fix #175: door BSP collision poses at the motion-table closed pose

The Facility Hub double door (Setup 0x02000C9D) embeds the player into
the visual panel from one side and blocks with a phantom slab on the
other: its Setup PLACEMENT frames pose the two panels AJAR (yaw
-150/-30 deg, 0.44 m behind the doorway plane — dat-confirmed by the
Issue175 inspection) while the rendered door poses them CLOSED from
the wire-supplied motion table via the sequencer. ShadowShapeBuilder
read placement frames, so the 1.66x0.29x2.95 m physics slabs
registered at the ajar pose. Retail tests each part's LIVE
CPhysicsPart pose — for an idle door, the motion table's default
(closed) state.

Fix: ShadowShapeBuilder.FromSetup gains partPoseOverride (BSP part
shapes only); RegisterServerEntityCollision derives it from the spawn
MotionTableId via GameWindow.MotionTableDefaultPose (default style ->
first cycle -> LowFrame part frames). Null/short poses fall back
per-part to placement frames — table-less entities and landblock
statics unchanged. One-shot snapshot vs retail's per-frame live pose
is register row AP-84 (equivalent for the door lifecycle: closed ==
default pose; open == ETHEREAL bypasses collision, #150).

Pins: FromSetup_PartPoseOverride_ReplacesPlacementFrames /
_NoOverride_KeepsPlacementFrames / _ShortOverride_FallsBackPerPart.
Suites: Core 2539 / App 713 / UI 425 / Net 385 green.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

src/AcDream.App/Rendering/GameWindow.cs

@@ -4163,9 +4163,22 @@ public sealed class GameWindow : IDisposable
         // span the doorway gap, so the player could walk through. With
         // this change the door also registers the part-0 BSP slab
         // (1.9 × 0.26 × 2.5 m) that retail uses for the real block.
+        // #175 (2026-07-05): BSP part shapes must pose at the motion table's
+        // DEFAULT-STATE frame (the closed pose — what the sequencer renders
+        // for an idle entity and what retail's live CPhysicsPart pose is),
+        // not the Setup's placement frame. The Facility Hub double door
+        // (Setup 0x02000C9D) places its panels AJAR in the placement frame
+        // (yaw −150°/−30°, −0.44 m behind the doorway) while rendering
+        // closed — the user embedded into the visual door on one side and
+        // hit a phantom slab on the other. Null (no motion table / no
+        // cycle / part-count mismatch) falls back to placement frames.
+        var closedPose = MotionTableDefaultPose(
+            spawn.MotionTableId ?? 0u, setup.Parts.Count);
+
         var raw = AcDream.Core.Physics.ShadowShapeBuilder.FromSetup(
             setup, entScale,
-            id => _physicsDataCache.GetGfxObj(id)?.BSP?.Root is not null);
+            id => _physicsDataCache.GetGfxObj(id)?.BSP?.Root is not null,
+            partPoseOverride: closedPose);
 
         // Substitute the real bounding-sphere radius for BSP shapes —
         // the pure builder's 2.0 placeholder works for typical doors
@@ -4254,6 +4267,37 @@ public sealed class GameWindow : IDisposable
         }
     }
 
+    /// <summary>
+    /// #175: the motion table's default-state pose — frame LowFrame of the
+    /// default style's first cycle animation — the pose an idle entity's
+    /// parts hold (retail: CPartArray init runs the motion table's default
+    /// state; collision tests the resulting live CPhysicsPart poses). Used
+    /// as the BSP shadow-shape part-pose override at registration. Returns
+    /// null (→ placement-frame fallback) when the entity has no motion
+    /// table, the table has no default cycle, or the frame doesn't cover
+    /// <paramref name="partCount"/> parts.
+    /// </summary>
+    private IReadOnlyList<DatReaderWriter.Types.Frame>? MotionTableDefaultPose(
+        uint motionTableId, int partCount)
+    {
+        if (motionTableId == 0u || partCount == 0 || _dats is null) return null;
+
+        var mt = _dats.Get<DatReaderWriter.DBObjs.MotionTable>(motionTableId);
+        if (mt is null) return null;
+
+        if (!mt.Cycles.TryGetValue((int)mt.DefaultStyle, out var cycle)
+            || cycle.Anims.Count == 0)
+            return null;
+
+        var animRef = cycle.Anims[0];
+        var anim = _dats.Get<DatReaderWriter.DBObjs.Animation>(animRef.AnimId);
+        if (anim is null || anim.PartFrames.Count == 0) return null;
+
+        int idx = System.Math.Clamp((int)animRef.LowFrame, 0, anim.PartFrames.Count - 1);
+        var frames = anim.PartFrames[idx].Frames;
+        return frames.Count >= partCount ? frames : null;
+    }
+
     /// <summary>
     /// R3-W4: one-time per-remote wiring of the animation-dispatch stack —
     /// the persistent <see cref="RemoteMotion.Sink"/> (ObservedOmega turn