diff --git a/crates/difftest/src/units/boolean_merge_p2.rs b/crates/difftest/src/units/boolean_merge_p2.rs
index e91cd66c7..a997b105f 100644
--- a/crates/difftest/src/units/boolean_merge_p2.rs
+++ b/crates/difftest/src/units/boolean_merge_p2.rs
@@ -32,6 +32,7 @@ use solidcore::geom::object::{NotifyOperation, ObjectRef};
 use solidcore::heal::stitch::p1::{DefaultStitchCallback, Stitch};
 use solidcore::kernel::Kernel;
 use solidcore::topology;
+use solidcore::topology::brep_cache::{arena_identity, CacheObject};
 use solidcore::topology::topology::Topology;
 use solidcore::topology::topology_traverser::Marks;
 use solidcore::topology::{
@@ -637,6 +638,14 @@ fn run_rust(i: &Inputs, p: &Prepared) -> Result<Output, HarnessError> {
             let edge_dest = |e: EdgeId| key(2_000_000, edge::TYPE, e.index());
             let face_source = |f: FaceId| key(5_000_000, face::p2::TYPE, f.index());
             let face_dest = |f: FaceId| key(4_000_000, face::p2::TYPE, f.index());
+            // The operands' edges and faces own their curves and surfaces under these
+            // names, as the library names them (`MakeFace`'s infinite-region rays solve
+            // on a B-rep cache whose trees hold only geometry owned under them).
+            let brep = Some(arena_identity(CacheObject::Brep));
+            crate::util::own_edge_curves(&mut a, &edge_dest, brep);
+            crate::util::own_face_surfaces(&mut a, &face_dest);
+            crate::util::own_edge_curves(b, &edge_source, brep);
+            crate::util::own_face_surfaces(b, &face_source);
             let mut copy = TopologyCopy {
                 vertices: VertexCopy {
                     records: &mut records,
diff --git a/crates/difftest/src/units/topology_brep_p6.rs b/crates/difftest/src/units/topology_brep_p6.rs
index 0695002e8..cc26783f3 100644
--- a/crates/difftest/src/units/topology_brep_p6.rs
+++ b/crates/difftest/src/units/topology_brep_p6.rs
@@ -927,6 +927,11 @@ fn make_faces_rust(i: &Inputs) -> Result<Output, HarnessError> {
     counts(&fixture.graph).ok_or_else(|| harness("fixture construction failed"))?;
     let (mut b, _) = shared::import(&fixture.graph)?;
     b.set_key(ObjectKey(0xB000_0000));
+    // The fixture's edges own their curves, as its faces own their surfaces (the import
+    // gives those the face names of `key_of`). The ray fires of the infinite-region
+    // search find an edge from its curve's owner, under the runner's names.
+    let brep = solidcore::topology::brep::p2::brep_ref(&b);
+    crate::util::own_edge_curves(&mut b, &|e| key_of(EntityRef::Edge(e)), Some(brep));
     let resolved = resolve(i, &b)?;
     let mut records = seeded_records(&b);
     let mut attributes = AttributeStore::default();
diff --git a/crates/difftest/src/util.rs b/crates/difftest/src/util.rs
index 8819dcfd2..fd08b1a10 100644
--- a/crates/difftest/src/util.rs
+++ b/crates/difftest/src/util.rs
@@ -1,8 +1,9 @@
 //! Small conversions shared by the unit runners in [`crate::units`].
 
+use solidcore::geom::object::ObjectRef;
 use solidcore::math::{Point2, Vec3};
 use solidcore::topology::brep_cache::{arena_identity, CacheObject};
-use solidcore::topology::Brep;
+use solidcore::topology::{Brep, EdgeId, FaceId};
 
 /// A JSON `[x, y, z]` as a [`Vec3`].
 #[must_use]
@@ -182,19 +183,38 @@ fn nurb_bits(b: &solidcore::nurbs::b_spline_surface::BSplineSurface) -> Option<V
 /// B-rep's geometry has (its edge or face, by [`arena_identity`]; curves also the
 /// B-rep), which the B-rep cache solves read (the import leaves geometry unowned).
 pub fn own_arena_geometry(b: &mut Brep) {
+    own_edge_curves(
+        b,
+        &|id| arena_identity(CacheObject::Edge(id)),
+        Some(arena_identity(CacheObject::Brep)),
+    );
+    own_face_surfaces(b, &|id| arena_identity(CacheObject::Face(id)));
+}
+
+/// Gives every edge curve of an imported B-rep its edge as owner, under `edge_key`:
+/// the name the runner hands the library for that edge (its `key_of` or cache keys).
+/// The topology solver's B-rep trees and edge lookups compare owners with those names;
+/// `brep` is the owner edge's B-rep as `Curve::set_owner` takes it.
+pub fn own_edge_curves(
+    b: &mut Brep,
+    edge_key: &dyn Fn(EdgeId) -> ObjectRef,
+    brep: Option<ObjectRef>,
+) {
     let edges: Vec<_> = b.edges().ids().collect();
     for id in edges {
         if let Some(curve) = b.edge_mut(id).ok().and_then(|e| e.curve.as_mut()) {
-            let _ = curve.set_owner(
-                Some(arena_identity(CacheObject::Edge(id))),
-                Some(arena_identity(CacheObject::Brep)),
-            );
+            let _ = curve.set_owner(Some(edge_key(id)), brep);
         }
     }
+}
+
+/// Gives every face surface of an imported B-rep its face as owner, under `face_key`
+/// (as [`own_edge_curves`] for edges).
+pub fn own_face_surfaces(b: &mut Brep, face_key: &dyn Fn(FaceId) -> ObjectRef) {
     let faces: Vec<_> = b.faces().ids().collect();
     for id in faces {
         if let Some(surface) = b.face_mut(id).ok().and_then(|f| f.surface.as_mut()) {
-            let _ = surface.set_owner(Some(arena_identity(CacheObject::Face(id))));
+            let _ = surface.set_owner(Some(face_key(id)));
         }
     }
 }