant-sum custom-accounting path).
+        IERC20(Currency.unwrap(currency0)).approve(address(hook), 1000e18);
+        IERC20(Currency.unwrap(currency1)).approve(address(hook), 1000e18);
+        hook.addLiquidity(key, 1000e18);
+
+        targetContract(address(this));
+    }
+
+    // ── fuzz action: single swap through the constant-sum curve ──
+    function h_swap(uint256 seed) public {
+        bool zeroForOne = (seed % 2 == 0);
+        int256 amountSpecified = -int256(bound(seed, 1e6, 1e13));
+        swap(key, zeroForOne, amountSpecified, ZERO_BYTES);
+    }
+
+    // ── fuzz action: round-trip 0->1->0. On a 1:1 constant-sum curve a clean round-trip nets
+    //    EXACTLY 0 wei -- any positive margin means the curve leaked value to the swapper.
+    function h_round_trip_swap(uint256 seed) public {
+        uint256 c0Before = IERC20Minimal(Currency.unwrap(currency0)).balanceOf(address(this));
+        int256 amt = -int256(bound(seed, 1e6, 1e13));
+        BalanceDelta d = swap(key, true, amt, ZERO_BYTES);
+        int128 out1 = d.amount1();
+        if (out1 > 0) {
+            swap(key, false, -int256(int128(out1)), ZERO_BYTES);
+            uint256 c0After = IERC20Minimal(Currency.unwrap(currency0)).balanceOf(address(this));
+            int256 rt = int256(c0After) - int256(c0Before);
+            if (rt > maxSwapRtDelta) maxSwapRtDelta = rt;
+            if (c0After > c0Before) swapRoundTripProfit = true;
+        }
+    }
+
+    // ── fuzz action: ACCESS CONTROL. Direct-call each hook callback from a NON-PoolManager
+    //    address. A correctly-guarded hook reverts every call; if any executes, the hook's
+    //    privileged logic is callable out-of-band -- the missing-onlyPoolManager class.
+    function h_attack_callbacks(uint256 seed) public {
+        seed;
+        bool ok;
+        (ok,) = address(hook).call(abi.encodeWithSelector(
+            IHooks.beforeSwap.selector, address(this), key, _sp(), ZERO_BYTES));
+        if (ok) callbackUnguarded = true;
+        (ok,) = address(hook).call(abi.encodeWithSelector(
+            IHooks.beforeAddLiquidity.selector, address(this), key, _mlp(), ZERO_BYTES));
+        if (ok) callbackUnguarded = true;
+    }
+
+    function _sp() internal pure returns (IPoolManager.SwapParams memory) {
+        return IPoolManager.SwapParams({zeroForOne: true, amountSpecified: -1e12, sqrtPriceLimitX96: 4295128740});
+    }
+    function _mlp() internal pure returns (IPoolManager.ModifyLiquidityParams memory) {
+        return IPoolManager.ModifyLiquidityParams({tickLower: -60, tickUpper: 60, liquidityDelta: 1e12, salt: bytes32(0)});
+    }
+
+    // ── INVARIANT #1 -- the constant-sum value-conservation claim.
+    function invariant_no_free_swap_round_trip() public view {
+        assertFalse(swapRoundTripProfit,
+            "round-trip swap (0->1->0) returned more than spent on the constant-sum curve");
+    }
+
+    // ── INVARIANT #2 -- the universal v4 hook access-control claim.
+    function invariant_callbacks_reject_non_poolmanager() public view {
+        assertFalse(callbackUnguarded,
+            "hook callback executed for non-PoolManager caller: missing onlyPoolManager guard");
+    }
+
+    // ── informational: surface the worst-case round-trip delta as a wei-level number.
+    function afterInvariant() public {
+        if (maxSwapRtDelta != type(int256).min) emit log_named_int("HUNTER_MAX_SWAP_RT_DELTA", maxSwapRtDelta);
+    }
+}