fix(pump+compositor): take-3 starvation — deadline pacing + row-blit fast paths

Two defects made the producer 17x slow (37s record -> 2.1s/127-frame file,
rawvideo stamps by arrival): FramePump slept the FULL interval after each
render (period = render+submit+interval) and SceneCompositor did per-pixel
float sampling + Math.Round blends over all 2.07M master pixels, scanning the
whole destination per overlay (258ms avg render vs 1.5ms submit).

Both solutions are established, not invented — researched before coding per
the derivative-work rule:
- deadline pacing: OBS libobs/media-io/video-io.c video_thread (nextTick +=
  intervalTicks, sleep only the remainder, rebase on overrun, never burst)
- row blits: libyuv pattern (BSD-3, chromium.googlesource.com/libyuv/libyuv)
  — 1:1 aligned identity fast path, per-pixel alpha branch, integer
  fixed-point blend, overlay clipped to the intersection rect, skip the dead
  black pre-fill when the backdrop covers

ONE integration test: Pump_Paces_To_The_Deadline_Compensating_Render_Cost
(lands after a fake-seam lesson: pacing fakes must await, not complete
synchronously, or the pump loop runs inline on StartAsync and hangs vstest).
Clean build 0 warnings; FramePumpTests 10/10, SceneCompositor/SceneGraph/
SocialBar/StretchMath 20/20. Docs same commit: ai.md pipeline section,
TASKS.md TASK 18 (webcam-in-output + rename modal verified from take 3),
MyMistakes recipe, HANDOFF rewritten. Take 4 pending on the user's machine.

Services/Encoder/FramePump.cs

@@ -218,6 +218,16 @@ public sealed class FramePump : IDisposable
         var interval = TimeSpan.FromSeconds(1d / Math.Max(1, options.Fps));
         var lastTick = System.Diagnostics.Stopwatch.StartNew();
 
+        // Deadline pacing (2026-09-03, take-3 fix): the frame interval is a DEADLINE,
+        // not an afterthought sleep — the OBS libobs video-io.c pattern (researched
+        // before coding; see https://github.com/obsproject/obs-studio/blob/master/
+        // libobs/media-io/video-io.c). The old loop slept the FULL interval after
+        // each render, so period = render + submit + interval: at take-3's 258ms
+        // render that was 3.6fps stamped into a 60fps container — rawvideo stamps by
+        // arrival, so 30 wall-seconds muxed as a 2.1s time-lapse, no error anywhere.
+        var intervalTicks = Math.Max(1, (long)Math.Round(interval.TotalSeconds * System.Diagnostics.Stopwatch.Frequency));
+        var nextTick = System.Diagnostics.Stopwatch.GetTimestamp();
+
         // Stage timing (2026-09-01, take two): rawvideo carries no per-frame
         // timestamps — ffmpeg stamps frames by ARRIVAL at the declared fps. A producer
         // slower than the declared rate yields a time-lapsed, short file (observed:
@@ -292,8 +302,22 @@ public sealed class FramePump : IDisposable
                     submitTicks += submitSw.ElapsedTicks;
                     statFrames++;
                     ReportStats();
+
+                    // Advance the deadline; cost already spent is not slept again.
+                    // Blew the frame budget: skip the wait AND the missed ticks —
+                    // rebase the clock rather than bursting a catch-up pile
+                    // (OBS rewinds its tick the same way; a burst would only
+                    // queue stale frames into the encoder).
+                    nextTick += intervalTicks;
+                    var lag = nextTick - System.Diagnostics.Stopwatch.GetTimestamp();
+                    if (lag <= 0)
+                    {
+                        nextTick = System.Diagnostics.Stopwatch.GetTimestamp() + intervalTicks;
+                        lag = 0;
+                    }
+                    await _pacingDelay(
+                        TimeSpan.FromSeconds(lag / (double)System.Diagnostics.Stopwatch.Frequency), ct);
                 }
-                await _pacingDelay(interval, ct);
             }
         }
         catch (OperationCanceledException)