diff --git a/module/services/accounts/code/fixtures/installations.go b/module/services/accounts/code/fixtures/installations.go
index d30749f41..ad56195fd 100644
--- a/module/services/accounts/code/fixtures/installations.go
+++ b/module/services/accounts/code/fixtures/installations.go
@@ -150,8 +150,13 @@ func (i *Installations) Converge(ctx context.Context) error {
 				w.Info("fixture installation installed", wool.Field("installation", row.declared.describe()), wool.Field("installation_id", installation.GetId()))
 			}
 			// The authority core holds the same installation, which the host
-			// interfaces decide with (coreInstall).
-			if err := i.coreInstall(ctx, row); err != nil {
+			// interfaces decide with (coreInstall). A target the core has not
+			// composed yet keeps the row for the next pass.
+			coreWaits := false
+			switch err := i.coreInstall(ctx, row); {
+			case errors.Is(err, errCoreTargetNotComposed):
+				coreWaits = true
+			case err != nil:
 				failures = append(failures, fmt.Errorf("fixture installation %s: %w", row.declared.describe(), err))
 			}
 			// Each declared team is exposed once the installation admits it (an
@@ -164,7 +169,7 @@ func (i *Installations) Converge(ctx context.Context) error {
 					unexposed = append(unexposed, teamID)
 				}
 			}
-			if row.teamIDs = unexposed; len(row.teamIDs) > 0 {
+			if row.teamIDs = unexposed; len(row.teamIDs) > 0 || coreWaits {
 				remaining = append(remaining, row)
 			}
 		}
@@ -173,6 +178,10 @@ func (i *Installations) Converge(ctx context.Context) error {
 	return errors.Join(failures...)
 }
 
+// errCoreTargetNotComposed is a declared installation whose target the
+// authority core has not composed yet; the next pass installs it there.
+var errCoreTargetNotComposed = errors.New("the authority core has not composed this target yet")
+
 // coreInstall performs the declared installation in the authority core as the
 // host's own setup (InstallAsHost), then grants the installer role to its
 // owner and its role to each declared team (GrantRoleAsHost), as the local
@@ -187,8 +196,17 @@ func (i *Installations) coreInstall(ctx context.Context, row pendingInstallation
 		return err
 	}
 	// A module's installation is accounts' own record, which Converge's install
-	// made; the core reads it and installs no module itself.
-	if m, err := core.Composed(ctx, row.declared.Target); err == nil && m.Kind != domain.KindSolution {
+	// made; the core reads it and installs no module itself. A target the core
+	// has not composed yet is waited on: the pass that applies its delivery
+	// composes it.
+	m, err := core.Composed(ctx, row.declared.Target)
+	if code, ok := domain.CodeOf(err); ok && code == domain.NotFound {
+		return fmt.Errorf("%w: %s", errCoreTargetNotComposed, row.declared.Target)
+	}
+	if err != nil {
+		return fmt.Errorf("the authority core: %w", err)
+	}
+	if m.Kind != domain.KindSolution {
 		return nil
 	}
 	inst, err := core.InstallAsHost(ctx, row.orgID, row.declared.Target, row.declared.Role, row.ownerID, i.service.AuthorityInstallStep())
@@ -224,7 +242,7 @@ func (i *Installations) ConvergeAuthority(ctx context.Context) error {
 	var failures []error
 	for _, row := range i.pending {
 		err := i.coreInstall(ctx, row)
-		if code, ok := domain.CodeOf(err); ok && code == domain.NotFound {
+		if code, ok := domain.CodeOf(err); errors.Is(err, errCoreTargetNotComposed) || ok && code == domain.NotFound {
 			continue
 		}
 		if err != nil {
diff --git a/module/services/accounts/code/pkg/adapters/host_interface_conformance_test.go b/module/services/accounts/code/pkg/adapters/host_interface_conformance_test.go
index 3a63a8d51..19f5f5975 100644
--- a/module/services/accounts/code/pkg/adapters/host_interface_conformance_test.go
+++ b/module/services/accounts/code/pkg/adapters/host_interface_conformance_test.go
@@ -828,6 +828,39 @@ func runHostInterfaceFixture(t *testing.T) {
 		require.Greater(t, count, 0, "the suite's revocations are audited")
 	})
 
+	// A solution the composition delivers once the host is running is composed
+	// in the authority core by the pass that applies it, before the fixture's
+	// installations converge in that same pass: the declared installation is
+	// then the core's too, active at the declaring organization alone, and the
+	// declared team holds its role there.
+	t.Run("a solution delivered to a running host is installed where the fixture declares it", func(t *testing.T) {
+		reconciler.AfterEachPass(installations.Converge)
+		t.Cleanup(func() { reconciler.AfterEachPass(nil) })
+		note := wireScope("conformance-late.note", "read")
+		deliverSolution(t, ctx, conn, signer, conformanceSolution{alias: "conformance-late", generation: 1, ceilings: []*authorityv1.WorkScopeV1{note},
+			roles: map[string][]*authorityv1.WorkScopeV1{"installer": {note}, "viewer": {note}}})
+		installed := func(caller authority.Person, org string) (domain.Installation, bool) {
+			t.Helper()
+			all, err := core.Installations(ctx, caller, org)
+			require.NoError(t, err)
+			for _, inst := range all {
+				if inst.Target == "conformance-late" {
+					return inst, true
+				}
+			}
+			return domain.Installation{}, false
+		}
+		inst, ok := installed(alex, fixtureOrganization)
+		require.True(t, ok, "the pass that applied the delivery installed it in the core")
+		require.Equal(t, domain.Active, inst.Status)
+		_, ok = installed(authority.Person{ID: conformanceZoe, Organization: globexOrganization, SessionID: "conformance-harness"}, globexOrganization)
+		require.False(t, ok, "and nowhere the fixture does not declare it")
+		grants, err := core.ListRoleGrants(ctx, alex, fixtureOrganization, inst.ID)
+		require.NoError(t, err)
+		finance := teamNamed(t, ctx, svc, fixtureOrganization, "Finance")
+		require.Contains(t, grants, domain.RoleGrant{InstallationID: inst.ID, Role: "viewer", TeamID: finance}, "the declared team holds its role")
+	})
+
 	// Last, because the envelope it writes becomes every module's ceiling: a
 	// real envelope write that narrows a module's binding (the write
 	// PutModuleEnvelope makes, without its platform administrator check) is
diff --git a/module/services/accounts/code/pkg/adapters/testdata/host-interface-conformance.yaml b/module/services/accounts/code/pkg/adapters/testdata/host-interface-conformance.yaml
index e7ec4f9e4..37aa1ab2e 100644
--- a/module/services/accounts/code/pkg/adapters/testdata/host-interface-conformance.yaml
+++ b/module/services/accounts/code/pkg/adapters/testdata/host-interface-conformance.yaml
@@ -152,3 +152,6 @@ installations:
   - {org: Acme Corp, target: conformance-proposals, role: viewer, owner: alex@acme.test, teams: [Finance]}
   # The assistant solution acts for itself down a chain of modules.
   - {org: Acme Corp, target: conformance-assistant, role: viewer, owner: alex@acme.test}
+  # Delivered only once the host is running, as a composition delivers a
+  # solution after boot: installed at Acme alone, and reached by its finance team.
+  - {org: Acme Corp, target: conformance-late, role: viewer, owner: alex@acme.test, teams: [Finance]}
diff --git a/module/services/accounts/code/pkg/business/authority_core_delivery.go b/module/services/accounts/code/pkg/business/authority_core_delivery.go
index 7135736a3..3a53612d4 100644
--- a/module/services/accounts/code/pkg/business/authority_core_delivery.go
+++ b/module/services/accounts/code/pkg/business/authority_core_delivery.go
@@ -138,8 +138,7 @@ func coreDeliveryError(err error) error {
 // reconcileAuthorityCore composes, in the core, every delivery accounts has
 // applied: what a host runs once its core is built, so a module delivered
 // before this host decided through the core, or while its core could not be
-// built, is composed there too. Each is read from the inbox's exact applied
-// generation, the signed documents accounts verified when it took them.
+// built, is composed there too.
 func (s *Service) reconcileAuthorityCore(ctx context.Context) error {
 	if s.deliveryStore == nil {
 		return nil
@@ -150,29 +149,57 @@ func (s *Service) reconcileAuthorityCore(ctx context.Context) error {
 	}
 	var failures []error
 	for _, record := range records {
-		manifest, err := record.AppliedManifest()
-		if err != nil || manifest == nil {
-			continue
-		}
-		var delivered *SolutionDeliveryRecord
-		if err := s.store.WithControlPlane(ctx, func(ctx context.Context) error {
-			var err error
-			delivered, err = s.deliveryStore.ReadDeliveredDocument(ctx, record.BindingID, record.Applied.Generation)
-			return err
-		}); err != nil {
-			failures = append(failures, fmt.Errorf("binding %s: %w", record.BindingID, err))
-			continue
-		}
-		if delivered == nil {
-			continue
-		}
-		var signed *compositionv1.SignedManifestV1
-		if len(delivered.AuthorityDocument) > 0 {
-			signed = &compositionv1.SignedManifestV1{Document: delivered.AuthorityDocument, Envelope: delivered.AuthorityEnvelope}
-		}
-		if _, err := s.applyCoreModule(ctx, manifest, delivered.Payload, signed); err != nil {
+		if err := s.composeAppliedDelivery(ctx, record); err != nil {
 			failures = append(failures, fmt.Errorf("binding %s: %w", record.BindingID, err))
 		}
 	}
 	return errors.Join(failures...)
 }
+
+// composeAppliedDelivery composes one binding's applied generation in the
+// core, read from the inbox's exact applied generation: the signed documents
+// accounts verified when it took them. Every delivery path reaches the core
+// this way, the composition interface's and the host's delivery endpoint
+// alike, so a solution delivered to a running host is one the core can
+// install. A generation the core already holds changes nothing.
+func (s *Service) composeAppliedDelivery(ctx context.Context, record *SolutionHostBindingRecord) error {
+	if s.deliveryStore == nil || record == nil {
+		return nil
+	}
+	manifest, err := record.AppliedManifest()
+	if err != nil || manifest == nil {
+		return nil
+	}
+	var delivered *SolutionDeliveryRecord
+	if err := s.store.WithControlPlane(ctx, func(ctx context.Context) error {
+		var err error
+		delivered, err = s.deliveryStore.ReadDeliveredDocument(ctx, record.BindingID, record.Applied.Generation)
+		return err
+	}); err != nil {
+		return err
+	}
+	if delivered == nil {
+		return nil
+	}
+	var signed *compositionv1.SignedManifestV1
+	if len(delivered.AuthorityDocument) > 0 {
+		signed = &compositionv1.SignedManifestV1{Document: delivered.AuthorityDocument, Envelope: delivered.AuthorityEnvelope}
+	}
+	_, err = s.applyCoreModule(ctx, manifest, delivered.Payload, signed)
+	return err
+}
+
+// composeAppliedBinding composes binding's applied generation in the core,
+// right after a pass applied it.
+func (s *Service) composeAppliedBinding(ctx context.Context, binding string) error {
+	records, err := s.ListSolutionHostBindings(ctx)
+	if err != nil {
+		return err
+	}
+	for _, record := range records {
+		if record.BindingID == binding {
+			return s.composeAppliedDelivery(ctx, record)
+		}
+	}
+	return nil
+}
diff --git a/module/services/accounts/code/pkg/business/solution_host_bindings.go b/module/services/accounts/code/pkg/business/solution_host_bindings.go
index f253c5993..6aab5c03b 100644
--- a/module/services/accounts/code/pkg/business/solution_host_bindings.go
+++ b/module/services/accounts/code/pkg/business/solution_host_bindings.go
@@ -391,6 +391,14 @@ func (r *SolutionHostBindingReconciler) RunOnce(ctx context.Context) error {
 			}
 			failures = append(failures, fmt.Errorf("apply binding %q generation %d: %w",
 				applied.Document.Binding, applied.Document.Generation, err))
+			continue
+		}
+		// The applied generation is composed in the authority core at once,
+		// whichever path delivered it: a solution the host's delivery endpoint
+		// took is then one the core installs and the host interfaces decide.
+		if err := r.service.composeAppliedBinding(ctx, applied.Document.Binding); err != nil {
+			failures = append(failures, fmt.Errorf("compose binding %q generation %d in the authority core: %w",
+				applied.Document.Binding, applied.Document.Generation, err))
 		}
 	}
 
diff --git a/module/services/accounts/code/pkg/infra/testdata/control_plane_call_sites.txt b/module/services/accounts/code/pkg/infra/testdata/control_plane_call_sites.txt
index bcd45c8a4..46ea6b557 100644
--- a/module/services/accounts/code/pkg/infra/testdata/control_plane_call_sites.txt
+++ b/module/services/accounts/code/pkg/infra/testdata/control_plane_call_sites.txt
@@ -29,7 +29,7 @@ pkg/auth/pg/session_store.go: (*SessionStore).RotateRefresh: WithControlPlane
 pkg/business/audit.go: (*DurableAuditEmitter).Emit: WithControlPlane
 pkg/business/audit.go: (*Service).AggregateAuditLog: WithControlPlane
 pkg/business/audit.go: (*Service).QueryAuditLog: WithControlPlane
-pkg/business/authority_core_delivery.go: (*Service).reconcileAuthorityCore: WithControlPlane
+pkg/business/authority_core_delivery.go: (*Service).composeAppliedDelivery: WithControlPlane
 pkg/business/authority_delivery.go: (*Service).verifyAppliedAuthorityDocument: WithControlPlane
 pkg/business/connector_credentials.go: (*Service).SourceSigningSecret: WithControlPlane
 pkg/business/current_installation.go: (*Service).ModuleCurrentInstallation: WithControlPlane