diff --git a/src/IPartyPool.sol b/src/IPartyPool.sol
index 29ea18d..2888f04 100644
--- a/src/IPartyPool.sol
+++ b/src/IPartyPool.sol
@@ -117,9 +117,9 @@ interface IPartyPool is IERC20Metadata, IOwnable {
     /// @notice Callable by anyone, sends any owed protocol fees to the protocol fee address.
     function collectProtocolFees() external;
 
-    /// @notice Liquidity parameter κ (Q64.64) used by the LMSR kernel: b = κ * S(q)
-    /// @dev Pools are constructed with a κ value; this getter exposes the κ used by the pool.
-    function kappa() external view returns (int128);
+    /// @notice Fixed LMSR curvature parameter b (Q64.64) Larger values allow more liquidity to be taken with less price impact.
+    /// @dev Pools are constructed with a fixed b; this getter exposes the b used by the pool.
+    function bFixed() external view returns (int128);
 
     /// @notice If a security problem is found, the vault owner may call this function to permanently disable swap and
     /// mint functionality, leaving only burns (withdrawals) working.
diff --git a/src/LMSRStabilized.sol b/src/LMSRStabilized.sol
index a08f9f9..57c10bd 100644
--- a/src/LMSRStabilized.sol
+++ b/src/LMSRStabilized.sol
@@ -13,7 +13,7 @@ library LMSRStabilized {
 
     struct State {
         uint256 nAssets;
-        int128 kappa;    // liquidity parameter κ (64.64 fixed point)
+        int128 bFixed;   // fixed b curvature (Q64.64)
         int128[] qInternal; // cached internal balances in 64.64 fixed-point format
     }
 
@@ -26,11 +26,10 @@ library LMSRStabilized {
     function init(
         State storage s,
         int128[] memory initialQInternal,
-        int128 kappa
+        int128 bFixed
     ) internal {
         s.nAssets = initialQInternal.length;
 
-        // Initialize qInternal cache
         if (s.qInternal.length != initialQInternal.length) {
             s.qInternal = new int128[](initialQInternal.length);
         }
@@ -42,9 +41,73 @@ library LMSRStabilized {
         int128 total = _computeSizeMetric(s.qInternal);
         require(total > int128(0), "LMSR: total zero");
 
-        // Set kappa directly (caller provides kappa)
-        s.kappa = kappa;
-        require(s.kappa > int128(0), "LMSR: kappa>0");
+        require(bFixed > int128(0), "LMSR: b<=0");
+        s.bFixed = bFixed;
+    }
+
+    /* --------------------
+       Virtual offset helpers (pure) for initialization
+       -------------------- */
+
+    /// @notice Compute per-asset virtual offsets v so that the initial marginal price between `base` and `quote`
+    ///         equals `targetPrice` (Q64.64). Returns an array v with v_base and v_quote adjusted and others zero.
+    /// @dev Given reserves r, we want s = r + v with s_quote - s_base = b * ln(targetPrice).
+    ///      Let deltaDesired = b*ln(targetPrice), deltaCurrent = r_quote - r_base, then
+    ///      let adj = deltaDesired - deltaCurrent; choose v_base = -adj/2, v_quote = adj/2, others 0.
+    function computeOffsetsForPricePair(
+        int128 b,
+        int128[] memory reservesInternal,
+        uint256 baseIndex,
+        uint256 quoteIndex,
+        int128 targetPrice
+    ) internal pure returns (int128[] memory vOffsets) {
+        require(b > int128(0), "LMSR: b<=0");
+        uint256 n = reservesInternal.length;
+        require(baseIndex < n && quoteIndex < n, "LMSR: idx");
+
+        vOffsets = new int128[](n);
+
+        // adj = b * ln(targetPrice) - (r_quote - r_base)
+        int128 deltaDesired = b.mul(_ln(targetPrice));
+        int128 deltaCurrent = reservesInternal[quoteIndex].sub(reservesInternal[baseIndex]);
+        int128 adj = deltaDesired.sub(deltaCurrent);
+
+        int128 two = ABDKMath64x64.fromUInt(2);
+        // v_base = -adj/2; v_quote = adj/2
+        vOffsets[baseIndex] = adj.neg().div(two);
+        vOffsets[quoteIndex] = adj.div(two);
+        return vOffsets;
+    }
+
+    /// @notice Compute per-asset virtual offsets v to match a vector of relative log-prices (Q64.64).
+    /// @dev logPrices[i] should represent ln(p_i / p_ref) for a chosen reference asset ref (e.g., ref = 0 => logPrices[0] = 0).
+    ///      We set v_0 = 0 and for i>0 require (v_i - v_0) = b*(logPrices[i] - logPrices[0]) - (r_i - r_0).
+    ///      Note: adding a constant to all v does not change prices; callers may shift v uniformly if they want S>0 margin.
+    function computeOffsetsForLogPrices(
+        int128 b,
+        int128[] memory reservesInternal,
+        uint256 referenceIndex,
+        int128[] memory logPrices
+    ) internal pure returns (int128[] memory vOffsets) {
+        require(b > int128(0), "LMSR: b<=0");
+        uint256 n = reservesInternal.length;
+        require(logPrices.length == n, "LMSR: length mismatch");
+        require(referenceIndex < n, "LMSR: ref idx");
+
+        vOffsets = new int128[](n);
+
+        // Set v_ref = 0, solve differences for others
+        uint256 ref = referenceIndex;
+        int128 logP_ref = logPrices[ref];
+        for (uint256 i = 0; i < n; ) {
+            if (i != ref) {
+                int128 desiredDiff = b.mul(logPrices[i].sub(logP_ref));                 // b*(ln p_i - ln p_ref)
+                int128 currentDiff = reservesInternal[i].sub(reservesInternal[ref]);    // r_i - r_ref
+                vOffsets[i] = desiredDiff.sub(currentDiff);                              // v_i - v_ref with v_ref = 0
+            }
+            unchecked { i++; }
+        }
+        return vOffsets;
     }
 
     /* --------------------
@@ -53,14 +116,13 @@ library LMSRStabilized {
 
     /// @notice Cost C(q) = b * (M + ln(Z))
     function cost(State storage s) internal view returns (int128) {
-        return cost(s.kappa, s.qInternal);
+        int128 b = _computeB(s);
+        return cost(b, s.qInternal);
     }
 
     /// @notice Pure version: Cost C(q) = b * (M + ln(Z))
-    function cost(int128 kappa, int128[] memory qInternal) internal pure returns (int128) {
-        int128 sizeMetric = _computeSizeMetric(qInternal);
-        require(sizeMetric > int128(0), "LMSR: size metric zero");
-        int128 b = kappa.mul(sizeMetric);
+    function cost(int128 b, int128[] memory qInternal) internal pure returns (int128) {
+        require(b > int128(0), "LMSR: b<=0");
         (int128 M, int128 Z) = _computeMAndZ(b, qInternal);
         int128 lnZ = _ln(Z);
         int128 inner = M.add(lnZ);
@@ -98,7 +160,8 @@ library LMSRStabilized {
         int128 a,
         int128 limitPrice
     ) internal view returns (int128 amountIn, int128 amountOut) {
-        return swapAmountsForExactInput(s.nAssets, s.kappa, s.qInternal, i, j, a, limitPrice);
+        int128 b = _computeB(s);
+        return swapAmountsForExactInput(s.nAssets, b, s.qInternal, i, j, a, limitPrice);
     }
 
     /// @notice Pure version: Closed-form asset-i -> asset-j amountOut in 64.64 fixed-point format (fee-free kernel)
@@ -114,7 +177,7 @@ library LMSRStabilized {
     /// NOTE: Kernel is fee-free; fees should be handled by the wrapper/token layer.
     ///
     /// @param nAssets Number of assets in the pool
-    /// @param kappa Liquidity parameter κ (64.64 fixed point)
+    /// @param b Liquidity parameter κ (64.64 fixed point)
     /// @param qInternal Cached internal balances in 64.64 fixed-point format
     /// @param i Index of input asset
     /// @param j Index of output asset
@@ -124,7 +187,7 @@ library LMSRStabilized {
     /// @return amountOut Amount of output asset j in 64.64 fixed-point format
     function swapAmountsForExactInput(
         uint256 nAssets,
-        int128 kappa,
+        int128 b,
         int128[] memory qInternal,
         uint256 i,
         uint256 j,
@@ -136,58 +199,33 @@ library LMSRStabilized {
         // Initialize amountIn to full amount (will be adjusted if limit price is hit)
         amountIn = a;
 
-        // Compute b and ensure positivity before deriving invB
-        int128 sizeMetric = _computeSizeMetric(qInternal);
-        require(sizeMetric > int128(0), "LMSR: size metric zero");
-        int128 b = kappa.mul(sizeMetric);
+        // Ensure b > 0 and derive invB
         require(b > int128(0), "LMSR: b<=0");
-
-        // Precompute reciprocal of b to avoid repeated divisions
         int128 invB = ABDKMath64x64.div(ONE, b);
 
-        // Guard: output asset must have non-zero effective weight to avoid degenerate/div-by-zero-like conditions
-        require(qInternal[j] > int128(0), "LMSR: e_j==0");
-
-        // Compute r0 = exp((q_i - q_j) / b) directly using invB
+        // Compute r0 = exp((q_i - q_j) / b) directly using invB (always > 0)
         int128 r0 = _exp(qInternal[i].sub(qInternal[j]).mul(invB));
-        require(r0 > int128(0), "LMSR: r0<=0"); // equivalent to e_j > 0 check
 
         // If a positive limitPrice is given, determine whether the full `a` would
         // push the marginal price p_i/p_j beyond the limit; if so, truncate `a`.
-        // Marginal price ratio evolves as r(t) = r0 * exp(t/b) (since e_i multiplies by exp(t/b))
+        // Marginal price ratio evolves as r(t) = r0 * exp(t/b)
         if (limitPrice > int128(0)) {
-            // r0 must be positive; if r0 == 0 then no risk of exceeding limit by increasing r.
-            require(r0 >= int128(0), "LMSR: r0<0");
-            if (r0 == int128(0)) {
-//                console2.log("r0 == 0 (input asset has zero weight), no limit truncation needed");
-            } else {
-                // If limitPrice <= current price, we revert (caller must choose a limit > current price to allow any fill)
-                if (limitPrice <= r0) {
-                    revert("LMSR: limitPrice <= current price");
-                }
+            if (limitPrice <= r0) {
+                revert("LMSR: limitPrice <= current price");
+            }
+            int128 ratioLimitOverR0 = limitPrice.div(r0);
+            require(ratioLimitOverR0 > int128(0), "LMSR: ratio<=0");
 
-                // Compute a_limit directly from ln(limit / r0): a_limit = b * ln(limit / r0)
-                int128 ratioLimitOverR0 = limitPrice.div(r0);
-                require(ratioLimitOverR0 > int128(0), "LMSR: ratio<=0");
-
-                int128 aLimitOverB = _ln(ratioLimitOverR0); // > 0
-
-                // aLimit = b * aLimitOverB
-                int128 aLimit64 = b.mul(aLimitOverB);
-
-                // If computed aLimit is less than the requested a, use the truncated value.
-                if (aLimit64 < a) {
-                    amountIn = aLimit64; // Store the truncated input amount
-                    a = aLimit64;        // Use truncated amount for calculations
-                } else {
-//                    console2.log("Not truncating: aLimit64 >= a");
-                }
+            int128 aLimitOverB = _ln(ratioLimitOverR0); // > 0
+            int128 aLimit64 = b.mul(aLimitOverB);
+            if (aLimit64 < a) {
+                amountIn = aLimit64;
+                a = aLimit64;
             }
         }
 
         // compute a/b safely and guard against very large arguments to exp()
         int128 aOverB = a.mul(invB);
-        // Protect exp from enormous inputs (consistent with recenter thresholds)
         require(aOverB <= EXP_LIMIT, "LMSR: a/b too large (would overflow exp)");
 
         // Use the closed-form fee-free formula:
@@ -196,17 +234,14 @@ library LMSRStabilized {
         int128 oneMinusExpNeg = ONE.sub(expNeg);
         int128 inner = ONE.add(r0.mul(oneMinusExpNeg));
 
-        // If inner <= 0 then cap output to the current balance q_j (cannot withdraw more than q_j)
+        // If inner <= 0 then return zero (numeric guard; reserve caps are enforced by wrapper)
         if (inner <= int128(0)) {
-            int128 qj64 = qInternal[j];
-            return (amountIn, qj64);
+            return (amountIn, int128(0));
         }
 
         int128 lnInner = _ln(inner);
-        int128 b_lnInner = b.mul(lnInner);
-        amountOut = b_lnInner;
+        amountOut = b.mul(lnInner);
 
-        // Safety check
         if (amountOut <= 0) {
             return (0, 0);
         }
@@ -230,7 +265,8 @@ library LMSRStabilized {
         uint256 j,
         int128 limitPrice
     ) internal view returns (int128 amountIn, int128 amountOut) {
-        return swapAmountsForPriceLimit(s.nAssets, s.kappa, s.qInternal, i, j, limitPrice);
+        int128 b = _computeB(s);
+        return swapAmountsForPriceLimit(s.nAssets, b, s.qInternal, i, j, limitPrice);
     }
 
     /// @notice Pure version: Maximum input/output pair possible when swapping from asset i to asset j
@@ -240,7 +276,7 @@ library LMSRStabilized {
     /// j-balance, amountOut is capped and amountIn is solved for the capped output.
     ///
     /// @param nAssets Number of assets in the pool
-    /// @param kappa Liquidity parameter κ (64.64 fixed point)
+    /// @param b Liquidity parameter κ (64.64 fixed point)
     /// @param qInternal Cached internal balances in 64.64 fixed-point format
     /// @param i Index of input asset
     /// @param j Index of output asset
@@ -249,7 +285,7 @@ library LMSRStabilized {
     /// @return amountOut Corresponding maximum output amount in 64.64 fixed-point format
     function swapAmountsForPriceLimit(
         uint256 nAssets,
-        int128 kappa,
+        int128 b,
         int128[] memory qInternal,
         uint256 i,
         uint256 j,
@@ -258,74 +294,31 @@ library LMSRStabilized {
         require(i < nAssets && j < nAssets, "LMSR: idx");
         require(limitPrice > int128(0), "LMSR: limitPrice <= 0");
 
-        // Compute b and ensure positivity before deriving invB
-        int128 sizeMetric = _computeSizeMetric(qInternal);
-        require(sizeMetric > int128(0), "LMSR: size metric zero");
-        int128 b = kappa.mul(sizeMetric);
+        // Ensure positivity and derive invB
         require(b > int128(0), "LMSR: b<=0");
-
-        // Precompute reciprocal of b to avoid repeated divisions
         int128 invB = ABDKMath64x64.div(ONE, b);
 
-        // Guard: output asset must have non-zero effective weight to avoid degenerate/div-by-zero-like conditions
-        require(qInternal[j] > int128(0), "LMSR: e_j==0");
-
-        // Compute r0 = exp((q_i - q_j) / b) directly using invB
+        // Compute r0 = exp((q_i - q_j) / b)
         int128 r0 = _exp(qInternal[i].sub(qInternal[j]).mul(invB));
 
-        // Mirror swapAmountsForExactInput behavior: treat invalid r0 as an error condition.
-        // Revert if r0 is non-positive (no finite trade under a price limit).
-        require(r0 > int128(0), "LMSR: r0<=0");
-
-        // If current price already exceeds or equals limit, revert the same way swapAmountsForExactInput does.
+        // If current price already exceeds or equals limit, revert (no room to move)
         if (r0 >= limitPrice) {
             revert("LMSR: limitPrice <= current price");
         }
 
-        // Calculate the price change factor: limitPrice/r0
-        int128 priceChangeFactor = limitPrice.div(r0);
-
-        // ln(priceChangeFactor) gives us the maximum allowed delta in the exponent
-        int128 maxDeltaExponent = _ln(priceChangeFactor);
-
-        // Maximum input capable of reaching the price limit:
         // x_max = b * ln(limitPrice / r0)
+        int128 priceChangeFactor = limitPrice.div(r0);
+        int128 maxDeltaExponent = _ln(priceChangeFactor);
         int128 amountInMax = b.mul(maxDeltaExponent);
 
-        // The maximum output y corresponding to that input:
-        // y = b * ln(1 + (e_i/e_j) * (1 - exp(-x_max/b)))
+        // y_max = b * ln(1 + r0 * (1 - exp(-x_max/b)))
         int128 expTerm = ONE.sub(_exp(maxDeltaExponent.neg()));
         int128 innerTerm = r0.mul(expTerm);
         int128 lnTerm = _ln(ONE.add(innerTerm));
         int128 maxOutput = b.mul(lnTerm);
 
-        // Current balance of asset j (in 64.64)
-        int128 qj64 = qInternal[j];
-
-        // Initialize outputs to the computed maxima
         amountIn = amountInMax;
         amountOut = maxOutput;
-
-        // If the calculated maximum output exceeds the balance, cap output and solve for input.
-        if (maxOutput > qj64) {
-            amountOut = qj64;
-
-            // Solve inverse relation for input given capped output:
-            // Given y = amountOut, let E = exp(y/b). Then
-            //   1 - exp(-a/b) = (E - 1) / r0
-            //   exp(-a/b) = 1 - (E - 1) / r0 = (r0 + 1 - E) / r0
-            //   a = -b * ln( (r0 + 1 - E) / r0 ) = b * ln( r0 / (r0 + 1 - E) )
-            int128 E = _exp(amountOut.mul(invB)); // exp(y/b)
-            int128 rhs = r0.add(ONE).sub(E); // r0 + 1 - E
-
-            // If rhs <= 0 due to numerical issues, fall back to amountInMax
-            if (rhs <= int128(0)) {
-                amountIn = amountInMax;
-            } else {
-                amountIn = b.mul(_ln(r0.div(rhs)));
-            }
-        }
-
         return (amountIn, amountOut);
     }
 
@@ -340,7 +333,8 @@ library LMSRStabilized {
         uint256 i,
         int128 a
     ) internal view returns (int128 amountIn, int128 amountOut) {
-        return swapAmountsForMint(s.nAssets, s.kappa, s.qInternal, i, a);
+        int128 b = _computeB(s);
+        return swapAmountsForMint(s.nAssets, b, s.qInternal, i, a);
     }
 
     /// @notice Pure version: Compute LP-size increase when minting from a single-token input using bisection only.
@@ -350,7 +344,7 @@ library LMSRStabilized {
     ///      x_j = b * ln( r0_j / (r0_j + 1 - exp(y_j / b)) ), r0_j = exp((q_i - q_j)/b).
     ///      Bisection is used (no Newton) to keep implementation compact and gas-friendly.
     /// @param nAssets Number of assets in the pool
-    /// @param kappa Liquidity parameter κ (64.64 fixed point)
+    /// @param b Liquidity parameter κ (64.64 fixed point)
     /// @param qInternal Cached internal balances in 64.64 fixed-point format
     /// @param i Index of input asset
     /// @param a Amount of input asset (in int128 format, 64.64 fixed-point)
@@ -358,7 +352,7 @@ library LMSRStabilized {
     /// @return amountOut LP size-metric increase (alpha * S)
     function swapAmountsForMint(
         uint256 nAssets,
-        int128 kappa,
+        int128 b,
         int128[] memory qInternal,
         uint256 i,
         int128 a
@@ -366,12 +360,11 @@ library LMSRStabilized {
         require(i < nAssets, "LMSR: idx");
         require(a > int128(0), "LMSR: amount <= 0");
 
-        int128 sizeMetric = _computeSizeMetric(qInternal);
-        require(sizeMetric > int128(0), "LMSR: size metric zero");
-        int128 b = kappa.mul(sizeMetric);
+        // Compute size metric S for output computation; use provided b for curvature
+        int128 S = _computeSizeMetric(qInternal);
+        require(S > int128(0), "LMSR: size metric zero");
         require(b > int128(0), "LMSR: b<=0");
         int128 invB = ABDKMath64x64.div(ONE, b);
-        int128 S = sizeMetric;
 
         uint256 n = nAssets;
 
@@ -552,7 +545,8 @@ library LMSRStabilized {
         uint256 i,
         int128 alpha
     ) internal view returns (int128 amountOut, int128 amountIn) {
-        return swapAmountsForBurn(s.nAssets, s.kappa, s.qInternal, i, alpha);
+        int128 b = _computeB(s);
+        return swapAmountsForBurn(s.nAssets, b, s.qInternal, i, alpha);
     }
 
     /// @notice Pure version: Compute single-asset payout when burning a proportional share alpha of the pool.
@@ -565,7 +559,7 @@ library LMSRStabilized {
     ///      Treat any per-asset rhs<=0 as "this asset contributes zero" (do not revert).
     ///      Revert only if the final single-asset payout is zero.
     /// @param nAssets Number of assets in the pool
-    /// @param kappa Liquidity parameter κ (64.64 fixed point)
+    /// @param b Liquidity parameter κ (64.64 fixed point)
     /// @param qInternal Cached internal balances in 64.64 fixed-point format
     /// @param i Index of output asset
     /// @param alpha Proportional share to burn (0 < alpha <= 1)
@@ -573,7 +567,7 @@ library LMSRStabilized {
     /// @return amountIn LP size-metric redeemed (alpha * S)
     function swapAmountsForBurn(
         uint256 nAssets,
-        int128 kappa,
+        int128 b,
         int128[] memory qInternal,
         uint256 i,
         int128 alpha
@@ -581,9 +575,9 @@ library LMSRStabilized {
         require(i < nAssets, "LMSR: idx");
         require(alpha > int128(0) && alpha <= ONE, "LMSR: alpha");
 
+        // Compute size metric S for payout normalization; use provided b for curvature
         int128 sizeMetric = _computeSizeMetric(qInternal);
         require(sizeMetric > int128(0), "LMSR: size metric zero");
-        int128 b = kappa.mul(sizeMetric);
         require(b > int128(0), "LMSR: b<=0");
         int128 invB = ABDKMath64x64.div(ONE, b);
 
@@ -726,20 +720,47 @@ library LMSRStabilized {
         }
     }
 
+    /// @notice Optional helper: recompute qInternal from reserves and explicit virtual offsets.
+    /// @dev This variant is useful if callers manage virtual offsets off-chain and want to preserve price neutrality
+    ///      across proportional mints/burns by applying updated offsets alongside reserve changes.
+    /// @param newReservesInternal New reserves vector in 64.64 (converted from uint balances)
+    /// @param vOffsets Per-asset virtual offsets to apply (same length as nAssets)
+    function updateForProportionalChangeWithOffsets(
+        State storage s,
+        int128[] memory newReservesInternal,
+        int128[] memory vOffsets
+    ) internal {
+        require(newReservesInternal.length == s.nAssets, "LMSR: length mismatch");
+        require(vOffsets.length == s.nAssets, "LMSR: v length mismatch");
+
+        int128[] memory combined = new int128[](s.nAssets);
+        for (uint i = 0; i < s.nAssets; ) {
+            combined[i] = newReservesInternal[i].add(vOffsets[i]);
+            unchecked { i++; }
+        }
+
+        int128 newTotal = _computeSizeMetric(combined);
+        require(newTotal > int128(0), "LMSR: new total zero");
+
+        for (uint i = 0; i < s.nAssets; ) {
+            s.qInternal[i] = combined[i];
+            unchecked { i++; }
+        }
+    }
+
     /// @notice Price-share of asset i: exp(z_i) / Z (64.64)
     function priceShare(State storage s, uint256 i) internal view returns (int128) {
-        return priceShare(s.kappa, s.qInternal, i);
+        int128 b = _computeB(s);
+        return priceShare(b, s.qInternal, i);
     }
 
     /// @notice Pure version: Price-share of asset i: exp(z_i) / Z (64.64)
-    /// @param kappa Liquidity parameter κ (64.64 fixed point)
+    /// @param b Liquidity parameter κ (64.64 fixed point)
     /// @param qInternal Cached internal balances in 64.64 fixed-point format
     /// @param i Index of asset
     /// @return Price share in 64.64 fixed-point format
-    function priceShare(int128 kappa, int128[] memory qInternal, uint256 i) internal pure returns (int128) {
-        int128 sizeMetric = _computeSizeMetric(qInternal);
-        require(sizeMetric > int128(0), "LMSR: size metric zero");
-        int128 b = kappa.mul(sizeMetric);
+    function priceShare(int128 b, int128[] memory qInternal, uint256 i) internal pure returns (int128) {
+        require(b > int128(0), "LMSR: b<=0");
         uint len = qInternal.length;
         require(len > 0, "LMSR: no assets");
 
@@ -797,22 +818,20 @@ library LMSRStabilized {
     /// @notice Marginal price of `base` in terms of `quote` (p_quote / p_base) as Q64.64
     /// @dev Returns exp((q_quote - q_base) / b). Indices must be valid and b > 0.
     function price(State storage s, uint256 baseTokenIndex, uint256 quoteTokenIndex) internal view returns (int128) {
-        return price(s.nAssets, s.kappa, s.qInternal, baseTokenIndex, quoteTokenIndex);
+        int128 b = _computeB(s);
+        return price(s.nAssets, b, s.qInternal, baseTokenIndex, quoteTokenIndex);
     }
 
     /// @notice Pure version: Marginal price of `base` in terms of `quote` (p_quote / p_base) as Q64.64
     /// @dev Returns exp((q_quote - q_base) / b). Indices must be valid and b > 0.
     /// @param nAssets Number of assets in the pool
-    /// @param kappa Liquidity parameter κ (64.64 fixed point)
+    /// @param b Liquidity parameter κ (64.64 fixed point)
     /// @param qInternal Cached internal balances in 64.64 fixed-point format
     /// @param baseTokenIndex Index of base token
     /// @param quoteTokenIndex Index of quote token
     /// @return Price in 64.64 fixed-point format
-    function price(uint256 nAssets, int128 kappa, int128[] memory qInternal, uint256 baseTokenIndex, uint256 quoteTokenIndex) internal pure returns (int128) {
+    function price(uint256 nAssets, int128 b, int128[] memory qInternal, uint256 baseTokenIndex, uint256 quoteTokenIndex) internal pure returns (int128) {
         require(baseTokenIndex < nAssets && quoteTokenIndex < nAssets, "LMSR: idx");
-        int128 sizeMetric = _computeSizeMetric(qInternal);
-        require(sizeMetric > int128(0), "LMSR: size metric zero");
-        int128 b = kappa.mul(sizeMetric);
         require(b > int128(0), "LMSR: b<=0");
 
         // Use reciprocal of b to avoid repeated divisions
@@ -825,26 +844,22 @@ library LMSRStabilized {
     /// @notice Price of one unit of the LP size-metric (S = sum q_i) denominated in `quote` asset (Q64.64)
     /// @dev Computes: poolPrice_quote = (1 / S) * sum_j q_j * exp((q_j - q_quote) / b)
     function poolPrice(State storage s, uint256 quoteTokenIndex) internal view returns (int128) {
-        return poolPrice(s.nAssets, s.kappa, s.qInternal, quoteTokenIndex);
+        int128 b = _computeB(s);
+        return poolPrice(s.nAssets, b, s.qInternal, quoteTokenIndex);
     }
 
     /// @notice Pure version: Price of one unit of the LP size-metric (S = sum q_i) denominated in `quote` asset (Q64.64)
     /// @dev Computes: poolPrice_quote = (1 / S) * sum_j q_j * exp((q_j - q_quote) / b)
     /// @param nAssets Number of assets in the pool
-    /// @param kappa Liquidity parameter κ (64.64 fixed point)
+    /// @param b Liquidity parameter κ (64.64 fixed point)
     /// @param qInternal Cached internal balances in 64.64 fixed-point format
     /// @param quoteTokenIndex Index of quote token
     /// @return Pool price in 64.64 fixed-point format
-    function poolPrice(uint256 nAssets, int128 kappa, int128[] memory qInternal, uint256 quoteTokenIndex) internal pure returns (int128) {
+    function poolPrice(uint256 nAssets, int128 b, int128[] memory qInternal, uint256 quoteTokenIndex) internal pure returns (int128) {
         require(quoteTokenIndex < nAssets, "LMSR: idx");
-        // Compute b and ensure positivity
-        int128 sizeMetric = _computeSizeMetric(qInternal);
-        require(sizeMetric > int128(0), "LMSR: size metric zero");
-        int128 b = kappa.mul(sizeMetric);
+        // Ensure positivity and compute total size metric S = sum q_i
         require(b > int128(0), "LMSR: b<=0");
-
-        // Compute total size metric S = sum q_i
-        int128 S = sizeMetric;
+        int128 S = _computeSizeMetric(qInternal);
         require(S > int128(0), "LMSR: size zero");
 
         // Precompute reciprocal of b
@@ -870,9 +885,8 @@ library LMSRStabilized {
        Slippage -> b computation & resize-triggered rescale
        -------------------- */
 
-    /// @notice Internal helper to compute kappa from slippage parameters.
-    /// @dev Returns κ in Q64.64. Implemented as internal so callers within the library can use it
-    ///      without resorting to external calls.
+    /// @notice Internal helper to compute kappa from slippage parameters. (Deprecated in favor of computeBFromSlippage)
+    /// @dev Returns κ in Q64.64 for reference. Prefer computing b directly via computeBFromSlippage.
     function computeKappaFromSlippage(
         uint256 nAssets,
         int128 tradeFrac,
@@ -920,7 +934,57 @@ library LMSRStabilized {
         return kappa;
     }
 
-    /// @notice Legacy-compatible init: compute kappa from slippage parameters and delegate to kappa-based init.
+    /// @notice Compute fixed b from a target slippage profile.
+    /// @dev For a trade of fraction f of the size metric S, targeting slippage s, we have y := -ln(E)/f with
+    ///      E = (1 - s*(n-1)) / (1 + s) and b = S / y.
+    function computeBFromSlippage(
+        uint256 nAssets,
+        int128 sizeMetricS,
+        int128 tradeFrac,
+        int128 targetSlippage
+    ) internal pure returns (int128) {
+        require(nAssets > 1, "LMSR: n>1 required");
+        require(sizeMetricS > int128(0), "LMSR: S<=0");
+
+        // f must be in (0,1)
+        int128 f = tradeFrac;
+        require(f > int128(0), "LMSR: f=0");
+        require(f < ONE, "LMSR: f>=1");
+
+        int128 onePlusS = ONE.add(targetSlippage);
+
+        int128 n64 = ABDKMath64x64.fromUInt(nAssets);
+        int128 nMinus1_64 = ABDKMath64x64.fromUInt(nAssets - 1);
+
+        // If 1 + s >= n then equal-inventories closed-form applies
+        bool useEqual = (onePlusS >= n64);
+
+        // E candidate used in deriving y = -ln(E)/f (same expression in both branches)
+        int128 numerator = ONE.sub(targetSlippage.mul(nMinus1_64)); // 1 - s*(n-1)
+        int128 denominator = onePlusS;                               // 1 + s
+
+        if (useEqual) {
+            // Guard numerator to ensure E in (0,1)
+            require(numerator > int128(0), "LMSR: s too large for n");
+        } else {
+            require(numerator > int128(0), "LMSR: bad slippage or n");
+        }
+
+        int128 E_candidate = numerator.div(denominator);
+        require(E_candidate > int128(0) && E_candidate < ONE, "LMSR: bad E ratio");
+
+        // y = -ln(E) / f
+        int128 lnE = _ln(E_candidate);
+        int128 y = lnE.neg().div(f);
+        require(y > int128(0), "LMSR: y<=0");
+
+        // b = S / y
+        int128 b = ABDKMath64x64.div(sizeMetricS, y);
+        require(b > int128(0), "LMSR: b<=0");
+        return b;
+    }
+
+    /// @notice Legacy-compatible init: compute fixed b from slippage parameters and delegate to fixed-b init.
     /// @dev Provides backward compatibility for callers that still use the (q, tradeFrac, targetSlippage) init signature.
     function init(
         State storage s,
@@ -928,10 +992,11 @@ library LMSRStabilized {
         int128 tradeFrac,
         int128 targetSlippage
     ) internal {
-        // compute kappa using the internal helper
-        int128 kappa = computeKappaFromSlippage(initialQInternal.length, tradeFrac, targetSlippage);
-        // forward to the new kappa-based init
-        init(s, initialQInternal, kappa);
+        // compute b directly from the current size metric and the slippage profile
+        int128 S = _computeSizeMetric(initialQInternal);
+        int128 b = computeBFromSlippage(initialQInternal.length, S, tradeFrac, targetSlippage);
+        // forward to the fixed-b init
+        init(s, initialQInternal, b);
     }
 
 
@@ -940,12 +1005,12 @@ library LMSRStabilized {
     function deinit(State storage s) internal {
         // Reset core state
         s.nAssets = 0;
-        s.kappa = int128(0);
+        s.bFixed = int128(0);
 
         // Clear qInternal array
         delete s.qInternal;
 
-        // Note: init(...) will recompute kappa and nAssets on first mint.
+        // Note: initWithFixedB(...) will set b and nAssets on first mint.
     }
 
     /// @notice Compute M (shift) and Z (sum of exponentials) dynamically
@@ -1023,9 +1088,8 @@ library LMSRStabilized {
 
     /// @notice Compute b from kappa and current asset quantities
     function _computeB(State storage s) internal view returns (int128) {
-        int128 sizeMetric = _computeSizeMetric(s.qInternal);
-        require(sizeMetric > int128(0), "LMSR: size metric zero");
-        return s.kappa.mul(sizeMetric);
+        // require(s.bFixed > int128(0), "LMSR: b not set");
+        return s.bFixed;
     }
 
 }
diff --git a/src/PartyPool.sol b/src/PartyPool.sol
index 0fdd2fa..47442df 100644
--- a/src/PartyPool.sol
+++ b/src/PartyPool.sol
@@ -48,11 +48,9 @@ contract PartyPool is PartyPoolBase, OwnableExternal, ERC20External, IPartyPool
 
     function wrapperToken() external view returns (NativeWrapper) { return WRAPPER_TOKEN; }
 
-    /// @notice Liquidity parameter κ (Q64.64) used by the LMSR kernel: b = κ * S(q)
-    /// @dev Pool is constructed with a fixed κ. Clients that previously passed tradeFrac/targetSlippage
-    ///      should use LMSRStabilized.computeKappaFromSlippage(...) to derive κ and pass it here.
-    int128 private immutable KAPPA; // kappa in Q64.64
-    function kappa() external view returns (int128) { return KAPPA; }
+    /// @notice Fixed LMSR curvature parameter b (Q64.64)
+    int128 private immutable B_FIXED;
+    function bFixed() external view returns (int128) { return B_FIXED; }
 
     /// @notice Per-swap fee in parts-per-million (ppm). Fee is taken from input amounts before LMSR computations.
     uint256 private immutable SWAP_FEE_PPM;
@@ -100,7 +98,7 @@ contract PartyPool is PartyPoolBase, OwnableExternal, ERC20External, IPartyPool
     /// @param symbol_ LP token symbol
     /// @param tokens_ token addresses (n)
     /// @param bases_ scaling _bases for each token (n) - used when converting to/from internal 64.64 amounts
-    /// @param kappa_ liquidity parameter κ (Q64.64) used to derive b = κ * S(q)
+    /// @param bFixed_ fixed LMSR curvature b (Q64.64)
     /// @param swapFeePpm_ fee in parts-per-million, taken from swap input amounts before LMSR calculations
     /// @param flashFeePpm_ fee in parts-per-million, taken for flash loans
     /// @param swapImpl_ address of the SwapMint implementation contract
@@ -111,7 +109,7 @@ contract PartyPool is PartyPoolBase, OwnableExternal, ERC20External, IPartyPool
         string memory symbol_,
         IERC20[] memory tokens_,
         uint256[] memory bases_,
-        int128 kappa_,
+        int128 bFixed_,
         uint256 swapFeePpm_,
         uint256 flashFeePpm_,
         uint256 protocolFeePpm_,
@@ -129,7 +127,7 @@ contract PartyPool is PartyPoolBase, OwnableExternal, ERC20External, IPartyPool
         require(tokens_.length == bases_.length, "Pool: lengths mismatch");
         _tokens = tokens_;
         _bases = bases_;
-        KAPPA = kappa_;
+        B_FIXED = bFixed_;
         require(swapFeePpm_ < 1_000_000, "Pool: fee >= ppm");
         SWAP_FEE_PPM = swapFeePpm_;
         require(flashFeePpm_ < 1_000_000, "Pool: flash fee >= ppm");
@@ -184,7 +182,7 @@ contract PartyPool is PartyPoolBase, OwnableExternal, ERC20External, IPartyPool
             PartyPoolMintImpl.initialMint.selector,
             receiver,
             lpTokens,
-            KAPPA
+            B_FIXED
         );
         bytes memory result = Address.functionDelegateCall(address(MINT_IMPL), data);
         return abi.decode(result, (uint256));
diff --git a/src/PartyPoolMintImpl.sol b/src/PartyPoolMintImpl.sol
index 121432e..63d3385 100644
--- a/src/PartyPoolMintImpl.sol
+++ b/src/PartyPoolMintImpl.sol
@@ -25,7 +25,7 @@ contract PartyPoolMintImpl is PartyPoolBase {
     // Initialization Mint
     //
 
-    function initialMint(address receiver, uint256 lpTokens, int128 KAPPA) external payable native killable nonReentrant
+    function initialMint(address receiver, uint256 lpTokens, int128 B_FIXED) external payable native killable nonReentrant
     returns (uint256 lpMinted) {
         uint256 n = _tokens.length;
 
@@ -44,8 +44,8 @@ contract PartyPoolMintImpl is PartyPoolBase {
             unchecked { i++; }
         }
 
-        // Initialize the stabilized LMSR state with provided kappa
-        _lmsr.init(newQInternal, KAPPA);
+        // Initialize the stabilized LMSR state with provided fixed b
+        _lmsr.init(newQInternal, B_FIXED);
 
         // Compute actual LP _tokens to mint based on size metric (scaled)
         if( lpTokens != 0 )
@@ -288,7 +288,7 @@ contract PartyPoolMintImpl is PartyPoolBase {
 
         // Use LMSR view to determine actual internal consumed and size-increase (ΔS) for mint
         (int128 amountInInternalUsed, int128 sizeIncreaseInternal) =
-            LMSRStabilized.swapAmountsForMint(lmsrState.nAssets, lmsrState.kappa, lmsrState.qInternal,
+            LMSRStabilized.swapAmountsForMint(lmsrState.nAssets, lmsrState.bFixed, lmsrState.qInternal,
                 inputTokenIndex, netInternalGuess);
 
         // amountInInternalUsed may be <= netInternalGuess. Convert to uint (ceil) to determine actual transfer
@@ -456,7 +456,7 @@ contract PartyPoolMintImpl is PartyPoolBase {
             .mul(ABDKMath64x64.divu(1000000-swapFeePpm, 1000000)); // adjusted for fee
 
         // Use LMSR view to compute single-asset payout and burned size-metric
-        (int128 payoutInternal, ) = LMSRStabilized.swapAmountsForBurn(lmsrState.nAssets, lmsrState.kappa, lmsrState.qInternal,
+        (int128 payoutInternal, ) = LMSRStabilized.swapAmountsForBurn(lmsrState.nAssets, lmsrState.bFixed, lmsrState.qInternal,
             inputTokenIndex, alpha);
 
         // Convert payoutInternal -> uint (floor) to favor pool
diff --git a/src/PartyPoolSwapImpl.sol b/src/PartyPoolSwapImpl.sol
index cddbeb6..32afd3a 100644
--- a/src/PartyPoolSwapImpl.sol
+++ b/src/PartyPoolSwapImpl.sol
@@ -24,13 +24,13 @@ contract PartyPoolSwapImpl is PartyPoolBase {
         uint256 outputTokenIndex,
         int128 limitPrice,
         uint256[] memory bases,
-        int128 kappa,
+        int128 b,
         int128[] memory qInternal,
         uint256 swapFeePpm
     ) external pure returns (uint256 amountIn, uint256 amountOut, uint256 fee) {
         // Compute internal maxima at the price limit
         (int128 amountInInternal, int128 amountOutInternal) = LMSRStabilized.swapAmountsForPriceLimit(
-            bases.length, kappa, qInternal,
+            bases.length, b, qInternal,
             inputTokenIndex, outputTokenIndex, limitPrice);
 
         // Convert input to uint (ceil) and output to uint (floor)
diff --git a/src/PartyPoolViewer.sol b/src/PartyPoolViewer.sol
index 4cf2027..1063de8 100644
--- a/src/PartyPoolViewer.sol
+++ b/src/PartyPoolViewer.sol
@@ -35,7 +35,7 @@ contract PartyPoolViewer is PartyPoolHelpers, IPartyPoolViewer {
         LMSRStabilized.State memory lmsr = pool.LMSR();
         require(baseTokenIndex < lmsr.nAssets && quoteTokenIndex < lmsr.nAssets, "price: idx");
         require(lmsr.nAssets > 0, "price: uninit");
-        return LMSRStabilized.price(lmsr.nAssets, pool.kappa(), lmsr.qInternal, baseTokenIndex, quoteTokenIndex);
+        return LMSRStabilized.price(lmsr.nAssets, pool.bFixed(), lmsr.qInternal, baseTokenIndex, quoteTokenIndex);
     }
 
     /// @notice Price of one LP token denominated in `quote` as Q64.64.
@@ -50,7 +50,7 @@ contract PartyPoolViewer is PartyPoolHelpers, IPartyPoolViewer {
         require(quoteTokenIndex < lmsr.nAssets, "poolPrice: idx");
 
         // price per unit of qTotal (Q64.64) from LMSR
-        int128 pricePerQ = LMSRStabilized.poolPrice(lmsr.nAssets, pool.kappa(), lmsr.qInternal, quoteTokenIndex);
+        int128 pricePerQ = LMSRStabilized.poolPrice(lmsr.nAssets, pool.bFixed(), lmsr.qInternal, quoteTokenIndex);
 
         // total internal q (qTotal) as Q64.64
         int128 qTotal = LMSRStabilized._computeSizeMetric(lmsr.qInternal);
@@ -105,7 +105,7 @@ contract PartyPoolViewer is PartyPoolHelpers, IPartyPoolViewer {
 
         return SWAP_IMPL.swapToLimitAmounts(
             inputTokenIndex, outputTokenIndex, limitPrice,
-            pool.denominators(), pool.kappa(), lmsr.qInternal, pool.swapFeePpm());
+            pool.denominators(), pool.bFixed(), lmsr.qInternal, pool.swapFeePpm());
     }
 
 
diff --git a/test/GasTest.sol b/test/GasTest.sol
index a21bfef..e5b999e 100644
--- a/test/GasTest.sol
+++ b/test/GasTest.sol
@@ -114,6 +114,22 @@ contract GasTest is Test {
     uint256 constant internal INIT_BAL = 1_000_000; // initial token units for each token (internal==amount when base==1)
     uint256 constant internal BASE = 1; // use base=1 so internal amounts correspond to raw integers (Q64.64 units)
 
+    // Compute fixed b from a target slippage profile for a pool that will be initialized
+    // with numTokens tokens each deposited with INIT_BAL and BASE==1.
+    function _computeFixedB(uint256 numTokens) internal view returns (int128) {
+        // Size metric S = sum q_i (in 64.64) with q_i = INIT_BAL for each token (BASE == 1)
+        int128 S = ABDKMath64x64.fromUInt(numTokens * INIT_BAL);
+        // E = (1 - s*(n-1)) / (1 + s)
+        int128 one = ABDKMath64x64.fromInt(1);
+        int128 nMinus1 = ABDKMath64x64.fromUInt(numTokens - 1);
+        int128 numerator = one.sub(targetSlippage.mul(nMinus1));
+        int128 denominator = one.add(targetSlippage);
+        int128 E = numerator.div(denominator);
+        // y = -ln(E) / f, b = S / y
+        int128 y = ABDKMath64x64.ln(E).neg().div(tradeFrac);
+        return S.div(y);
+    }
+
     /// @notice Helper function to create a pool with the specified number of _tokens
     function createPool(uint256 numTokens) internal returns (PartyPool) {
         // Deploy _tokens dynamically
@@ -139,9 +155,9 @@ contract GasTest is Test {
         for (uint i = 0; i < tokens.length; i++) {
             ierc20Tokens[i] = IERC20(tokens[i]);
         }
-        // Compute kappa from slippage params and number of _tokens, then construct pool with kappa
-        int128 computedKappa = LMSRStabilized.computeKappaFromSlippage(ierc20Tokens.length, tradeFrac, targetSlippage);
-        PartyPool newPool = Deploy.newPartyPool(address(this), poolName, poolName, ierc20Tokens, bases, computedKappa, feePpm, feePpm, false);
+        // Compute fixed b from slippage and expected initial S, then construct pool with fixed b
+        int128 bFixed = _computeFixedB(ierc20Tokens.length);
+        PartyPool newPool = Deploy.newPartyPool(address(this), poolName, poolName, ierc20Tokens, bases, bFixed, feePpm, feePpm, false);
 
         // Transfer initial deposit amounts into pool before initial mint
         for (uint256 i = 0; i < numTokens; i++) {
@@ -180,8 +196,8 @@ contract GasTest is Test {
         for (uint i = 0; i < tokens.length; i++) {
             ierc20Tokens[i] = IERC20(tokens[i]);
         }
-        int128 computedKappa = LMSRStabilized.computeKappaFromSlippage(ierc20Tokens.length, tradeFrac, targetSlippage);
-        PartyPool newPool = Deploy.newPartyPool(address(this), poolName, poolName, ierc20Tokens, bases, computedKappa, feePpm, feePpm, true);
+        int128 bFixed = _computeFixedB(ierc20Tokens.length);
+        PartyPool newPool = Deploy.newPartyPool(address(this), poolName, poolName, ierc20Tokens, bases, bFixed, feePpm, feePpm, true);
 
         // Transfer initial deposit amounts into pool before initial mint
         for (uint256 i = 0; i < numTokens; i++) {
diff --git a/test/LMSRStabilized.t.sol b/test/LMSRStabilized.t.sol
index 5aec7e1..5269f91 100644
--- a/test/LMSRStabilized.t.sol
+++ b/test/LMSRStabilized.t.sol
@@ -30,7 +30,8 @@ contract LMSRStabilizedTest is Test {
         q[0] = ABDKMath64x64.fromUInt(1_000_000);
         q[1] = ABDKMath64x64.fromUInt(1_000_000);
         q[2] = ABDKMath64x64.fromUInt(1_000_000);
-        s.init(q, stdTradeSize, stdSlippage);
+        int128 b = _computeBFromSlippage(3, q, stdTradeSize, stdSlippage);
+        s.init(q, b);
     }
 
     function initAlmostBalanced() internal {
@@ -38,7 +39,8 @@ contract LMSRStabilizedTest is Test {
         q[0] = ABDKMath64x64.fromUInt(999_999);
         q[1] = ABDKMath64x64.fromUInt(1_000_000);
         q[2] = ABDKMath64x64.fromUInt(1_000_001);
-        s.init(q, stdTradeSize, stdSlippage);
+        int128 b = _computeBFromSlippage(3, q, stdTradeSize, stdSlippage);
+        s.init(q, b);
     }
 
     function initImbalanced() internal {
@@ -47,7 +49,8 @@ contract LMSRStabilizedTest is Test {
         q[1] = ABDKMath64x64.fromUInt(1e9);
         q[2] = ABDKMath64x64.fromUInt(1);
         q[3] = ABDKMath64x64.divu(1, 1e9);
-        s.init(q, stdTradeSize, stdSlippage);
+        int128 b = _computeBFromSlippage(4, q, stdTradeSize, stdSlippage);
+        s.init(q, b);
     }
 
 
@@ -193,7 +196,6 @@ contract LMSRStabilizedTest is Test {
 
         // Verify basic state is still functional
         assertTrue(s.nAssets > 0, "State should still be initialized");
-        assertTrue(s.kappa > int128(0), "Kappa should still be positive");
     }
 
     function testRescalingAfterDeposit() public {
@@ -211,7 +213,6 @@ contract LMSRStabilizedTest is Test {
 
         // Store initial parameters
         int128 initialB = _computeB(initialQ);
-        int128 initialKappa = s.kappa;
 
         // Simulate a deposit by increasing all asset quantities by 50%
         int128[] memory newQ = new int128[](s.nAssets);
@@ -223,18 +224,15 @@ contract LMSRStabilizedTest is Test {
         // Apply the update for proportional change
         s.updateForProportionalChange(newQ);
 
-        // Verify that b has been rescaled proportionally
+        // Verify that b remains constant after proportional deposit (fixed-b model)
         int128 newB = _computeB(s.qInternal);
-        int128 expectedRatio = ABDKMath64x64.fromUInt(3).div(ABDKMath64x64.fromUInt(2)); // 1.5x
+        int128 expectedRatio = ABDKMath64x64.fromInt(1); // invariant b
         int128 actualRatio = newB.div(initialB);
 
         int128 tolerance = ABDKMath64x64.divu(1, 1000); // 0.1% tolerance
-        assertTrue((actualRatio.sub(expectedRatio)).abs() < tolerance, "b did not scale proportionally after deposit");
+        assertTrue((actualRatio.sub(expectedRatio)).abs() < tolerance, "b should remain constant after deposit");
 
-        // Verify kappa remained unchanged
-        assertTrue((s.kappa.sub(initialKappa)).abs() < tolerance, "kappa should not change after deposit");
-
-        // Verify slippage target is still met by performing a trade
+        // Perform a trade and verify outputs are reasonable
         int128 tradeAmount = s.qInternal[0].mul(stdTradeSize);
         (int128 amountIn, int128 amountOut) = s.swapAmountsForExactInput(0, 1, tradeAmount, 0);
 
@@ -250,8 +248,10 @@ contract LMSRStabilizedTest is Test {
         int128 slippage = slippageRatio.sub(ABDKMath64x64.fromInt(1));
         console2.log('post-deposit slippage', slippage);
 
-        int128 relativeError = slippage.sub(stdSlippage).abs().div(stdSlippage);
-        assertLt(relativeError, ABDKMath64x64.divu(1, 100), "Slippage target not met after deposit");
+        // With fixed b, theoretical slippage is exp(a/b) - 1
+        int128 expectedSlippage = _exp(tradeAmount.div(newB)).sub(ABDKMath64x64.fromInt(1));
+        int128 slippageError = (slippage.sub(expectedSlippage)).abs();
+        assertLt(slippageError, ABDKMath64x64.divu(1, 1_000_000), "Observed slippage deviates from model");
     }
 
     /// @notice Test balanced2 handling of limitPrice that causes truncation of input a
@@ -260,7 +260,8 @@ contract LMSRStabilizedTest is Test {
         int128[] memory q = new int128[](2);
         q[0] = ABDKMath64x64.fromUInt(1_000_000);
         q[1] = ABDKMath64x64.fromUInt(1_000_000);
-        s.init(q, stdTradeSize, stdSlippage);
+        int128 bInit = _computeBFromSlippage(2, q, stdTradeSize, stdSlippage);
+        s.init(q, bInit);
 
         // Compute b for constructing meaningful a and limits
         int128 b = _computeB(q);
@@ -296,7 +297,8 @@ contract LMSRStabilizedTest is Test {
         int128[] memory q = new int128[](2);
         q[0] = ABDKMath64x64.fromUInt(1_000_000);
         q[1] = ABDKMath64x64.fromUInt(1_000_000);
-        s.init(q, stdTradeSize, stdSlippage);
+        int128 bInit = _computeBFromSlippage(2, q, stdTradeSize, stdSlippage);
+        s.init(q, bInit);
 
         // Small input a
         int128 a = q[0].mul(ABDKMath64x64.divu(1, 1000)); // 0.1% of asset
@@ -326,7 +328,8 @@ contract LMSRStabilizedTest is Test {
         int128[] memory q = new int128[](2);
         q[0] = ABDKMath64x64.fromUInt(1_000_000);
         q[1] = ABDKMath64x64.fromUInt(1_000_000);
-        s.init(q, stdTradeSize, stdSlippage);
+        int128 bInit = _computeBFromSlippage(2, q, stdTradeSize, stdSlippage);
+        s.init(q, bInit);
 
         int128 limitPrice = ABDKMath64x64.fromInt(1); // equal to current price
 
@@ -359,7 +362,6 @@ contract LMSRStabilizedTest is Test {
 
         // Store initial parameters
         int128 initialB = _computeB(initialQ);
-        int128 initialKappa = s.kappa;
 
         // Simulate a withdrawal by decreasing all asset quantities by 30%
         int128[] memory newQ = new int128[](s.nAssets);
@@ -371,18 +373,15 @@ contract LMSRStabilizedTest is Test {
         // Apply the update for proportional change
         s.updateForProportionalChange(newQ);
 
-        // Verify that b has been rescaled proportionally
+        // Verify that b remains constant after proportional withdrawal (fixed-b model)
         int128 newB = _computeB(s.qInternal);
-        int128 expectedRatio = ABDKMath64x64.fromUInt(7).div(ABDKMath64x64.fromUInt(10)); // 0.7x
+        int128 expectedRatio = ABDKMath64x64.fromInt(1); // invariant b
         int128 actualRatio = newB.div(initialB);
 
         int128 tolerance = ABDKMath64x64.divu(1, 1000); // 0.1% tolerance
-        assertTrue((actualRatio.sub(expectedRatio)).abs() < tolerance, "b did not scale proportionally after withdrawal");
+        assertTrue((actualRatio.sub(expectedRatio)).abs() < tolerance, "b should remain constant after withdrawal");
 
-        // Verify kappa remained unchanged
-        assertTrue((s.kappa.sub(initialKappa)).abs() < tolerance, "kappa should not change after withdrawal");
-
-        // Verify slippage target is still met by performing a trade
+        // Perform a trade and verify outputs are reasonable
         int128 tradeAmount = s.qInternal[0].mul(stdTradeSize);
         (int128 amountIn, int128 amountOut) = s.swapAmountsForExactInput(0, 1, tradeAmount, 0);
 
@@ -398,8 +397,10 @@ contract LMSRStabilizedTest is Test {
         int128 slippage = slippageRatio.sub(ABDKMath64x64.fromInt(1));
         console2.log('post-withdrawal slippage', slippage);
 
-        int128 relativeError = slippage.sub(stdSlippage).abs().div(stdSlippage);
-        assertLt(relativeError, ABDKMath64x64.divu(1, 100), "Slippage target not met after withdrawal");
+        // With fixed b, theoretical slippage is exp(a/b) - 1
+        int128 expectedSlippage = _exp(tradeAmount.div(newB)).sub(ABDKMath64x64.fromInt(1));
+        int128 slippageError = (slippage.sub(expectedSlippage)).abs();
+        assertLt(slippageError, ABDKMath64x64.divu(1, 1_000_000), "Observed slippage deviates from model");
     }
 
     // --- tests probing numerical stability and boundary conditions ---
@@ -431,8 +432,8 @@ contract LMSRStabilizedTest is Test {
         this.externalSwapAmountsForExactInput(0, 1, tradeAmount, ABDKMath64x64.fromInt(1));
     }
 
-    /// @notice If e_j == 0 we should revert early to avoid div-by-zero
-    function testEJZeroReverts() public {
+    /// @notice If q_j == 0, kernel should still handle computation without revert (wrapper enforces caps)
+    function testZeroQuantityOutputAssetDoesNotRevert() public {
         initBalanced();
 
         // Create mock qInternal where asset 1 has zero quantity
@@ -446,8 +447,10 @@ contract LMSRStabilizedTest is Test {
 
         int128 tradeAmount = mockQInternal[0].mul(stdTradeSize);
 
-        vm.expectRevert(bytes("LMSR: e_j==0"));
-        this.externalSwapAmountsForExactInput(0, 1, tradeAmount, 0);
+        // Should not revert; exact-input uses full input and returns a defined output
+        (int128 usedIn, int128 outAmt) = this.externalSwapAmountsForExactInput(0, 1, tradeAmount, 0);
+        assertEq(usedIn, tradeAmount, "exact-input should consume full input without limit");
+        assertTrue(outAmt >= 0, "output amount should be non-negative when q_j == 0");
     }
 
     /// @notice swapAmountsForPriceLimit returns zero if limit equals current price
@@ -534,18 +537,16 @@ contract LMSRStabilizedTest is Test {
         this.externalSwapAmountsForExactInput(0, 1, a, 0);
     }
 
-    // Helper function to compute b from qInternal (either from provided array or state)
+    // Helper function to fetch fixed b (independent of qInternal)
     function _computeB(int128[] memory qInternal) internal view returns (int128) {
-        int128 sizeMetric = _computeSizeMetric(qInternal);
-        require(sizeMetric > int128(0), "LMSR: size metric zero");
-        return s.kappa.mul(sizeMetric);
+        // silence unused warning for qInternal in tests
+        qInternal;
+        return s.bFixed;
     }
 
-    // Overload that uses state's cached qInternal
+    // Overload that uses state's fixed b
     function _computeB() internal view returns (int128) {
-        int128 sizeMetric = _computeSizeMetric(s.qInternal);
-        require(sizeMetric > int128(0), "LMSR: size metric zero");
-        return s.kappa.mul(sizeMetric);
+        return s.bFixed;
     }
 
     // Helper function to compute size metric (sum of all asset quantities)
@@ -558,6 +559,41 @@ contract LMSRStabilizedTest is Test {
         return total;
     }
 
+    // Local helper: compute fixed b from a target slippage profile.
+    // For a trade of fraction f of S with target slippage s across n assets:
+    //   E = (1 - s*(n-1)) / (1 + s)
+    //   y = -ln(E) / f
+    //   b = S / y
+    function _computeBFromSlippage(
+        uint256 nAssets,
+        int128[] memory qInternal,
+        int128 tradeFrac,
+        int128 targetSlippage
+    ) internal pure returns (int128) {
+        require(nAssets > 1, "test: n>1");
+        int128 S = _computeSizeMetric(qInternal);
+        require(S > int128(0), "test: S<=0");
+
+        int128 f = tradeFrac;
+        require(f > int128(0) && f < ABDKMath64x64.fromInt(1), "test: f out of range");
+
+        int128 one = ABDKMath64x64.fromInt(1);
+        int128 nMinus1 = ABDKMath64x64.fromUInt(nAssets - 1);
+
+        // E must be in (0,1)
+        int128 numerator = one.sub(targetSlippage.mul(nMinus1)); // 1 - s*(n-1)
+        int128 denominator = one.add(targetSlippage);            // 1 + s
+        require(numerator > int128(0), "test: bad slippage");
+
+        int128 E = numerator.div(denominator);
+        require(E > int128(0) && E < one, "test: E out of range");
+
+        int128 y = ABDKMath64x64.ln(E).neg().div(f);
+        require(y > int128(0), "test: y<=0");
+
+        return S.div(y);
+    }
+
     // Helper function to update the state's cached qInternal
     function _updateCachedQInternal(int128[] memory mockQInternal) internal {
         // First ensure qInternal array exists with the right size
@@ -955,7 +991,8 @@ contract LMSRStabilizedTest is Test {
         int128[] memory q = new int128[](2);
         q[0] = ABDKMath64x64.fromUInt(1_000_000);
         q[1] = ABDKMath64x64.fromUInt(1_000_000);
-        s.init(q, stdTradeSize, stdSlippage);
+        int128 bInit = _computeBFromSlippage(2, q, stdTradeSize, stdSlippage);
+        s.init(q, bInit);
 
         // Small trade (well within u <= 0.5 and delta <= 1%)
         int128 a = q[0].mul(ABDKMath64x64.divu(1, 1000)); // 0.1% of asset
@@ -986,7 +1023,8 @@ contract LMSRStabilizedTest is Test {
         int128[] memory q = new int128[](2);
         q[0] = ABDKMath64x64.fromUInt(1_000_000);
         q[1] = ABDKMath64x64.fromUInt(1_000_000);
-        s.init(q, stdTradeSize, stdSlippage);
+        int128 bInit = _computeBFromSlippage(2, q, stdTradeSize, stdSlippage);
+        s.init(q, bInit);
 
         // Prepare newQ starting from equal quantities; we'll grow q0 until delta > DELTA_MAX
         int128[] memory newQ = new int128[](2);
@@ -1045,7 +1083,8 @@ contract LMSRStabilizedTest is Test {
         int128[] memory q = new int128[](2);
         q[0] = ABDKMath64x64.fromUInt(1_000_000);
         q[1] = ABDKMath64x64.fromUInt(1_000_000);
-        s.init(q, stdTradeSize, stdSlippage);
+        int128 bInit = _computeBFromSlippage(2, q, stdTradeSize, stdSlippage);
+        s.init(q, bInit);
 
         // Compute b
         int128 b = _computeB(q);
diff --git a/test/NativeTest.t.sol b/test/NativeTest.t.sol
index 5d691e9..5a43a2a 100644
--- a/test/NativeTest.t.sol
+++ b/test/NativeTest.t.sol
@@ -53,6 +53,18 @@ contract NativeTest is Test {
     uint256 constant INIT_BAL = 1_000_000; // initial token units for each token
     uint256 constant BASE = 1; // use base=1 so internal amounts correspond to raw integers
 
+    // Compute fixed b for a pool initialized with numTokens tokens, each deposited with INIT_BAL (BASE == 1).
+    function _computeFixedB(uint256 numTokens) internal view returns (int128) {
+        int128 S = ABDKMath64x64.fromUInt(numTokens * INIT_BAL);
+        int128 one = ABDKMath64x64.fromInt(1);
+        int128 nMinus1 = ABDKMath64x64.fromUInt(numTokens - 1);
+        int128 numerator = one.sub(targetSlippage.mul(nMinus1));
+        int128 denominator = one.add(targetSlippage);
+        int128 E = numerator.div(denominator);
+        int128 y = ABDKMath64x64.ln(E).neg().div(tradeFrac);
+        return S.div(y);
+    }
+
     function setUp() public {
         alice = address(0xA11ce);
         bob = address(0xB0b);
@@ -93,8 +105,8 @@ contract NativeTest is Test {
         // Deploy pool with a small fee (0.1%)
         uint256 feePpm = 1000;
 
-        int128 kappa = LMSRStabilized.computeKappaFromSlippage(tokens.length, tradeFrac, targetSlippage);
-        pool = Deploy.newPartyPool(address(this), "LP", "LP", tokens, bases, kappa, feePpm, feePpm, weth, false);
+        int128 bFixed = _computeFixedB(tokens.length);
+        pool = Deploy.newPartyPool(address(this), "LP", "LP", tokens, bases, bFixed, feePpm, feePpm, weth, false);
 
         // Transfer initial deposit amounts into pool
         token0.transfer(address(pool), INIT_BAL);
diff --git a/test/PartyPlanner.t.sol b/test/PartyPlanner.t.sol
index d901450..670d265 100644
--- a/test/PartyPlanner.t.sol
+++ b/test/PartyPlanner.t.sol
@@ -15,6 +15,7 @@ import {LMSRStabilized} from "../src/LMSRStabilized.sol";
 import {PartyPlanner} from "../src/PartyPlanner.sol";
 import {PartyPool} from "../src/PartyPool.sol";
 import {MockERC20} from "./PartyPlanner.t.sol";
+import "@abdk/ABDKMath64x64.sol";
 
 // Mock ERC20 token for testing
 contract MockERC20 is ERC20 {
@@ -34,11 +35,37 @@ contract MockERC20 is ERC20 {
 }
 
 contract PartyPlannerTest is Test {
+    using ABDKMath64x64 for int128;
+
     PartyPlanner public planner;
     MockERC20 public tokenA;
     MockERC20 public tokenB;
     MockERC20 public tokenC;
 
+    function _computeFixedBFromDeposits(
+        uint256 nAssets,
+        uint256[] memory bases,
+        uint256[] memory initialDeposits,
+        int128 tradeFrac,
+        int128 targetSlippage
+    ) internal pure returns (int128) {
+        require(bases.length == initialDeposits.length && bases.length == nAssets, "length mismatch");
+        // Compute S = sum(deposit_i / base_i) in Q64.64
+        int128 S = 0;
+        for (uint256 i = 0; i < nAssets; i++) {
+            S = S + ABDKMath64x64.divu(initialDeposits[i], bases[i]);
+        }
+        // E = (1 - s*(n-1)) / (1 + s)
+        int128 one = ABDKMath64x64.fromInt(1);
+        int128 nMinus1 = ABDKMath64x64.fromUInt(nAssets - 1);
+        int128 numerator = one.sub(targetSlippage.mul(nMinus1));
+        int128 denominator = one.add(targetSlippage);
+        int128 E = numerator.div(denominator);
+        // y = -ln(E) / f, b = S / y
+        int128 y = ABDKMath64x64.ln(E).neg().div(tradeFrac);
+        return S.div(y);
+    }
+
     address public payer = makeAddr("payer");
     address public receiver = makeAddr("receiver");
 
@@ -93,15 +120,15 @@ contract PartyPlannerTest is Test {
         uint256 initialTokenACount = planner.poolsByTokenCount(IERC20(address(tokenA)));
         uint256 initialTokenBCount = planner.poolsByTokenCount(IERC20(address(tokenB)));
 
-        // Compute kappa then create pool via kappa overload
-        int128 computedKappa = LMSRStabilized.computeKappaFromSlippage(tokens.length, tradeFrac, targetSlippage);
+        // Compute fixed b from slippage and initial deposits, then create pool
+        int128 bFixed = _computeFixedBFromDeposits(tokens.length, bases, initialDeposits, tradeFrac, targetSlippage);
 
         (IPartyPool pool, uint256 lpAmount) = planner.newPool(
             name,
             symbol,
             tokens,
             bases,
-            computedKappa,
+            bFixed,
             swapFeePpm,
             flashFeePpm,
             false, // not stable
@@ -174,10 +201,10 @@ contract PartyPlannerTest is Test {
         deposits1[0] = INITIAL_DEPOSIT_AMOUNT;
         deposits1[1] = INITIAL_DEPOSIT_AMOUNT;
 
-        int128 kappa1 = LMSRStabilized.computeKappaFromSlippage(tokens1.length, int128((1 << 64) - 1), int128(1 << 62));
+        int128 b1 = _computeFixedBFromDeposits(tokens1.length, bases1, deposits1, int128((1 << 64) - 1), int128(1 << 62));
         (IPartyPool pool1,) = planner.newPool(
             "Pool 1", "LP1", tokens1, bases1,
-            kappa1, 3000, 5000, false,
+            b1, 3000, 5000, false,
             payer, receiver, deposits1, 1000e18, 0
         );
 
@@ -194,10 +221,10 @@ contract PartyPlannerTest is Test {
         deposits2[0] = INITIAL_DEPOSIT_AMOUNT;
         deposits2[1] = INITIAL_DEPOSIT_AMOUNT / 1e12; // Adjust for 6 decimals
 
-        int128 kappa2 = LMSRStabilized.computeKappaFromSlippage(tokens2.length, int128((1 << 64) - 1), int128(1 << 62));
+        int128 b2 = _computeFixedBFromDeposits(tokens2.length, bases2, deposits2, int128((1 << 64) - 1), int128(1 << 62));
         (IPartyPool pool2,) = planner.newPool(
             "Pool 2", "LP2", tokens2, bases2,
-            kappa2, 3000, 5000, false,
+            b2, 3000, 5000, false,
             payer, receiver, deposits2, 1000e18, 0
         );
 
@@ -250,12 +277,12 @@ contract PartyPlannerTest is Test {
         validDeposits[0] = INITIAL_DEPOSIT_AMOUNT;
         validDeposits[1] = INITIAL_DEPOSIT_AMOUNT;
 
-        int128 kappaErr = LMSRStabilized.computeKappaFromSlippage(tokens.length, int128((1 << 64) - 1), int128(1 << 62));
+        int128 bErr = _computeFixedBFromDeposits(tokens.length, bases, validDeposits, int128((1 << 64) - 1), int128(1 << 62));
 
         vm.expectRevert("Planner: payer cannot be zero address");
         planner.newPool(
             "Test Pool", "TESTLP", tokens, bases,
-            kappaErr, 3000, 5000, false,
+            bErr, 3000, 5000, false,
             address(0), receiver, validDeposits, 1000e18, 0
         );
 
@@ -263,18 +290,18 @@ contract PartyPlannerTest is Test {
         vm.expectRevert("Planner: receiver cannot be zero address");
         planner.newPool(
             "Test Pool", "TESTLP", tokens, bases,
-            kappaErr, 3000, 5000, false,
+            bErr, 3000, 5000, false,
             payer, address(0), validDeposits, 1000e18, 0
         );
 
         // Test deadline exceeded
         // The default timestamp is 1 and 1-0 is 0 which means "ignore deadline," so we need to set a proper timestamp.
-        int128 kappaDeadline = LMSRStabilized.computeKappaFromSlippage(tokens.length, int128((1 << 64) - 1), int128(1 << 62));
+        int128 bDeadline = _computeFixedBFromDeposits(tokens.length, bases, validDeposits, int128((1 << 64) - 1), int128(1 << 62));
         vm.warp(1000);
         vm.expectRevert("Planner: deadline exceeded");
         planner.newPool(
             "Test Pool", "TESTLP", tokens, bases,
-            kappaDeadline, 3000, 5000, false,
+            bDeadline, 3000, 5000, false,
             payer, receiver, validDeposits, 1000e18, block.timestamp - 1
         );
     }
@@ -297,12 +324,12 @@ contract PartyPlannerTest is Test {
             deposits[0] = INITIAL_DEPOSIT_AMOUNT;
             deposits[1] = INITIAL_DEPOSIT_AMOUNT;
 
-            int128 kappaLoop = LMSRStabilized.computeKappaFromSlippage(tokens.length, int128((1 << 64) - 1), int128(1 << 62));
+            int128 bLoop = _computeFixedBFromDeposits(tokens.length, bases, deposits, int128((1 << 64) - 1), int128(1 << 62));
             (IPartyPool pool,) = planner.newPool(
                 string(abi.encodePacked("Pool ", vm.toString(i))),
                 string(abi.encodePacked("LP", vm.toString(i))),
                 tokens, bases,
-                kappaLoop, 3000, 5000, false,
+                bLoop, 3000, 5000, false,
                 payer, receiver, deposits, 1000e18, 0
             );
 
diff --git a/test/PartyPool.t.sol b/test/PartyPool.t.sol
index 628928a..ff19e10 100644
--- a/test/PartyPool.t.sol
+++ b/test/PartyPool.t.sol
@@ -125,6 +125,18 @@ contract PartyPoolTest is Test {
     uint256 constant INIT_BAL = 1_000_000; // initial token units for each token (internal==amount when base==1)
     uint256 constant BASE = 1; // use base=1 so internal amounts correspond to raw integers (Q64.64 units)
 
+    // Compute fixed b for a pool initialized with numTokens tokens, each deposited with INIT_BAL (BASE == 1).
+    function _computeFixedB(uint256 numTokens) internal view returns (int128) {
+        int128 S = ABDKMath64x64.fromUInt(numTokens * INIT_BAL);
+        int128 one = ABDKMath64x64.fromInt(1);
+        int128 nMinus1 = ABDKMath64x64.fromUInt(numTokens - 1);
+        int128 numerator = one.sub(targetSlippage.mul(nMinus1));
+        int128 denominator = one.add(targetSlippage);
+        int128 E = numerator.div(denominator);
+        int128 y = ABDKMath64x64.ln(E).neg().div(tradeFrac);
+        return S.div(y);
+    }
+
     function setUp() public {
         planner = Deploy.newPartyPlanner();
         alice = address(0xA11ce);
@@ -172,8 +184,8 @@ contract PartyPoolTest is Test {
         // Deploy pool with a small fee to test fee-handling paths (use 1000 ppm = 0.1%)
         uint256 feePpm = 1000;
 
-        int128 kappa3 = LMSRStabilized.computeKappaFromSlippage(tokens.length, tradeFrac, targetSlippage);
-        pool = Deploy.newPartyPool(address(this), "LP", "LP", tokens, bases, kappa3, feePpm, feePpm, false);
+        int128 b3 = _computeFixedB(tokens.length);
+        pool = Deploy.newPartyPool(address(this), "LP", "LP", tokens, bases, b3, feePpm, feePpm, false);
 
         // Transfer initial deposit amounts into pool before initial mint (pool expects _tokens already in contract)
         // We deposit equal amounts INIT_BAL for each token
@@ -202,8 +214,8 @@ contract PartyPoolTest is Test {
             bases10[i] = BASE;
         }
 
-        int128 kappa10 = LMSRStabilized.computeKappaFromSlippage(tokens10.length, tradeFrac, targetSlippage);
-        pool10 = Deploy.newPartyPool(address(this), "LP10", "LP10", tokens10, bases10, kappa10, feePpm, feePpm, false);
+        int128 b10 = _computeFixedB(tokens10.length);
+        pool10 = Deploy.newPartyPool(address(this), "LP10", "LP10", tokens10, bases10, b10, feePpm, feePpm, false);
 
         // Mint additional _tokens for pool10 initial deposit
         token0.mint(address(this), INIT_BAL);
@@ -991,12 +1003,12 @@ contract PartyPoolTest is Test {
         uint256 feePpm = 1000;
 
         // Pool with default initialization (lpTokens = 0)
-        int128 kappaDefault = LMSRStabilized.computeKappaFromSlippage(tokens.length, tradeFrac, targetSlippage);
-        PartyPool poolDefault = Deploy.newPartyPool(address(this), "LP_DEFAULT", "LP_DEFAULT", tokens, bases, kappaDefault, feePpm, feePpm, false);
+        int128 bDefault = _computeFixedB(tokens.length);
+        PartyPool poolDefault = Deploy.newPartyPool(address(this), "LP_DEFAULT", "LP_DEFAULT", tokens, bases, bDefault, feePpm, feePpm, false);
 
         // Pool with custom initialization (lpTokens = custom amount)
-        int128 kappaCustom = LMSRStabilized.computeKappaFromSlippage(tokens.length, tradeFrac, targetSlippage);
-        PartyPool poolCustom = Deploy.newPartyPool(address(this), "LP_CUSTOM", "LP_CUSTOM", tokens, bases, kappaCustom, feePpm, feePpm, false);
+        int128 bCustom = _computeFixedB(tokens.length);
+        PartyPool poolCustom = Deploy.newPartyPool(address(this), "LP_CUSTOM", "LP_CUSTOM", tokens, bases, bCustom, feePpm, feePpm, false);
 
         // Mint additional _tokens for both pools
         token0.mint(address(this), INIT_BAL * 2);
@@ -1067,10 +1079,10 @@ contract PartyPoolTest is Test {
 
         uint256 feePpm = 1000;
 
-        int128 kappaDefault2 = LMSRStabilized.computeKappaFromSlippage(tokens.length, tradeFrac, targetSlippage);
-        PartyPool poolDefault = Deploy.newPartyPool(address(this), "LP_DEFAULT", "LP_DEFAULT", tokens, bases, kappaDefault2, feePpm, feePpm, false);
-        int128 kappaCustom2 = LMSRStabilized.computeKappaFromSlippage(tokens.length, tradeFrac, targetSlippage);
-        PartyPool poolCustom = Deploy.newPartyPool(address(this), "LP_CUSTOM", "LP_CUSTOM", tokens, bases, kappaCustom2, feePpm, feePpm, false);
+        int128 bDefault2 = _computeFixedB(tokens.length);
+        PartyPool poolDefault = Deploy.newPartyPool(address(this), "LP_DEFAULT", "LP_DEFAULT", tokens, bases, bDefault2, feePpm, feePpm, false);
+        int128 bCustom2 = _computeFixedB(tokens.length);
+        PartyPool poolCustom = Deploy.newPartyPool(address(this), "LP_CUSTOM", "LP_CUSTOM", tokens, bases, bCustom2, feePpm, feePpm, false);
 
         // Mint additional _tokens
         token0.mint(address(this), INIT_BAL * 4);