diff --git a/modules/mesh-delivery-assigner/cmd/mesh-delivery-assigner/integration_test.go b/modules/mesh-delivery-assigner/cmd/mesh-delivery-assigner/integration_test.go
index eac7f57..152b03e 100644
--- a/modules/mesh-delivery-assigner/cmd/mesh-delivery-assigner/integration_test.go
+++ b/modules/mesh-delivery-assigner/cmd/mesh-delivery-assigner/integration_test.go
@@ -406,6 +406,32 @@ func TestWantsAreWrittenAndNoDifferenceIs(t *testing.T) {
 	if !cleared {
 		t.Errorf("the condition of web on neither list on g14 was not cleared once g14 got its want")
 	}
+
+	// Issue 1126 (ADR 0547 §2): the catalogue's placement reaches the indexer's state naming web on every node the
+	// assignments name it on. Each node then composes its own: its want names the build alone (Self, no composition), and
+	// its own want says it composes its own, which the node agent reads (mesh-host's TestNats...ComposesAndAppliesItsOwn).
+	for _, node := range []string{"ace", "g14", "shanks"} {
+		pl, err := delivery.EncodePlacement(delivery.Placement{Node: node, Modules: []delivery.PlacedModule{{Module: "web"}}})
+		if err != nil {
+			t.Fatal(err)
+		}
+		pkey, _ := delivery.PlacementKey(node)
+		b.putJSON(t, delivery.PlacementBucket, pkey, pl)
+	}
+	if w := b.wantNow(t, "ace", "web", "ace's want once placed: the build alone, composed by the node", func(w delivery.Want) bool { return w.Self }); w.Composed != "" || w.FP != fNew {
+		t.Errorf("ace's want once placed = %+v", w)
+	}
+	nkey, _ := delivery.WantNodeKey("ace")
+	var self bool
+	for deadline := time.Now().Add(10 * time.Second); time.Now().Before(deadline) && !self; time.Sleep(100 * time.Millisecond) {
+		if e, err := b.buckets[delivery.AssignerWantsBucket].Get(b.ctx, nkey); err == nil {
+			nw, err := delivery.DecodeNodeWant(e.Value())
+			self = err == nil && nw.Self
+		}
+	}
+	if !self {
+		t.Error("ace's own want does not say it composes its own once placed")
+	}
 }
 
 // 1297/B9 (the assigner's half, ADR 0528 clause 6): started whole, the assigner holds a fingerprint whose health check