diff --git a/Directory.Build.props b/Directory.Build.props
index 7ed6fb6e8..190e89780 100644
--- a/Directory.Build.props
+++ b/Directory.Build.props
@@ -6,8 +6,8 @@
     <CultLibRevision>45c2f4006f5f7dab357426cabd3197e8d0a17f66</CultLibRevision>
     <CultMathRoot Condition="'$(CultMathRoot)' == '' and '$(CULTMATH_ROOT)' != ''">$(CULTMATH_ROOT)</CultMathRoot>
     <CultMathRoot Condition="'$(CultMathRoot)' == ''">$(CultLibRoot)</CultMathRoot>
-    <!-- CultMath: cultmath-unity-v0.4.0 in Packages/manifest.json. -->
-    <CultMathRevision>252e226c51826d626f4113673f31d96577b67ec9</CultMathRevision>
+    <!-- CultMath: cultmath-unity-v0.4.1 in Packages/manifest.json. -->
+    <CultMathRevision>9c1b06cd703bfa44352050e819b0d0659cf5978a</CultMathRevision>
     <GitExecutable Condition="'$(GitExecutable)' == '' and Exists('C:\Program Files\Git\cmd\git.exe')">C:\Program Files\Git\cmd\git.exe</GitExecutable>
     <GitExecutable Condition="'$(GitExecutable)' == ''">git</GitExecutable>
   </PropertyGroup>
diff --git a/Packages/manifest.json b/Packages/manifest.json
index a04f36e20..2dd2a3bb3 100644
--- a/Packages/manifest.json
+++ b/Packages/manifest.json
@@ -54,6 +54,6 @@
     "com.unity.modules.xr": "1.0.0",
     "org.gamecult.caching.unity": "https://github.com/GameCult/CultLib.git?path=/src/GameCult.Unity/Assets/Caching#caching-unity-v1.4.0",
     "org.gamecult.cultlib": "https://github.com/GameCult/CultLib.git?path=/unity/org.gamecult.cultlib#cultlib-unity-v1.0.60",
-    "org.gamecult.cultmath": "https://github.com/GameCult/CultLib.git?path=/packages/cultmath/unity/org.gamecult.cultmath#cultmath-unity-v0.4.0"
+    "org.gamecult.cultmath": "https://github.com/GameCult/CultLib.git?path=/packages/cultmath/unity/org.gamecult.cultmath#cultmath-unity-v0.4.1"
   }
 }
diff --git a/Packages/packages-lock.json b/Packages/packages-lock.json
index f4c128708..5d26bd587 100644
--- a/Packages/packages-lock.json
+++ b/Packages/packages-lock.json
@@ -272,11 +272,11 @@
       "hash": "45c2f4006f5f7dab357426cabd3197e8d0a17f66"
     },
     "org.gamecult.cultmath": {
-      "version": "https://github.com/GameCult/CultLib.git?path=/packages/cultmath/unity/org.gamecult.cultmath#cultmath-unity-v0.4.0",
+      "version": "https://github.com/GameCult/CultLib.git?path=/packages/cultmath/unity/org.gamecult.cultmath#cultmath-unity-v0.4.1",
       "depth": 0,
       "source": "git",
       "dependencies": {},
-      "hash": "252e226c51826d626f4113673f31d96577b67ec9"
+      "hash": "9c1b06cd703bfa44352050e819b0d0659cf5978a"
     },
     "com.unity.modules.accessibility": {
       "version": "1.0.0",
diff --git a/tests/Aetheria.Shared.Tests/ThrustAllocatorTests.cs b/tests/Aetheria.Shared.Tests/ThrustAllocatorTests.cs
index 7e36f5569..228b2e630 100644
--- a/tests/Aetheria.Shared.Tests/ThrustAllocatorTests.cs
+++ b/tests/Aetheria.Shared.Tests/ThrustAllocatorTests.cs
@@ -265,6 +265,39 @@ public class ThrustAllocatorTests
         }
     }
 
+    // A cruiser-like hull, n thrusters each pushing along one body axis with a lever-arm yaw (the finding's fixture
+    // generator: Synthetic(8, 7005)).
+    static float3[] Synthetic(int n, int seed)
+    {
+        var rng = new System.Random(seed);
+        var cols = new float3[n];
+        for (var i = 0; i < n; i++)
+        {
+            var a = 20f + 40f * (float)rng.NextDouble();
+            var yaw = (float)(rng.NextDouble() * 2 - 1) * 120f;
+            var dir = rng.Next(10);
+            cols[i] = dir < 4 ? Col(0, a, yaw) : dir < 6 ? Col(0, -a, yaw) : dir < 8 ? Col(a, 0, yaw) : Col(-a, 0, yaw);
+        }
+        return cols;
+    }
+
+    // Finding solver-converged-early: on this hull a fresh allocator's eighth intent of a seeded random walk stopped at a
+    // non-optimal point (throttle 7 at 1.0 against .922 warm). The answer is the same from a cold and from a warm start.
+    [Fact]
+    public void ColdAndWarmStartsAgreeOnTheHullThatStoppedEarly()
+    {
+        var hull = Synthetic(8, 7005);
+        var rng = new System.Random(5);
+        var warm = new ThrustAllocator();
+        for (var step = 0; step < 8; step++)
+        {
+            float x = (float)rng.NextDouble() * 2 - 1, y = (float)rng.NextDouble() * 2 - 1, turn = (float)rng.NextDouble() * 2 - 1;
+            var fromWarm = Solve(warm, hull, x, y, turn);
+            var fromCold = Solve(hull, x, y, turn);
+            for (var i = 0; i < hull.Length; i++) Assert.True(MathF.Abs(fromWarm[i] - fromCold[i]) <= 1e-5f, $"step {step}: throttle {i} {fromCold[i]} cold vs {fromWarm[i]} warm");
+        }
+    }
+
     [Fact]
     public void EqualThrustersShareTheDemand()
     {