diff --git a/docs/architecture.md b/docs/architecture.md
index 73905cc..276ba19 100644
--- a/docs/architecture.md
+++ b/docs/architecture.md
@@ -132,11 +132,18 @@ public static partial class GameAssets
 - Порядок сортировки: **слой → depth (или Y) → текстура**; спрайты с одной
   текстурой сливаются в один draw call (динамический vertex buffer + общий
   quad index buffer).
+- Сортировка — **стабильный LSD radix sort**: спрайты с равным ключом сохраняют
+  порядок сабмита между кадрами (нет мерцания), сложность O(n); проходы по
+  одинаковым у всех ключей разрядам пропускаются.
+- Горячий путь без тригонометрии и корней: для спрайтов без поворота SinCos
+  не вычисляется, радиус culling-окружности берётся из предрассчитанной
+  диагонали региона.
 - Текстурные атласы — первоклассный гражданин: `Sprite` хранит регион атласа,
   спрайты одного атласа батчатся автоматически.
 - Цель по производительности: ≥100k спрайтов при 60 FPS на среднем десктопе,
-  0 аллокаций на кадр. Контролируется бенчмарками (BenchmarkDotNet) и
-  стресс-сценой в Sample.
+  0 аллокаций на кадр. Контролируется стресс-сценой в Sample: 100k сущностей
+  (~61k в кадре) ≈ 124 FPS в Release. **Производительность измеряется только
+  в Release** — Debug-сборка медленнее в 5–6 раз (нет инлайнинга JIT).
 
 ## Сцены и переходы
 
diff --git a/docs/roadmap.md b/docs/roadmap.md
index 942cd28..c8a05c6 100644
--- a/docs/roadmap.md
+++ b/docs/roadmap.md
@@ -20,5 +20,5 @@
 - Particles
 - UI
 - Бенчмарки BenchmarkDotNet для систем (сейчас производительность контролируется стресс-сценой)
-- Стабильная сортировка спрайтов с равным ключом (сейчас порядок не гарантирован между кадрами)
 - Spatial hash для culling на очень больших мирах (если профилирование покажет необходимость)
+- Параллельная запись вершин (Parallel.For по чанкам), если упрёмся в CPU на ещё больших сценах
diff --git a/samples/MrGameEng.Sample/Program.cs b/samples/MrGameEng.Sample/Program.cs
index d4009a1..15145c3 100644
--- a/samples/MrGameEng.Sample/Program.cs
+++ b/samples/MrGameEng.Sample/Program.cs
@@ -9,6 +9,7 @@ using var host = new GameHost(
         Width = 1280,
         Height = 720,
         ClearColor = new Color(24, 26, 32),
+        VSync = false, // техдемо: показываем реальный FPS, не ограниченный частотой монитора
     },
     new MainScene());
 
diff --git a/src/MrGameEng.Graphics/CullingMath.cs b/src/MrGameEng.Graphics/CullingMath.cs
index e1dee80..b75c334 100644
--- a/src/MrGameEng.Graphics/CullingMath.cs
+++ b/src/MrGameEng.Graphics/CullingMath.cs
@@ -14,19 +14,40 @@ public static class CullingMath
     {
         var scaledW = regionWidth * transform.Scale.X;
         var scaledH = regionHeight * transform.Scale.Y;
+        var center = SpriteCenter(in transform, scaledW, scaledH, origin);
+        var radius = 0.5f * MathF.Sqrt(scaledW * scaledW + scaledH * scaledH);
+        return (center, radius);
+    }
 
+    /// <summary>
+    /// Hot-path variant used by the renderer: the radius comes from the region's precomputed
+    /// diagonal (no square root per sprite; conservative for non-uniform scale, exact for uniform).
+    /// </summary>
+    public static (Vector2 Center, float Radius) SpriteBoundingCircle(
+        in Transform2D transform, Texture2DRegion region, Vector2 origin)
+    {
+        var center = SpriteCenter(
+            in transform, region.Width * transform.Scale.X, region.Height * transform.Scale.Y, origin);
+        var maxScale = MathF.Max(MathF.Abs(transform.Scale.X), MathF.Abs(transform.Scale.Y));
+        return (center, 0.5f * region.Diagonal * maxScale);
+    }
+
+    private static Vector2 SpriteCenter(in Transform2D transform, float scaledW, float scaledH, Vector2 origin)
+    {
         // Offset from the pivot (= transform.Position) to the sprite's geometric center.
         var toCenter = new Vector2(
             scaledW / 2f - origin.X * transform.Scale.X,
             scaledH / 2f - origin.Y * transform.Scale.Y);
 
+        if (transform.Rotation == 0f)
+        {
+            return transform.Position + toCenter;
+        }
+
         var (sin, cos) = MathF.SinCos(transform.Rotation);
-        var center = transform.Position + new Vector2(
+        return transform.Position + new Vector2(
             toCenter.X * cos - toCenter.Y * sin,
             toCenter.X * sin + toCenter.Y * cos);
-
-        var radius = 0.5f * MathF.Sqrt(scaledW * scaledW + scaledH * scaledH);
-        return (center, radius);
     }
 
     /// <summary>True when the circle overlaps the rectangle.</summary>
diff --git a/src/MrGameEng.Graphics/Renderer2D.cs b/src/MrGameEng.Graphics/Renderer2D.cs
index ec8f5d7..5ee91e3 100644
--- a/src/MrGameEng.Graphics/Renderer2D.cs
+++ b/src/MrGameEng.Graphics/Renderer2D.cs
@@ -97,7 +97,7 @@ public sealed class Renderer2D : IDisposable
         }
 
         var layer = Layers[sprite.Layer];
-        var (center, radius) = CullingMath.SpriteBoundingCircle(transform, region.Width, region.Height, sprite.Origin);
+        var (center, radius) = CullingMath.SpriteBoundingCircle(in transform, region, sprite.Origin);
 
         if (layer.Space == LayerSpace.World &&
             !CullingMath.CircleIntersectsRect(center, radius, Camera.CullRect))
@@ -203,9 +203,19 @@ public sealed class Renderer2D : IDisposable
                 (v0, v1) = (v1, v0);
             }
 
-            var (sin, cos) = MathF.SinCos(instance.Rotation);
-            var rx = new Vector2(instance.HalfSize.X * cos, instance.HalfSize.X * sin);
-            var ry = new Vector2(-instance.HalfSize.Y * sin, instance.HalfSize.Y * cos);
+            Vector2 rx, ry;
+            if (instance.Rotation == 0f)
+            {
+                rx = new Vector2(instance.HalfSize.X, 0f);
+                ry = new Vector2(0f, instance.HalfSize.Y);
+            }
+            else
+            {
+                var (sin, cos) = MathF.SinCos(instance.Rotation);
+                rx = new Vector2(instance.HalfSize.X * cos, instance.HalfSize.X * sin);
+                ry = new Vector2(-instance.HalfSize.Y * sin, instance.HalfSize.Y * cos);
+            }
+
             var center = instance.Center;
 
             var vertex = i * 4;
diff --git a/src/MrGameEng.Graphics/SpriteBatcher.cs b/src/MrGameEng.Graphics/SpriteBatcher.cs
index da85c53..d69747f 100644
--- a/src/MrGameEng.Graphics/SpriteBatcher.cs
+++ b/src/MrGameEng.Graphics/SpriteBatcher.cs
@@ -29,14 +29,22 @@ public struct SpriteInstance
 
 /// <summary>
 /// CPU side of the renderer: collects <see cref="SpriteInstance"/>s with their sort keys
-/// and orders them layer → depth → texture. Allocation-free after warm-up
-/// (arrays grow geometrically and are reused across frames).
+/// and orders them layer → depth → texture using a stable LSD radix sort — sprites with
+/// equal keys keep their submission order across frames (no flicker), and sorting stays
+/// O(n) on large counts. Allocation-free after warm-up (arrays grow geometrically and are
+/// reused across frames).
 /// </summary>
 public sealed class SpriteBatcher
 {
+    private const int RadixBits = 16;
+    private const int RadixSize = 1 << RadixBits;
+
     private SpriteInstance[] _instances;
     private ulong[] _keys;
+    private ulong[] _keysTemp;
     private int[] _order;
+    private int[] _orderTemp;
+    private readonly int[] _histogram = new int[RadixSize];
     private int _count;
 
     /// <summary>Creates a batcher with the given initial capacity.</summary>
@@ -44,7 +52,9 @@ public sealed class SpriteBatcher
     {
         _instances = new SpriteInstance[initialCapacity];
         _keys = new ulong[initialCapacity];
+        _keysTemp = new ulong[initialCapacity];
         _order = new int[initialCapacity];
+        _orderTemp = new int[initialCapacity];
     }
 
     /// <summary>Number of sprites submitted this frame.</summary>
@@ -64,18 +74,74 @@ public sealed class SpriteBatcher
     }
 
     /// <summary>
-    /// Sorts all submitted sprites and returns their indices in draw order.
-    /// Valid until the next <see cref="Clear"/>.
+    /// Sorts all submitted sprites (stable: equal keys keep submission order) and returns
+    /// their indices in draw order. Valid until the next <see cref="Clear"/>.
     /// </summary>
     public ReadOnlySpan<int> Sort()
     {
-        for (var i = 0; i < _count; i++)
+        var n = _count;
+        for (var i = 0; i < n; i++)
         {
             _order[i] = i;
         }
 
-        Array.Sort(_keys, _order, 0, _count);
-        return _order.AsSpan(0, _count);
+        if (n < 2)
+        {
+            return _order.AsSpan(0, n);
+        }
+
+        // Биты, различающиеся хотя бы у одной пары ключей: проходы по одинаковым
+        // разрядам (один слой, одна глубина) пропускаются целиком.
+        ulong orBits = 0, andBits = ~0UL;
+        for (var i = 0; i < n; i++)
+        {
+            orBits |= _keys[i];
+            andBits &= _keys[i];
+        }
+
+        var differing = orBits ^ andBits;
+        var keys = _keys;
+        var order = _order;
+        var keysOut = _keysTemp;
+        var orderOut = _orderTemp;
+
+        for (var shift = 0; shift < 64; shift += RadixBits)
+        {
+            if ((differing >> shift & (RadixSize - 1)) == 0)
+            {
+                continue;
+            }
+
+            Array.Clear(_histogram, 0, RadixSize);
+            for (var i = 0; i < n; i++)
+            {
+                _histogram[(int)(keys[i] >> shift & (RadixSize - 1))]++;
+            }
+
+            var running = 0;
+            for (var digit = 0; digit < RadixSize; digit++)
+            {
+                var bucket = _histogram[digit];
+                _histogram[digit] = running;
+                running += bucket;
+            }
+
+            for (var i = 0; i < n; i++)
+            {
+                var position = _histogram[(int)(keys[i] >> shift & (RadixSize - 1))]++;
+                keysOut[position] = keys[i];
+                orderOut[position] = order[i];
+            }
+
+            (keys, keysOut) = (keysOut, keys);
+            (order, orderOut) = (orderOut, order);
+        }
+
+        _keys = keys;
+        _keysTemp = keysOut;
+        _order = order;
+        _orderTemp = orderOut;
+        return _order.AsSpan(0, n);
     }
 
     /// <summary>Returns the instance at <paramref name="index"/> (an index from <see cref="Sort"/>).</summary>
@@ -89,6 +155,8 @@ public sealed class SpriteBatcher
         var capacity = _instances.Length * 2;
         Array.Resize(ref _instances, capacity);
         Array.Resize(ref _keys, capacity);
+        Array.Resize(ref _keysTemp, capacity);
         Array.Resize(ref _order, capacity);
+        Array.Resize(ref _orderTemp, capacity);
     }
 }
diff --git a/src/MrGameEng.Graphics/Texture2DRegion.cs b/src/MrGameEng.Graphics/Texture2DRegion.cs
index 6483b86..5ba23d7 100644
--- a/src/MrGameEng.Graphics/Texture2DRegion.cs
+++ b/src/MrGameEng.Graphics/Texture2DRegion.cs
@@ -23,6 +23,7 @@ public sealed class Texture2DRegion
     public int Height => Bounds.Height;
 
     internal readonly int TextureSortKey;
+    internal readonly float Diagonal;
 
     /// <summary>Creates a region covering part of <paramref name="texture"/>.</summary>
     public Texture2DRegion(Texture2D texture, Rectangle bounds)
@@ -30,6 +31,7 @@ public sealed class Texture2DRegion
         Texture = texture;
         Bounds = bounds;
         TextureSortKey = System.Runtime.CompilerServices.RuntimeHelpers.GetHashCode(texture);
+        Diagonal = MathF.Sqrt((float)bounds.Width * bounds.Width + (float)bounds.Height * bounds.Height);
     }
 
     /// <summary>Creates a region covering the whole <paramref name="texture"/>.</summary>
diff --git a/tests/MrGameEng.Graphics.Tests/CullingTests.cs b/tests/MrGameEng.Graphics.Tests/CullingTests.cs
index f68231b..bcf5e0c 100644
--- a/tests/MrGameEng.Graphics.Tests/CullingTests.cs
+++ b/tests/MrGameEng.Graphics.Tests/CullingTests.cs
@@ -37,6 +37,33 @@ public class CullingTests
         Assert.Equal(0.5f * MathF.Sqrt(800f), radius, 3);
     }
 
+    [Fact]
+    public void BoundingCircle_RegionOverload_MatchesSizeOverload_ForUniformScale()
+    {
+        var region = new Texture2DRegion(null!, new Rectangle(0, 0, 48, 24));
+        var transform = new Transform2D(new Vector2(10f, 20f), rotation: 0.6f, scale: new Vector2(1.5f, 1.5f));
+        var origin = new Vector2(5f, 7f);
+
+        var (centerA, radiusA) = CullingMath.SpriteBoundingCircle(transform, 48f, 24f, origin);
+        var (centerB, radiusB) = CullingMath.SpriteBoundingCircle(in transform, region, origin);
+
+        Assert.Equal(centerA.X, centerB.X, 3);
+        Assert.Equal(centerA.Y, centerB.Y, 3);
+        Assert.Equal(radiusA, radiusB, 3);
+    }
+
+    [Fact]
+    public void BoundingCircle_RegionOverload_IsConservative_ForNonUniformScale()
+    {
+        var region = new Texture2DRegion(null!, new Rectangle(0, 0, 100, 10));
+        var transform = new Transform2D(Vector2.Zero, scale: new Vector2(1f, 3f));
+
+        var (_, exact) = CullingMath.SpriteBoundingCircle(transform, 100f, 10f, Vector2.Zero);
+        var (_, conservative) = CullingMath.SpriteBoundingCircle(in transform, region, Vector2.Zero);
+
+        Assert.True(conservative >= exact);
+    }
+
     [Theory]
     [InlineData(50f, 50f, true)]    // inside
     [InlineData(-4f, 50f, true)]    // touching from the left (radius 5)
diff --git a/tests/MrGameEng.Graphics.Tests/SpriteBatcherTests.cs b/tests/MrGameEng.Graphics.Tests/SpriteBatcherTests.cs
index ae89194..8fcc727 100644
--- a/tests/MrGameEng.Graphics.Tests/SpriteBatcherTests.cs
+++ b/tests/MrGameEng.Graphics.Tests/SpriteBatcherTests.cs
@@ -39,6 +39,66 @@ public class SpriteBatcherTests
         Assert.Equal(99, order[0]); // последний сабмит имеет наименьший ключ
     }
 
+    [Fact]
+    public void Sort_IsStable_EqualKeysKeepSubmissionOrder()
+    {
+        var batcher = new SpriteBatcher();
+        var key = SpriteSortKey.Make(1, 5f, 7);
+
+        for (byte i = 0; i < 50; i++)
+        {
+            batcher.Submit(Instance(i), key); // одинаковый ключ у всех
+        }
+
+        var order = batcher.Sort();
+
+        for (var i = 0; i < 50; i++)
+        {
+            Assert.Equal(i, order[i]);
+        }
+    }
+
+    [Fact]
+    public void Sort_IsStable_WithinMixedKeys()
+    {
+        var batcher = new SpriteBatcher();
+        var keyA = SpriteSortKey.Make(0, 0f, 1);
+        var keyB = SpriteSortKey.Make(2, 3f, 9);
+
+        // Чередуем два ключа: внутри каждой группы порядок сабмита должен сохраниться.
+        for (byte i = 0; i < 20; i++)
+        {
+            batcher.Submit(Instance(i), i % 2 == 0 ? keyA : keyB);
+        }
+
+        var order = batcher.Sort();
+
+        var expectedA = new[] { 0, 2, 4, 6, 8, 10, 12, 14, 16, 18 };
+        var expectedB = new[] { 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 };
+        Assert.Equal(expectedA, order[..10].ToArray());
+        Assert.Equal(expectedB, order[10..].ToArray());
+    }
+
+    [Fact]
+    public void Sort_LargeRandomSet_FullyOrdered()
+    {
+        var batcher = new SpriteBatcher(initialCapacity: 16);
+        var random = new Random(123);
+        var keys = new ulong[5000];
+        for (var i = 0; i < keys.Length; i++)
+        {
+            keys[i] = (ulong)random.NextInt64();
+            batcher.Submit(Instance(0), keys[i]);
+        }
+
+        var order = batcher.Sort();
+
+        for (var i = 1; i < order.Length; i++)
+        {
+            Assert.True(keys[order[i - 1]] <= keys[order[i]]);
+        }
+    }
+
     [Fact]
     public void Clear_ResetsCount_KeepsWorking()
     {