TASK 31: SceneGraph component + baked-crust compositor optimization

- Add ElementKind (Static/Dynamic) to SceneElement base; Source/WebcamSceneConfig classify
- Services/SceneGraph.cs: owns the Scenes collection (ViewModel's Scenes delegates to it),
  the element mutation surface (Add/Insert/Remove/Move, each invalidating the bake), and the
  queries that were scattered LINQ (GetBackground/GetWebcam/GetChatBoxes/GetSplitPoint/IsStatic)
- SceneCompositor: split-aware BakeStaticBase + CompositeLayers + Render(.., staticBase, split);
  builds/caches the static base below the split point in source-rect space
- FramePump: optional SceneGraph -> optimized bake+composite path; falls back to full render
- MainViewModel: routes element mutations through the graph; invalidates the bake on static
  layout/opacity/visibility/useDefaultBackground changes and after background heal/Ensure
- Integration test SceneGraphTests.BakedStaticBase_WithDynamicLayer_CompositesCorrectly

Derivative survey (mandated): tried before writing — OBS does per-source opacity/visibility
caching and static-scene baking; this mirrors OBS's 'cached static source' optimization.
3 documented defensive deviations from the spec (ChatOverlayLayer stays decoupled;
background helpers stay VM-static for direct testability; full facade peel deferred post-1.0)
in TASKS.md + ai.md. Scope check passed; clean build 0 warnings.

ViewModels/MainViewModel.Background.cs

@@ -388,6 +388,7 @@ public partial class MainViewModel
         NormalizeBackgrounds(Scenes);
         foreach (var scene in Scenes)
         {
+            _sceneGraph.InvalidateBake(scene);
             var background = scene.Elements.OfType<Source>().FirstOrDefault(s => s.IsBackground);
             if (background != null)
                 StampDefaultBackgroundAsset(background, scene.Name);

ViewModels/MainViewModel.Scenes.cs

@@ -16,7 +16,10 @@ public partial class MainViewModel
     // TASK 20 step 2 — hotkey bindings (custom chord per action)
     private Dictionary<HotkeyId, HotkeyChord> _hotkeyBindings = new();
 
-    public ObservableCollection<Scene> Scenes { get; } = new();
+    // TASK 31: the scene collection is owned by the SceneGraph (single owner of the
+    // element inventory + mutation surface). The ViewModel exposes it as-is so the
+    // XAML bindings and MainViewModel call sites keep working unchanged.
+    public ObservableCollection<Scene> Scenes => _sceneGraph.Scenes;
 
     public Scene? StagedScene
     {
@@ -36,6 +39,7 @@ public partial class MainViewModel
                     var background = EnsureBackground(value);
                     if (background != null)
                         StampDefaultBackgroundAsset(background, value.Name);
+                    _sceneGraph.InvalidateBake(value);
                 }
                 OnPropertyChanged(nameof(ShowChatInactiveMessage));
                 OnPropertyChanged(nameof(ShowEmptySceneHint));
@@ -251,6 +255,22 @@ public partial class MainViewModel
     {
         if (sender is WebcamSceneConfig && e.PropertyName == nameof(SceneElement.IsVisible))
             OnPropertyChanged(nameof(CanShowWebcamInStagedScene));
+
+        // A Static element's baked pixels depend on its layout, opacity and
+        // visibility — any of those changing invalidates the cached base.
+        if (sender is SceneElement { Kind: ElementKind.Static } el)
+        {
+            var bakedSurface = e.PropertyName is nameof(SceneElement.X) or nameof(SceneElement.Y)
+                or nameof(SceneElement.Width) or nameof(SceneElement.Height)
+                or nameof(SceneElement.Opacity) or nameof(SceneElement.IsVisible)
+                or nameof(SceneElement.ClipShape) or nameof(SceneElement.IsMirrored);
+            if (bakedSurface)
+            {
+                var containingScene = Scenes.FirstOrDefault(s => s.Elements.Contains(el));
+                if (containingScene != null)
+                    _sceneGraph.InvalidateBake(containingScene);
+            }
+        }
         ScheduleSave();
     }
 

ViewModels/MainViewModel.Sources.cs

@@ -53,7 +53,7 @@ public partial class MainViewModel
             Width = sourceType == SourceType.WebSource ? 640 : sourceType == SourceType.ChatBox ? 500 : 0,
             Height = sourceType == SourceType.WebSource ? 480 : sourceType == SourceType.ChatBox ? 648 : 0,
         };
-        scene.Elements.Add(source);
+        _sceneGraph.AddElement(scene, source);
 
         if (sourceType == SourceType.WebSource)
         {
@@ -208,7 +208,7 @@ public partial class MainViewModel
             source.Y = (1080 - source.Height) / 2;
         }
 
-        scene.Elements.Add(source);
+        _sceneGraph.AddElement(scene, source);
         SelectedElement = source;
         OnPropertyChanged(nameof(ShowEmptySceneHint));
         OnPropertyChanged(nameof(ShowSourcesEmptyHint));
@@ -233,7 +233,7 @@ public partial class MainViewModel
         }
         if (element is Source { Type: SourceType.WebSource } webSource)
             _webView2Manager?.Unregister(webSource.Id);
-        scene.Elements.Remove(element);
+        _sceneGraph.RemoveElement(scene, element);
 
         if (element is WebcamSceneConfig && _webcam != null
             && !Scenes.Any(s => s.Elements.OfType<WebcamSceneConfig>().Any()))

ViewModels/MainViewModel.Webcam.cs

@@ -187,7 +187,7 @@ public partial class MainViewModel
             Y = MasterFrameHeight - 270 - 32,
         };
 
-        scene.Elements.Add(config);
+        _sceneGraph.AddElement(scene, config);
         SelectedElement = config;
         OnPropertyChanged(nameof(ShowEmptySceneHint));
         OnPropertyChanged(nameof(ShowSourcesEmptyHint));

ViewModels/MainViewModel.cs

@@ -37,6 +37,11 @@ public partial class MainViewModel : ViewModelBase
     // tier's FPS and paces frames into the encoder. The RTMP URL seam stays null
     // until the live-stream create flow (TASK 5) supplies the reusable stream URL.
     private readonly Func<string?> _rtmpUrlProvider;
+
+    // Scene graph (TASK 31): owns the scene collection + element inventory and the
+    // baked-crust compositor cache. The ViewModel exposes Scenes/StagedScene/LiveScene
+    // on top of it; the scene collection itself lives here.
+    private SceneGraph _sceneGraph = null!;
     private readonly TransitionService _transition = new();
 
     private WebView2Manager? _webView2Manager;
@@ -70,6 +75,7 @@ public partial class MainViewModel : ViewModelBase
     {
         if (e.PropertyName == nameof(SceneElement.UseDefaultBackground))
         {
+            if (StagedScene != null) _sceneGraph.InvalidateBake(StagedScene);
             UpdateBackgroundImage();
             RefreshSnapshotsAsync();
             ScheduleSave();
@@ -276,6 +282,7 @@ public partial class MainViewModel : ViewModelBase
 
         _chatLayer = new ChatOverlayLayer(new ChatBoxRenderer());
 
+        _sceneGraph = new SceneGraph();
         _rtmpUrlProvider = () => _reusableStreamUrl; // TASK 5: the reusable stream's ingest URL
         _framePump = new FramePump(
             sceneProvider: () => StagedScene,
@@ -286,7 +293,8 @@ public partial class MainViewModel : ViewModelBase
             log: message => AppLog.Write(message),
             socialBar: () => (_socialBarFrame, _socials?.BarPosition ?? SocialBarPosition.Bottom),
             transition: _transition,
-            fromSceneProvider: () => LiveScene);
+            fromSceneProvider: () => LiveScene,
+            sceneGraph: _sceneGraph);
         _framePump.Failed += OnFramePumpFailed;
         _framePump.HealthUpdated += OnFramePumpHealthUpdated;