diff --git a/Assets/Scripts/ServerShared/ThrustAllocator.cs b/Assets/Scripts/ServerShared/ThrustAllocator.cs
new file mode 100644
index 000000000..09b37aebf
--- /dev/null
+++ b/Assets/Scripts/ServerShared/ThrustAllocator.cs
@@ -0,0 +1,99 @@
+/* This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at https://mozilla.org/MPL/2.0/. */
+
+using System;
+using CultMath;
+
+/// <summary>
+/// Turns intent (which way to go, which way to turn) into every thruster's throttle, whatever the thrusters' actual
+/// strength and position. One per ship. A column is one thruster's effect per unit throttle: x starboard acceleration,
+/// y forward acceleration, z clockwise yaw rate in rad/s. Throttles are bounded to [0,1].
+///
+/// One <see cref="BoundedLeastSquares"/> solve per call over the n throttles and four error variables (the unwanted or
+/// missing translation on each half-axis, paid for linearly). Yaw is a heavily weighted row, so a hold is exact and a
+/// turn is served first; the linear translation cost means the actuator with the least translation per unit of turn
+/// serves first and the next joins only as it saturates. Nothing classifies a column as attitude or drive: the onset
+/// at which a second actuator joins a turn falls out of the columns.
+/// </summary>
+public sealed class ThrustAllocator
+{
+    const float TranslationWeight = 100f;
+    const float YawWeight = 1000f;
+    const float ErrorCostWeight = .3f;
+    const float ErrorCostOffset = 10f;
+    const float Ridge = .1f;
+    const float ErrorMax = 2f;
+    const double KktRelativeTolerance = 1e-12;
+    const int ErrorVariables = 4;
+    const int FixedRows = 3 + ErrorVariables;
+
+    int _columns = -1;
+    float[] _a, _b, _lo, _hi, _x, _workspace;
+
+    public void Allocate(ReadOnlySpan<float3> columns, float2 move, float turn, Span<float> throttle)
+    {
+        var n = columns.Length;
+        if (n != _columns) Resize(n);
+        for (var i = 0; i < n; i++) throttle[i] = 0;
+
+        var vars = n + ErrorVariables;
+        var rows = FixedRows + n;
+        Array.Clear(_a, 0, rows * vars);
+        Array.Clear(_b, 0, rows);
+
+        // Rows 0 and 1 are the translation axes (starboard, forward), row 2 the yaw.
+        for (var axis = 0; axis < 3; axis++)
+        {
+            float plus = 0, minus = 0;
+            for (var i = 0; i < n; i++)
+            {
+                var c = Component(columns[i], axis);
+                if (c > 0) plus += c;
+                else if (c < 0) minus -= c;
+            }
+            var extreme = Math.Max(plus, minus);
+            var intent = Math.Min(Math.Max(axis == 0 ? move.x : axis == 1 ? move.y : turn, -1f), 1f);
+            var weight = axis == 2 ? YawWeight : TranslationWeight;
+            // Intent is a fraction of the half-axis extreme it points into.
+            var demand = intent >= 0 ? intent * plus : intent * minus;
+            var scale = extreme > 0 ? weight / extreme : 0f;
+            var row = axis * vars;
+            for (var i = 0; i < n; i++) _a[row + i] = Component(columns[i], axis) * scale;
+            _b[axis] = demand * scale;
+            if (axis < 2 && extreme > 0)
+            {
+                _a[row + n + 2 * axis] = -weight;
+                _a[row + n + 2 * axis + 1] = weight;
+            }
+        }
+
+        // A linear cost on each error variable, as w*e = -w*kappa, and a ridge on each throttle.
+        for (var k = 0; k < ErrorVariables; k++)
+        {
+            _a[(3 + k) * vars + n + k] = ErrorCostWeight;
+            _b[3 + k] = -ErrorCostWeight * ErrorCostOffset;
+        }
+        for (var i = 0; i < n; i++) _a[(FixedRows + i) * vars + i] = Ridge;
+
+        var status = BoundedLeastSquares.Solve(rows, vars, _a, _b, _lo, _hi, _x, _workspace, out _, KktRelativeTolerance);
+        if (status == BoundedLeastSquaresStatus.InvalidInput) return;
+        for (var i = 0; i < n; i++) throttle[i] = _x[i];
+    }
+
+    static float Component(float3 c, int axis) => axis == 0 ? c.x : axis == 1 ? c.y : c.z;
+
+    void Resize(int n)
+    {
+        _columns = n;
+        var vars = n + ErrorVariables;
+        var rows = FixedRows + n;
+        _a = new float[rows * vars];
+        _b = new float[rows];
+        _lo = new float[vars];
+        _hi = new float[vars];
+        _x = new float[vars];
+        _workspace = new float[BoundedLeastSquares.WorkspaceLength(vars)];
+        for (var i = 0; i < vars; i++) _hi[i] = i < n ? 1f : ErrorMax;
+    }
+}
diff --git a/Assets/Scripts/ServerShared/ThrustAllocator.cs.meta b/Assets/Scripts/ServerShared/ThrustAllocator.cs.meta
new file mode 100644
index 000000000..d7b82c1b3
--- /dev/null
+++ b/Assets/Scripts/ServerShared/ThrustAllocator.cs.meta
@@ -0,0 +1,11 @@
+fileFormatVersion: 2
+guid: 5b0e3f7a9c2d4e61a8f4d3c7b1e90a26
+MonoImporter:
+  externalObjects: {}
+  serializedVersion: 2
+  defaultReferences: []
+  executionOrder: 0
+  icon: {instanceID: 0}
+  userData: 
+  assetBundleName: 
+  assetBundleVariant: 
diff --git a/tests/Aetheria.Shared.Tests/ThrustAllocatorTests.cs b/tests/Aetheria.Shared.Tests/ThrustAllocatorTests.cs
new file mode 100644
index 000000000..b12c077f9
--- /dev/null
+++ b/tests/Aetheria.Shared.Tests/ThrustAllocatorTests.cs
@@ -0,0 +1,281 @@
+using System;
+using System.Collections.Generic;
+using CultMath;
+using Xunit;
+
+namespace Aetheria.Shared.Tests;
+
+// ThrustAllocator on synthetic columns. A column is (starboard m/s^2, forward m/s^2, clockwise yaw rad/s) per unit
+// throttle; the fixtures are written in deg/s the way the probes measured them (map TA3, TA12).
+public class ThrustAllocatorTests
+{
+    const float Deg = MathF.PI / 180f;
+
+    static float3 Col(float starboard, float forward, float yawDeg) => new(starboard, forward, yawDeg * Deg);
+
+    // TA3, the Duel Longinus: two mismatched drives (0, 1) and two Talarias (2 clockwise, 3 counter-clockwise).
+    static float3[] Duel() => new[]
+    {
+        Col(0, 53.94f, 49.24f), Col(0, 61.19f, -55.86f), Col(29.08f, 0, 166.26f), Col(-21.80f, 0, -124.63f),
+    };
+
+    // The clockwise Talaria lost.
+    static float3[] DamagedDuel() => new[]
+    {
+        Col(0, 53.94f, 49.24f), Col(0, 61.19f, -55.86f), default, Col(-21.80f, 0, -124.63f),
+    };
+
+    // TA12's symmetric hull: mains, fore and aft laterals in torque-free pairs, a bow thruster.
+    static float3[] Symmetric() => new[]
+    {
+        Col(0, 50, 20), Col(0, 50, -20), Col(20, 0, 80), Col(-20, 0, -80), Col(20, 0, -60), Col(-20, 0, 60), Col(0, -30, 0),
+    };
+
+    // The hull's half-axis extremes, from the definition: the sum of a row's positive entries, or of the negated
+    // negative ones. Axis 0 starboard, 1 forward, 2 clockwise yaw.
+    static (float plus, float minus) Extremes(float3[] columns, int axis)
+    {
+        float plus = 0, minus = 0;
+        foreach (var c in columns)
+        {
+            var v = axis == 0 ? c.x : axis == 1 ? c.y : c.z;
+            if (v > 0) plus += v; else minus -= v;
+        }
+        return (plus, minus);
+    }
+
+    static float3 Net(float3[] columns, float[] throttle)
+    {
+        float3 net = default;
+        for (var i = 0; i < columns.Length; i++) net += columns[i] * throttle[i];
+        return net;
+    }
+
+    static float[] Solve(ThrustAllocator allocator, float3[] columns, float moveX, float moveY, float turn)
+    {
+        var throttle = new float[columns.Length];
+        allocator.Allocate(columns, new float2(moveX, moveY), turn, throttle);
+        return throttle;
+    }
+
+    static float[] Solve(float3[] columns, float moveX, float moveY, float turn) => Solve(new ThrustAllocator(), columns, moveX, moveY, turn);
+
+    static float YawDeg(float3[] columns, float[] throttle) => Net(columns, throttle).z / Deg;
+
+    [Fact]
+    public void AHoldIsExactWithMismatchedDrives()
+    {
+        var duel = Duel();
+        var throttle = Solve(duel, 0, 1, 0);
+        var clockwise = Extremes(duel, 2).plus;
+        var net = Net(duel, throttle);
+        Assert.True(MathF.Abs(net.z) <= 1e-5f * clockwise, $"yaw {net.z / Deg} deg/s");
+        Assert.True(net.y >= .99f * Extremes(duel, 1).plus, $"forward {net.y}");
+    }
+
+    [Theory]
+    [InlineData(0)]
+    [InlineData(1)]
+    public void ALostDriveIsBalancedByWhatIsLeft(int zeroed)
+    {
+        var columns = Duel();
+        var extreme = Extremes(columns, 2).plus;
+        columns[zeroed] = default;
+        var throttle = Solve(columns, 0, 1, 0);
+        var net = Net(columns, throttle);
+        Assert.True(MathF.Abs(net.z) <= 1e-5f * extreme, $"yaw {net.z / Deg} deg/s");
+        Assert.Equal(0f, throttle[zeroed]);
+        Assert.True(net.y > 0, $"forward {net.y}");
+    }
+
+    [Theory]
+    [InlineData(1f)]
+    [InlineData(.5f)]
+    [InlineData(-.5f)]
+    [InlineData(-1f)]
+    public void ATurnIsThatFractionOfTheBoxExtreme(float turn)
+    {
+        var duel = Duel();
+        var (plus, minus) = Extremes(duel, 2);
+        var expected = turn * (turn > 0 ? plus : minus);
+        var net = Net(duel, Solve(duel, 0, 0, turn));
+        Assert.True(MathF.Abs(net.z - expected) <= 1e-4f * MathF.Abs(expected), $"yaw {net.z / Deg} expected {expected / Deg}");
+    }
+
+    [Fact]
+    public void AttitudeServesFirstAndTheOnsetIsTheColumnsRatio()
+    {
+        var duel = Duel();
+        // The onset is the attitude thruster's yaw over the hull's extreme in that direction.
+        var clockwiseOnset = duel[2].z / Extremes(duel, 2).plus;
+        var counterOnset = -duel[3].z / Extremes(duel, 2).minus;
+        Assert.InRange(clockwiseOnset, .7714f, .7716f);
+        Assert.InRange(counterOnset, .6904f, .6906f);
+        var allocator = new ThrustAllocator();
+        for (var step = 0; step <= 1000; step++)
+        {
+            var turn = step * .001f;
+            var drive = Solve(allocator, duel, 0, 0, turn)[0];
+            if (turn <= clockwiseOnset - .005f) Assert.True(drive <= 1e-4f, $"clockwise turn {turn}: drive {drive}");
+            if (turn >= clockwiseOnset + .005f) Assert.True(drive > 1e-3f, $"clockwise turn {turn}: drive {drive}");
+        }
+        allocator = new ThrustAllocator();
+        for (var step = 0; step <= 1000; step++)
+        {
+            var turn = step * .001f;
+            var drive = Solve(allocator, duel, 0, 0, -turn)[1];
+            if (turn <= counterOnset - .005f) Assert.True(drive <= 1e-4f, $"counter-clockwise turn {turn}: drive {drive}");
+            if (turn >= counterOnset + .005f) Assert.True(drive > 1e-3f, $"counter-clockwise turn {turn}: drive {drive}");
+        }
+    }
+
+    [Fact]
+    public void TheOnsetMovesWithTheColumns()
+    {
+        // Clockwise Talaria lost: the drive serves a clockwise turn from the first touch.
+        var damaged = DamagedDuel();
+        var small = Solve(damaged, 0, 0, .01f);
+        Assert.True(small[0] > 0, $"drive {small[0]}");
+        Assert.True(MathF.Abs(YawDeg(damaged, small) - .01f * 49.24f) <= .01f * 49.24f * 1e-3f, $"yaw {YawDeg(damaged, small)}");
+        var full = Solve(damaged, 0, 0, 1f);
+        Assert.True(MathF.Abs(YawDeg(damaged, full) - 49.24f) <= 49.24f * 1e-3f, $"yaw {YawDeg(damaged, full)}");
+
+        // Clockwise Talaria halved: the onset is its new share of the clockwise extreme.
+        var halved = Duel();
+        halved[2] = halved[2] * .5f;
+        var onset = halved[2].z / Extremes(halved, 2).plus;
+        Assert.InRange(onset, .627f, .629f);
+        var allocator = new ThrustAllocator();
+        for (var step = 0; step <= 1000; step++)
+        {
+            var turn = step * .001f;
+            var drive = Solve(allocator, halved, 0, 0, turn)[0];
+            if (turn <= onset - .005f) Assert.True(drive <= 1e-4f, $"turn {turn}: drive {drive}");
+            if (turn >= onset + .005f) Assert.True(drive > 1e-3f, $"turn {turn}: drive {drive}");
+        }
+    }
+
+    [Fact]
+    public void EveryThrottleIsContinuousInTurn()
+    {
+        foreach (var columns in new[] { Duel(), DamagedDuel(), Symmetric() })
+        {
+            var allocator = new ThrustAllocator();
+            var previous = Solve(allocator, columns, 0, 0, -1f);
+            for (var step = -999; step <= 1000; step++)
+            {
+                var current = Solve(allocator, columns, 0, 0, step * .001f);
+                for (var i = 0; i < columns.Length; i++)
+                    Assert.True(MathF.Abs(current[i] - previous[i]) <= .02f, $"turn {step * .001f}: throttle {i} {previous[i]} -> {current[i]}");
+                previous = current;
+            }
+        }
+    }
+
+    [Fact]
+    public void PureTorqueNeedsNoTranslation()
+    {
+        var hull = Symmetric();
+        var allocator = new ThrustAllocator();
+        var starboard = Extremes(hull, 0).plus;
+        var forward = Extremes(hull, 1).plus;
+        for (var step = -87; step <= 87; step++)
+        {
+            var net = Net(hull, Solve(allocator, hull, 0, 0, step * .01f));
+            Assert.True(MathF.Abs(net.x) <= 1e-3f * starboard, $"turn {step * .01f}: starboard {net.x}");
+            Assert.True(MathF.Abs(net.y) <= 1e-3f * forward, $"turn {step * .01f}: forward {net.y}");
+        }
+        var strafe = Net(hull, Solve(hull, 1, 0, 0));
+        Assert.True(strafe.x >= .9f * starboard, $"strafe {strafe.x} of {starboard}");
+        Assert.True(MathF.Abs(strafe.z) <= 1e-3f * Extremes(hull, 2).plus, $"yaw {strafe.z / Deg}");
+    }
+
+    [Fact]
+    public void TurnComesBeforeTranslation()
+    {
+        var duel = Duel();
+        var throttle = Solve(duel, 0, 1, 1f);
+        var net = Net(duel, throttle);
+        var extreme = Extremes(duel, 2).plus;
+        Assert.True(MathF.Abs(net.z - extreme) <= 1e-4f * extreme, $"yaw {net.z / Deg} of {extreme / Deg}");
+        Assert.True(throttle[1] < .01f, $"counter-turning drive {throttle[1]}");
+    }
+
+    [Fact]
+    public void MovementIsThatFractionOfTheHalfAxis()
+    {
+        // A torque-free strafe pair of unequal strength and a torque-free main.
+        var columns = new[] { Col(30, 0, 0), Col(-20, 0, 0), Col(0, 60, 0) };
+        const float yaw = 1e-4f;
+        var right = Net(columns, Solve(columns, .5f, 0, 0));
+        Assert.True(MathF.Abs(right.x - 15f) <= 15e-3f && MathF.Abs(right.z) <= yaw, $"right {right.x}");
+        var left = Net(columns, Solve(columns, -.5f, 0, 0));
+        Assert.True(MathF.Abs(left.x + 10f) <= 10e-3f && MathF.Abs(left.z) <= yaw, $"left {left.x}");
+        var ahead = Net(columns, Solve(columns, 0, .5f, 0));
+        Assert.True(MathF.Abs(ahead.y - 30f) <= 30e-3f && MathF.Abs(ahead.z) <= yaw, $"ahead {ahead.y}");
+    }
+
+    [Fact]
+    public void IntentBeyondOneIsClamped()
+    {
+        var duel = Duel();
+        Assert.Equal(Solve(duel, 0, 0, 1f), Solve(duel, 0, 0, 3f));
+        Assert.Equal(Solve(duel, 1, -1, 0), Solve(duel, 3, -3, 0));
+        Assert.Equal(Solve(duel, 0, 0, -1f), Solve(duel, 0, 0, -3f));
+    }
+
+    [Fact]
+    public void NothingAskedNothingFired()
+    {
+        Assert.All(Solve(Duel(), 0, 0, 0), t => Assert.Equal(0f, t));
+        Assert.All(Solve(new float3[4], 1, 1, 1), t => Assert.Equal(0f, t));
+        new ThrustAllocator().Allocate(ReadOnlySpan<float3>.Empty, new float2(1, 1), 1, Span<float>.Empty);
+        var withNaN = Duel();
+        withNaN[2] = new float3(float.NaN, 0, 0);
+        Assert.All(Solve(withNaN, 0, 1, 1), t => Assert.Equal(0f, t));
+        var nanYaw = Duel();
+        nanYaw[0] = new float3(0, 1, float.NaN);
+        Assert.All(Solve(nanYaw, 0, 1, 0), t => Assert.Equal(0f, t));
+    }
+
+    [Fact]
+    public void TheStartDoesNotChangeTheAnswer()
+    {
+        var duel = Duel();
+        var cold = Solve(duel, .3f, .8f, .6f);
+        foreach (var previous in new[] { (1f, 1f, 1f), (-1f, -.5f, -1f), (0f, 0f, 0f) })
+        {
+            var allocator = new ThrustAllocator();
+            Solve(allocator, duel, previous.Item1, previous.Item2, previous.Item3);
+            var warm = Solve(allocator, duel, .3f, .8f, .6f);
+            for (var i = 0; i < duel.Length; i++) Assert.True(MathF.Abs(warm[i] - cold[i]) <= 1e-5f, $"previous {previous}: throttle {i} {cold[i]} vs {warm[i]}");
+        }
+    }
+
+    [Fact]
+    public void EqualThrustersShareTheDemand()
+    {
+        var columns = new[] { Col(0, 50, 0), Col(0, 50, 0) };
+        var throttle = Solve(columns, 0, .5f, 0);
+        Assert.True(MathF.Abs(throttle[0] - throttle[1]) <= 1e-4f, $"{throttle[0]} vs {throttle[1]}");
+        Assert.True(throttle[0] > .1f);
+    }
+
+    [Fact]
+    public void AColumnCountChangeResets()
+    {
+        var four = Duel();
+        var three = new[] { four[0], four[2], four[3] };
+        var allocator = new ThrustAllocator();
+        var steps = new List<(float3[] columns, float x, float y, float turn)>
+        {
+            (four, .2f, .9f, -.7f), (three, -.4f, 1f, .9f), (four, .2f, .9f, -.7f),
+        };
+        foreach (var (columns, x, y, turn) in steps)
+        {
+            var warm = Solve(allocator, columns, x, y, turn);
+            var fresh = Solve(columns, x, y, turn);
+            for (var i = 0; i < columns.Length; i++) Assert.True(MathF.Abs(warm[i] - fresh[i]) <= 1e-5f, $"{columns.Length} columns: throttle {i}");
+        }
+    }
+}