diff --git a/Ymir.slnx b/Ymir.slnx
index 2db5400..53b0fac 100644
--- a/Ymir.slnx
+++ b/Ymir.slnx
@@ -4,6 +4,7 @@
     <Project Path="src/Ymir.Core/Ymir.Core.csproj" />
   </Folder>
   <Folder Name="/tests/">
+    <Project Path="tests/Ymir.Box3D.Parity/Ymir.Box3D.Parity.csproj" />
     <Project Path="tests/Ymir.Tests/Ymir.Tests.csproj" />
   </Folder>
   <Project Path="../CultMath/src/CultMath/CultMath.csproj" />
diff --git a/docs/box3d-parity.md b/docs/box3d-parity.md
index d33f2b7..d6f129f 100644
--- a/docs/box3d-parity.md
+++ b/docs/box3d-parity.md
@@ -16,8 +16,9 @@ torque lifetime, and numeric tolerances.
 
 `native/Ymir.Box3D` statically links the pinned C17 library into one small
 shared-library facade. The facade exports only blittable sphere overlap,
-sphere cast, capsule-versus-sphere membership, and version operations. This
-keeps Box3D's alpha C ABI out of Ymir's public managed contracts.
+sphere cast, capsule-versus-sphere membership, planar pair stepping, torque
+lifetime, and version operations. This keeps Box3D's alpha C ABI out of Ymir's
+public managed contracts.
 
 `tests/Ymir.Box3D.Parity` builds that facade through CMake and invokes it with
 source-generated .NET interop. Run it with:
@@ -42,12 +43,16 @@ is retained in the pinned submodule.
   includes rounded start and end caps and the same overlap slop.
 - Box3D query callback order is not a contract. Ymir sorts projected results by
   distance and stable entity id.
+- Contact begin facts are emitted after the world step.
+- Restitution uses the maximum of the two shape materials.
+- Applied torque is transient and cleared by each world step; a continuous
+  torque must be submitted again for the next step.
 
 ## Cut Line
 
 The current managed collision formulas are transitional. They may exist only
-while differential tests prove compatibility. The next parity slice covers a
-planar sphere-world step, transient forces and torques, restitution mixing,
-and begin/end contact events. Once those facts are projected through a stable
-Ymir native port, the managed solver, query geometry, and spatial indexes are
-deleted rather than retained as fallback authority.
+while differential tests prove compatibility. The remaining parity slice
+covers retained world sessions, end-contact lifecycle, continuous collision,
+and replay. Once those facts are projected through a stable Ymir native port,
+the managed solver, query geometry, and spatial indexes are deleted rather
+than retained as fallback authority.
diff --git a/native/Ymir.Box3D/ymir_box3d.c b/native/Ymir.Box3D/ymir_box3d.c
index f1ed29e..0756e3c 100644
--- a/native/Ymir.Box3D/ymir_box3d.c
+++ b/native/Ymir.Box3D/ymir_box3d.c
@@ -1,4 +1,5 @@
 #include <box3d/base.h>
+#include <box3d/box3d.h>
 #include <box3d/collision.h>
 #include <box3d/constants.h>
 #include <box3d/math_functions.h>
@@ -28,11 +29,88 @@ typedef struct ymir_box3d_cast_result
     float normal_y;
 } ymir_box3d_cast_result;
 
+typedef struct ymir_box3d_body_input
+{
+    float position_x;
+    float position_y;
+    float velocity_x;
+    float velocity_y;
+    float radius;
+    float mass;
+    float restitution;
+    int is_static;
+} ymir_box3d_body_input;
+
+typedef struct ymir_box3d_body_output
+{
+    float position_x;
+    float position_y;
+    float velocity_x;
+    float velocity_y;
+    float angular_velocity;
+} ymir_box3d_body_output;
+
+typedef struct ymir_box3d_pair_step_result
+{
+    ymir_box3d_body_output body_a;
+    ymir_box3d_body_output body_b;
+    int begin_contact_count;
+    int end_contact_count;
+    int hit_contact_count;
+} ymir_box3d_pair_step_result;
+
+typedef struct ymir_box3d_torque_result
+{
+    float angular_velocity_after_applied_step;
+    float angular_velocity_after_unforced_step;
+} ymir_box3d_torque_result;
+
 static b3Vec3 ymir_vec(float x, float y)
 {
     return (b3Vec3){x, 0.0f, y};
 }
 
+static b3BodyId ymir_create_body(b3WorldId world_id, const ymir_box3d_body_input* input)
+{
+    b3BodyDef body_def = b3DefaultBodyDef();
+    body_def.type = input->is_static != 0 ? b3_staticBody : b3_dynamicBody;
+    body_def.position = ymir_vec(input->position_x, input->position_y);
+    body_def.linearVelocity = ymir_vec(input->velocity_x, input->velocity_y);
+    body_def.motionLocks.linearY = true;
+    body_def.motionLocks.angularX = true;
+    body_def.motionLocks.angularZ = true;
+    body_def.enableSleep = false;
+    b3BodyId body_id = b3CreateBody(world_id, &body_def);
+
+    b3ShapeDef shape_def = b3DefaultShapeDef();
+    if (input->is_static == 0)
+    {
+        float volume = 4.0f / 3.0f * B3_PI * input->radius * input->radius * input->radius;
+        shape_def.density = input->mass / volume;
+    }
+    shape_def.baseMaterial.friction = 0.0f;
+    shape_def.baseMaterial.restitution = input->restitution;
+    shape_def.enableContactEvents = true;
+    shape_def.enableHitEvents = true;
+    b3Sphere sphere = {{0.0f, 0.0f, 0.0f}, input->radius};
+    b3CreateSphereShape(body_id, &shape_def, &sphere);
+    return body_id;
+}
+
+static ymir_box3d_body_output ymir_read_body(b3BodyId body_id)
+{
+    b3Pos position = b3Body_GetPosition(body_id);
+    b3Vec3 velocity = b3Body_GetLinearVelocity(body_id);
+    b3Vec3 angular_velocity = b3Body_GetAngularVelocity(body_id);
+    return (ymir_box3d_body_output){
+        .position_x = position.x,
+        .position_y = position.z,
+        .velocity_x = velocity.x,
+        .velocity_y = velocity.z,
+        .angular_velocity = angular_velocity.y,
+    };
+}
+
 YMIR_EXPORT int ymir_box3d_get_version(int* major, int* minor, int* revision)
 {
     b3Version version = b3GetVersion();
@@ -132,3 +210,55 @@ YMIR_EXPORT ymir_box3d_cast_result ymir_box3d_cast_sphere(
         .normal_y = output.normal.z,
     };
 }
+
+YMIR_EXPORT void ymir_box3d_step_pair(
+    const ymir_box3d_body_input* body_a_input,
+    const ymir_box3d_body_input* body_b_input,
+    float time_step,
+    int sub_step_count,
+    float restitution_threshold,
+    ymir_box3d_pair_step_result* result)
+{
+    b3WorldDef world_def = b3DefaultWorldDef();
+    world_def.gravity = b3Vec3_zero;
+    world_def.enableSleep = false;
+    world_def.restitutionThreshold = restitution_threshold;
+    b3WorldId world_id = b3CreateWorld(&world_def);
+
+    b3BodyId body_a = ymir_create_body(world_id, body_a_input);
+    b3BodyId body_b = ymir_create_body(world_id, body_b_input);
+    b3World_Step(world_id, time_step, sub_step_count);
+
+    b3ContactEvents events = b3World_GetContactEvents(world_id);
+    result->body_a = ymir_read_body(body_a);
+    result->body_b = ymir_read_body(body_b);
+    result->begin_contact_count = events.beginCount;
+    result->end_contact_count = events.endCount;
+    result->hit_contact_count = events.hitCount;
+
+    b3DestroyWorld(world_id);
+}
+
+YMIR_EXPORT ymir_box3d_torque_result ymir_box3d_torque_lifetime(float torque, float time_step, int sub_step_count)
+{
+    b3WorldDef world_def = b3DefaultWorldDef();
+    world_def.gravity = b3Vec3_zero;
+    world_def.enableSleep = false;
+    b3WorldId world_id = b3CreateWorld(&world_def);
+
+    ymir_box3d_body_input input = {
+        .radius = 1.0f,
+        .mass = 1.0f,
+        .is_static = 0,
+    };
+    b3BodyId body_id = ymir_create_body(world_id, &input);
+    b3Body_ApplyTorque(body_id, (b3Vec3){0.0f, torque, 0.0f}, true);
+    b3World_Step(world_id, time_step, sub_step_count);
+    float after_applied_step = b3Body_GetAngularVelocity(body_id).y;
+
+    b3World_Step(world_id, time_step, sub_step_count);
+    float after_unforced_step = b3Body_GetAngularVelocity(body_id).y;
+    b3DestroyWorld(world_id);
+
+    return (ymir_box3d_torque_result){after_applied_step, after_unforced_step};
+}
diff --git a/tests/Ymir.Box3D.Parity/Box3DOracle.cs b/tests/Ymir.Box3D.Parity/Box3DOracle.cs
index ca9345c..5e501b0 100644
--- a/tests/Ymir.Box3D.Parity/Box3DOracle.cs
+++ b/tests/Ymir.Box3D.Parity/Box3DOracle.cs
@@ -40,6 +40,18 @@ internal static partial class Box3DOracle
         float bodyY,
         float bodyRadius,
         int canEncroach);
+
+    [LibraryImport(LibraryName)]
+    internal static partial void ymir_box3d_step_pair(
+        in Box3DBodyInput bodyA,
+        in Box3DBodyInput bodyB,
+        float timeStep,
+        int subStepCount,
+        float restitutionThreshold,
+        out Box3DPairStepResult result);
+
+    [LibraryImport(LibraryName)]
+    internal static partial Box3DTorqueResult ymir_box3d_torque_lifetime(float torque, float timeStep, int subStepCount);
 }
 
 [StructLayout(LayoutKind.Sequential)]
@@ -58,3 +70,35 @@ internal readonly record struct Box3DCastResult(
 {
     public bool IsHit => Hit != 0;
 }
+
+[StructLayout(LayoutKind.Sequential)]
+internal readonly record struct Box3DBodyInput(
+    float PositionX,
+    float PositionY,
+    float VelocityX,
+    float VelocityY,
+    float Radius,
+    float Mass,
+    float Restitution,
+    int IsStatic);
+
+[StructLayout(LayoutKind.Sequential)]
+internal readonly record struct Box3DBodyOutput(
+    float PositionX,
+    float PositionY,
+    float VelocityX,
+    float VelocityY,
+    float AngularVelocity);
+
+[StructLayout(LayoutKind.Sequential)]
+internal readonly record struct Box3DPairStepResult(
+    Box3DBodyOutput BodyA,
+    Box3DBodyOutput BodyB,
+    int BeginContactCount,
+    int EndContactCount,
+    int HitContactCount);
+
+[StructLayout(LayoutKind.Sequential)]
+internal readonly record struct Box3DTorqueResult(
+    float AngularVelocityAfterAppliedStep,
+    float AngularVelocityAfterUnforcedStep);
diff --git a/tests/Ymir.Box3D.Parity/Box3DParityTests.cs b/tests/Ymir.Box3D.Parity/Box3DParityTests.cs
index 2c740cd..828c501 100644
--- a/tests/Ymir.Box3D.Parity/Box3DParityTests.cs
+++ b/tests/Ymir.Box3D.Parity/Box3DParityTests.cs
@@ -83,4 +83,41 @@ public sealed class Box3DParityTests
 
         Assert.True(result.IsHit);
     }
+
+    [Fact]
+    public void PairStepEmitsBeginContactAndSeparatesOverlappingSpheres()
+    {
+        var bodyA = new Box3DBodyInput(-0.9f, 0.0f, 0.0f, 0.0f, 1.0f, 1.0f, 0.0f, 0);
+        var bodyB = new Box3DBodyInput(0.9f, 0.0f, 0.0f, 0.0f, 1.0f, 1.0f, 0.0f, 0);
+
+        Box3DOracle.ymir_box3d_step_pair(in bodyA, in bodyB, 1.0f / 60.0f, 4, 0.0f, out var result);
+
+        Assert.Equal(1, result.BeginContactCount);
+        Assert.True(result.BodyA.PositionX < -0.9f);
+        Assert.True(result.BodyB.PositionX > 0.9f);
+    }
+
+    [Fact]
+    public void PairStepUsesMaximumRestitution()
+    {
+        var bodyA = new Box3DBodyInput(-1.0f, 0.0f, 1.0f, 0.0f, 1.0f, 1.0f, 0.1f, 0);
+        var bodyB = new Box3DBodyInput(1.0f, 0.0f, -1.0f, 0.0f, 1.0f, 1.0f, 0.8f, 0);
+
+        Box3DOracle.ymir_box3d_step_pair(in bodyA, in bodyB, 1.0f / 60.0f, 4, 0.0f, out var result);
+
+        Assert.True(result.BodyA.VelocityX < -0.7f);
+        Assert.True(result.BodyB.VelocityX > 0.7f);
+    }
+
+    [Fact]
+    public void TorqueIsClearedAfterEachWorldStep()
+    {
+        var result = Box3DOracle.ymir_box3d_torque_lifetime(0.4f, 0.1f, 4);
+
+        Assert.True(result.AngularVelocityAfterAppliedStep > 0.0f);
+        Assert.Equal(
+            result.AngularVelocityAfterAppliedStep,
+            result.AngularVelocityAfterUnforcedStep,
+            precision: 5);
+    }
 }
diff --git a/tests/Ymir.Box3D.Parity/Ymir.Box3D.Parity.csproj b/tests/Ymir.Box3D.Parity/Ymir.Box3D.Parity.csproj
index 78d766d..79466d8 100644
--- a/tests/Ymir.Box3D.Parity/Ymir.Box3D.Parity.csproj
+++ b/tests/Ymir.Box3D.Parity/Ymir.Box3D.Parity.csproj
@@ -8,8 +8,8 @@
     <IsPackable>false</IsPackable>
     <NativeSourceDir>$(MSBuildThisFileDirectory)..\..\native\Ymir.Box3D</NativeSourceDir>
     <NativeBuildDir>$(MSBuildThisFileDirectory)..\..\artifacts\box3d-native\$(Configuration)</NativeBuildDir>
-    <CMakeExe Condition="'$(OS)' == 'Windows_NT'">C:\Program Files\CMake\bin\cmake.exe</CMakeExe>
-    <CMakeExe Condition="'$(OS)' != 'Windows_NT'">cmake</CMakeExe>
+    <CMakeExe Condition="'$(CMakeExe)' == '' and '$(OS)' == 'Windows_NT' and Exists('C:\Program Files\CMake\bin\cmake.exe')">C:\Program Files\CMake\bin\cmake.exe</CMakeExe>
+    <CMakeExe Condition="'$(CMakeExe)' == ''">cmake</CMakeExe>
   </PropertyGroup>
 
   <ItemGroup>