fix(motion): preserve signed TurnSpeed for remote turn animations

The wire-arrival animCycle picker in OnLiveMotionUpdated was passing
MathF.Abs(turnSpeed) to the sequencer, stripping the sign that ACE uses
to encode TurnLeft. Confirmed via live wire trace 2026-05-03: TurnLeft
input from a retail-driven character arrives as
turnCmd16=0x000D (TurnRight), TurnSpeed=-1.500 — mirroring retail's
adjust_motion convention on the wire. With Abs, both directions
collapsed onto motion=TurnRight + speedMod=+1.5, and the synthesize-
omega path computed -2.25 (CW = right) for both. Visible symptom:
TurnLeft animated as TurnRight then blipped to the correct facing on
the next UpdatePosition.

Pass the signed speed through unchanged. The sequencer's negative-
speed path (EnqueueMotionData multiplies MotionData.Omega by speedMod;
the synthesize-omega fallback uses -(pi/2)*adjustedSpeed) produces the
correct CCW omega for TurnLeft now that the sign survives.

Also adds a TURN_WIRE diagnostic gated on ACDREAM_REMOTE_VEL_DIAG=1
that prints every wire-arrived TurnCommand with reconstructed enum
and signed speed, plus splits the OMEGA_DIAG throttle off
LastVelDiagLogTime onto its own LastOmegaDiagLogTime so the two
diagnostics don't starve each other.

Verified with the same trace: TURN_WIRE speed=-1.500 -> OMEGA_DIAG
Z=+2.250 (CCW = TurnLeft), TURN_WIRE speed=+1.500 -> OMEGA_DIAG
Z=-2.250 (CW = TurnRight). Both directions now have correct sign.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

src/AcDream.App/Rendering/GameWindow.cs

@@ -376,6 +376,7 @@ public sealed class GameWindow : IDisposable
         public System.Numerics.Vector3 PrevServerPos;
         public double PrevServerPosTime;
         public double LastVelDiagLogTime;
+        public double LastOmegaDiagLogTime;
 
         public RemoteMotion()
         {
@@ -2862,7 +2863,17 @@ public sealed class GameWindow : IDisposable
                             .ReconstructFullCommand(turnForAnim);
                         if (turnFullForAnim == 0) turnFullForAnim = 0x65000000u | turnForAnim;
                         animCycle = turnFullForAnim;
-                        animSpeed = MathF.Abs(update.MotionState.TurnSpeed ?? 1f);
+                        // SIGNED — do NOT MathF.Abs. ACE encodes TurnLeft on the
+                        // wire as (TurnCommand=TurnRight, TurnSpeed=NEGATIVE),
+                        // mirroring retail's adjust_motion convention. The
+                        // sequencer's negative-speed path (EnqueueMotionData
+                        // multiplies MotionData.Omega by speedMod, the
+                        // synthesize-omega fallback flips zomega via
+                        // -(pi/2)*adjustedSpeed) only produces the correct
+                        // CCW rotation when the sign is preserved here.
+                        // Confirmed by live wire trace 2026-05-03: TurnLeft
+                        // input arrives as turnCmd16=0x000D, speed=-1.500.
+                        animSpeed = update.MotionState.TurnSpeed ?? 1f;
                     }
                 }
                 // K-fix17 (2026-04-26): preserve the Falling cycle while
@@ -2993,6 +3004,14 @@ public sealed class GameWindow : IDisposable
                             .ReconstructFullCommand(turnCmd16);
                         if (turnFull == 0) turnFull = 0x65000000u | turnCmd16;
                         float turnSpd = update.MotionState.TurnSpeed ?? 1f;
+                        if (System.Environment.GetEnvironmentVariable("ACDREAM_REMOTE_VEL_DIAG") == "1")
+                        {
+                            System.Console.WriteLine(
+                                $"[TURN_WIRE] guid={update.Guid:X8} turnCmd16=0x{turnCmd16:X4} "
+                                + $"turnFull=0x{turnFull:X8} low=0x{turnFull & 0xFFu:X2} "
+                                + $"({(((turnFull & 0xFFu) == 0x0D) ? "TurnRight" : ((turnFull & 0xFFu) == 0x0E) ? "TurnLeft" : "OTHER")}) "
+                                + $"speed={turnSpd:F3}");
+                        }
                         remoteMot.Motion.DoInterpretedMotion(
                             turnFull, turnSpd, modifyInterpretedState: true);
                         // Seed ObservedOmega with formula so rotation starts
@@ -5874,6 +5893,23 @@ public sealed class GameWindow : IDisposable
                         var rot = System.Numerics.Quaternion.CreateFromAxisAngle(axis, angleDelta);
                         rm.Body.Orientation = System.Numerics.Quaternion.Normalize(
                             System.Numerics.Quaternion.Concatenate(rm.Body.Orientation, rot));
+
+                        // Diagnostic (ACDREAM_REMOTE_VEL_DIAG=1): print seqOmega direction
+                        // once per remote per ~1 second so we can confirm whether the omega
+                        // sign actually being applied matches the retail-observed turn
+                        // direction. Z>0 = CCW (TurnLeft); Z<0 = CW (TurnRight).
+                        if (System.Environment.GetEnvironmentVariable("ACDREAM_REMOTE_VEL_DIAG") == "1")
+                        {
+                            double nowSec = (System.DateTime.UtcNow - System.DateTime.UnixEpoch).TotalSeconds;
+                            if (nowSec - rm.LastOmegaDiagLogTime > 0.5)
+                            {
+                                uint seqMotion = ae.Sequencer?.CurrentMotion ?? 0;
+                                System.Console.WriteLine(
+                                    $"[OMEGA_DIAG] guid={serverGuid:X8} motion=0x{seqMotion:X8} "
+                                    + $"seqOmega.Z={seqOmega.Z:F3} (Z>0=CCW=TurnLeft, Z<0=CW=TurnRight)");
+                                rm.LastOmegaDiagLogTime = nowSec;
+                            }
+                        }
                     }
 
                     // Step 3: calc_acceleration sets body.Acceleration from the Gravity flag