fix(integrate): sort boundary edges as pairs

Assisted-by: GLM 5.3 Flash

CHANGELOG.md

@@ -38,6 +38,12 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
   standard errors, t and F statistics read factored sums of squares
   instead of reporting infinity beside zero evidence.
 
+**Integration and optimisation.**
+
+- `TriangleMesh2D.BoundaryEdges` returns the mesh's own edges: the
+  boundary pairs sort as pairs, never as one flat index list that
+  interleaves the endpoints of unrelated edges.
+
 ## [1.0.0] - 2026-09-03
 
 The initial release of Tensor, a scientific computing library in pure

integrate/fem2d.go

@@ -114,13 +114,25 @@ func (m *TriangleMesh2D) BoundaryEdges() []int {
 		count[key(b, c)]++
 		count[key(c, a)]++
 	}
-	edges := make([]int, 0, 8)
+	sets := make([][2]int, 0, len(count))
 	for e, n := range count {
 		if n == 1 {
-			edges = append(edges, e[0], e[1])
+			sets = append(sets, e)
 		}
 	}
-	slices.Sort(edges)
+	// The pairs sort as pairs, never as one flat index list: a flat sort
+	// interleaves the endpoints of unrelated edges and hands back pairs
+	// the mesh does not carry.
+	slices.SortFunc(sets, func(x, y [2]int) int {
+		if x[0] != y[0] {
+			return x[0] - y[0]
+		}
+		return x[1] - y[1]
+	})
+	edges := make([]int, 0, 2*len(sets))
+	for _, e := range sets {
+		edges = append(edges, e[0], e[1])
+	}
 	return edges
 }
 

integrate/fem2d_test.go

@@ -434,6 +434,34 @@ func TestTriangleMesh2DBoundaryEdges(t *testing.T) {
 	}
 }
 
+// TestTriangleMesh2DBoundaryEdgesAreMeshEdges pins the pair contract of
+// BoundaryEdges: every returned pair must be an edge the mesh actually
+// carries, and the pairs must come out sorted, which a sort of the flat
+// index list cannot deliver (it interleaves unrelated endpoints).
+func TestTriangleMesh2DBoundaryEdgesAreMeshEdges(t *testing.T) {
+	mesh, err := GridTriangleMesh2D(0, 0, 1, 1, 1, 1)
+	if err != nil {
+		t.Fatalf("GridTriangleMesh2D: %v", err)
+	}
+	edges := mesh.BoundaryEdges()
+	// The square's four sides: (0,1), (0,2), (1,3), (2,3) in sorted
+	// pair order.
+	want := []int{0, 1, 0, 2, 1, 3, 2, 3}
+	if len(edges) != len(want) {
+		t.Fatalf("boundary edge count %d, want %d", len(edges)/2, len(want)/2)
+	}
+	for p := 0; p < len(edges); p += 2 {
+		if edges[p] > edges[p+1] {
+			t.Fatalf("edge [%d,%d] is not sorted as a pair", edges[p], edges[p+1])
+		}
+	}
+	for p := range len(want) {
+		if edges[p] != want[p] {
+			t.Fatalf("boundary edges %v, want %v", edges, want)
+		}
+	}
+}
+
 // TestSolvePoissonFEM2DDuplicateDirichletNode pins the documented rule
 // for a node listed more than once: the last value is the prescribed
 // one and the node enters the assembled system exactly once, so the