perf(compositor): slice 5 — paste cache for non-opaque layers (take-7/8 data)

The stamped build settled what slices 3-4 could not: chat cache works (resolve
~0.0ms) but render stayed 26-27ms -> 124-135/300. The cost was the compositor
re-rasterizing EVERY layer every tick: this Live scene re-samples chat (159k) +
web widget (271k) + image (95k) + cam (156k) ~ 680k px @ ~38ns — for layers
whose pixels do not change between chat/web/cam updates.

OBS shape: cache the surface, paste per tick. BlitCachedLayer rasterizes a
non-opaque layer ONCE into an element-space, transparent-based frame keyed by
(source-array identity, src W/H, ceil'd dst rect, round, mirror), then pastes:
integer position, row alpha-blend, opacity applied at paste. Producers hand out
fresh immutable arrays -> array-identity keys cannot serve stale content; dict
bounded (48, clears whole). Drag/opacity live in paste params, not keys, so
editing stops triggering resamples too. Opaque backdrop keeps the memcpy path;
the webcam keeps the direct path via its IsOpaque flag (revisit if take 9 is
borderline).

ONE integration test: PasteCache_RepeatRender_IsByteIdentical_And_ContentChange-
Propagates (byte-exact raster-vs-paste incl. round-clip margins, new-array
propagation); existing pixel suite guards sampler semantics. 85/85 across
compositor/pump/chat/capture/session classes, clean build 0 warnings. Also:
BuildStampTests.cs was written last commit but never staged — its own scope-check
slip, added here (the run had used the on-disk file; tracked now).

Docs same commit: ai.md slice 5 + stale 'general path only 130k' claim corrected,
TASKS.md take-9 gate, MyMistakes recipe (prove the stage; a fix that doesn't move
the stat wasn't the bottleneck), HANDOFF. take 9 expectation: 300/300, render
<= ~8ms -> saga closes, Unit B starts.

ytLive.Tests/BuildStampTests.cs

@@ -0,0 +1,59 @@
+using System;
+using System.Text.RegularExpressions;
+using System.Windows;
+using System.Windows.Controls;
+using System.Windows.Documents;
+using Xunit;
+using ytLive.Helpers;
+
+namespace ytLive.Tests;
+
+/// <summary>
+/// Build attribution (2026-09-04, after takes 3–6 could not be pinned to a binary):
+/// every build stamps a fresh GUID (ytLive.csproj GenerateBuildStamp), shown as the
+/// wordmark superscript and logged at startup. The unit pins the stamp shape; the
+/// RealApp test proves the wordmark ACTUALLY displays it (XAML wiring, live visual
+/// tree) — a stamp nobody can see would not have ended the guessing.
+/// </summary>
+public sealed class BuildStampTests
+{
+    [Fact]
+    public void Stamp_IsAFreshHexIdAndParsableTimestamp()
+    {
+        Assert.Matches(new Regex("^[0-9a-f]{8}$"), BuildStamp.Id);
+        Assert.True(DateTime.TryParseExact(BuildStamp.BuiltLocal, "yyyy-MM-dd HH:mm:ss",
+            null, System.Globalization.DateTimeStyles.None, out var built));
+        Assert.True(built <= DateTime.Now);
+        Assert.True(built.Date >= new DateTime(2026, 9, 4));
+    }
+}
+
+[Collection("RealApp")]
+public sealed class BuildStampDisplayTests
+{
+    private readonly RealAppHost _app;
+
+    public BuildStampDisplayTests(RealAppHost app) => _app = app;
+
+    [Fact]
+    public void Wordmark_Shows_The_Build_Stamp_As_Superscript()
+    {
+        _app.Run(() =>
+        {
+            var window = new MainWindow();
+            try
+            {
+                // TopBar is its own namescope (UserControl) — FindName from the
+                // control, never from the window (MyMistakes: namescoped FindName).
+                var topBar = (UserControl)window.FindName("TopBar")!;
+                var stamp = (Run)topBar.FindName("BuildIdStamp")!;
+                Assert.Equal(BuildStamp.Id, stamp.Text);
+                Assert.Equal(BaselineAlignment.Superscript, stamp.BaselineAlignment);
+            }
+            finally
+            {
+                window.Close();
+            }
+        });
+    }
+}

ytLive.Tests/SceneCompositorTests.cs

@@ -154,6 +154,63 @@ public class SceneCompositorTests
         Assert.DoesNotContain((byte)0xFD, output.BgraPixels); // full cover — nothing stale
     }
 
+    /// <summary>The ONE integration test for the paste cache (take-8): a second render of
+    /// the SAME frames must produce byte-identical output (the hit path pastes a cached
+    /// element-space raster — position/opacity/margins/round-clip must survive it), and a
+    /// NEW source array must propagate (the cache keys on frame identity, so a stale
+    /// raster can never outlive its content). Covers the margins the FullScene probe
+    /// pixels don't: outside-the-circle alpha and the black pre-fill interaction.</summary>
+    [Fact]
+    public void PasteCache_RepeatRender_IsByteIdentical_And_ContentChangePropagates()
+    {
+        var red = Solid(1920, 1080, 255, 0, 0);
+        var green = Solid(1280, 720, 0, 255, 0);
+        var blue = Solid(1280, 720, 0, 0, 255);
+
+        var background = new Source { Type = SourceType.DisplayCapture, IsBackground = true, CaptureKey = "monitor:0" };
+        var roundWebcam = new WebcamSceneConfig { X = 100, Y = 100, Width = 300, Height = 300, ClipShape = ClipShape.Round };
+        var scene = new Scene { Name = "Live" };
+        scene.Elements.Add(background);
+        scene.Elements.Add(roundWebcam);
+
+        VideoFrame? FrameFor(SceneElement e) => e switch
+        {
+            WebcamSceneConfig => green,
+            Source { IsBackground: true } => red,
+            _ => null,
+        };
+
+        var options = new CompositorOptions
+        {
+            SourceRectX = 0, SourceRectY = 0, SourceRectWidth = 1920, SourceRectHeight = 1080,
+            OutputWidth = 1920, OutputHeight = 1080,
+        };
+
+        var compositor = new SceneCompositor();
+        var first = compositor.Render(scene, FrameFor, null, options);
+        var second = compositor.Render(scene, FrameFor, null, options); // paste-cache hit
+        Assert.Equal(first.BgraPixels, second.BgraPixels);
+
+        // margins: inside the circle = webcam, outside = backdrop (both renders)
+        foreach (var f in new[] { first, second })
+        {
+            AssertColor(f, 250, 250, 0, 255, 0);
+            AssertColor(f, 101, 101, 255, 0, 0);
+            Assert.Equal((byte)255, f.BgraPixels[(250 * 1920 + 250) * 4 + 3]); // alpha stays opaque
+        }
+
+        // Content change (new array, same geometry) must show through the cache.
+        VideoFrame? FrameForBlue(SceneElement e) => e switch
+        {
+            WebcamSceneConfig => blue,
+            Source { IsBackground: true } => red,
+            _ => null,
+        };
+        var third = compositor.Render(scene, FrameForBlue, null, options);
+        AssertColor(third, 250, 250, 0, 0, 255);
+        AssertColor(third, 101, 101, 255, 0, 0);
+    }
+
     [Fact]
     public void Render_VerticalTier_Outputs_1080x1920_From_The_Center_Crop()
     {