diff --git a/controller/internal/web/funcmap.go b/controller/internal/web/funcmap.go
index b9c1c52..a8e2807 100644
--- a/controller/internal/web/funcmap.go
+++ b/controller/internal/web/funcmap.go
@@ -30,6 +30,20 @@ func getTimezone() *time.Location {
 	return webTimezone
 }
 
+// routeUnpublished reports whether the reverse proxy (Traefik) is withholding a deployed stack's public
+// route because the container is not healthy. Traefik's docker provider only publishes a route to a
+// container that is healthy (or has no healthcheck); an unhealthy or restarting container yields a 404
+// at its URL even though the card "looks deployed". Templates use this to surface that distinctly (F5),
+// so an unhealthy app with a dead URL isn't mistaken for a merely-degraded-but-reachable one.
+func routeUnpublished(state stacks.ContainerState) bool {
+	switch state {
+	case stacks.StateUnhealthy, stacks.StateRestarting:
+		return true
+	default:
+		return false
+	}
+}
+
 // templateFuncMap returns the FuncMap used by all HTML templates.
 func (s *Server) templateFuncMap() template.FuncMap {
 	loc := getTimezone()
@@ -102,6 +116,7 @@ func (s *Server) templateFuncMap() template.FuncMap {
 				return false
 			}
 		},
+		"routeUnpublished": routeUnpublished,
 		"logoURL": func(slug string) string {
 			return s.cfg.AppLogoURL(slug)
 		},
diff --git a/controller/internal/web/route_unpublished_test.go b/controller/internal/web/route_unpublished_test.go
new file mode 100644
index 0000000..a160463
--- /dev/null
+++ b/controller/internal/web/route_unpublished_test.go
@@ -0,0 +1,78 @@
+package web
+
+import (
+	"bytes"
+	"html/template"
+	"strings"
+	"testing"
+
+	"gitea.dooplex.hu/admin/felhom-controller/internal/config"
+	"gitea.dooplex.hu/admin/felhom-controller/internal/stacks"
+)
+
+// TestRouteUnpublished asserts F5: routeUnpublished is true exactly for the states where Traefik
+// withholds the public route (unhealthy / restarting) and false otherwise.
+func TestRouteUnpublished(t *testing.T) {
+	cases := []struct {
+		state stacks.ContainerState
+		want  bool
+	}{
+		{stacks.StateUnhealthy, true},
+		{stacks.StateRestarting, true},
+		{stacks.StateRunning, false},
+		{stacks.StateStarting, false},
+		{stacks.StateDeploying, false},
+		{stacks.StateStopped, false},
+		{stacks.StateExited, false},
+		{stacks.StateNotDeployed, false},
+		{stacks.StatePaused, false},
+	}
+	for _, c := range cases {
+		if got := routeUnpublished(c.state); got != c.want {
+			t.Errorf("routeUnpublished(%q) = %v, want %v", c.state, got, c.want)
+		}
+	}
+}
+
+// TestTemplatesParseWithFuncmap asserts the real embedded templates (including the stacks.html /
+// dashboard.html edits that reference routeUnpublished) parse with the production funcmap. Catches an
+// unregistered func or a template syntax error introduced by the F5 edits.
+func TestTemplatesParseWithFuncmap(t *testing.T) {
+	s := &Server{cfg: &config.Config{}}
+	if _, err := template.New("").Funcs(s.templateFuncMap()).ParseFS(templateFS, "templates/*.html"); err != nil {
+		t.Fatalf("templates failed to parse with funcmap: %v", err)
+	}
+}
+
+// TestRouteUnpublishedIndicatorRenders asserts the dashboard/stacks card guard renders the distinct
+// indicator for a DEPLOYED + unhealthy stack, and NOT for a healthy one — the exact condition both
+// edited templates use ({{if and .Deployed (routeUnpublished .State)}}).
+func TestRouteUnpublishedIndicatorRenders(t *testing.T) {
+	s := &Server{cfg: &config.Config{}}
+	const frag = `{{if and .Deployed (routeUnpublished .State)}}URL-NOT-PUBLISHED{{end}}`
+	tmpl, err := template.New("frag").Funcs(s.templateFuncMap()).Parse(frag)
+	if err != nil {
+		t.Fatal(err)
+	}
+	type row struct {
+		Deployed bool
+		State    stacks.ContainerState
+	}
+	render := func(r row) string {
+		var b bytes.Buffer
+		if err := tmpl.Execute(&b, r); err != nil {
+			t.Fatal(err)
+		}
+		return b.String()
+	}
+
+	if got := render(row{Deployed: true, State: stacks.StateUnhealthy}); !strings.Contains(got, "URL-NOT-PUBLISHED") {
+		t.Errorf("deployed+unhealthy should show the indicator, got %q", got)
+	}
+	if got := render(row{Deployed: true, State: stacks.StateRunning}); strings.Contains(got, "URL-NOT-PUBLISHED") {
+		t.Errorf("deployed+running must NOT show the indicator, got %q", got)
+	}
+	if got := render(row{Deployed: false, State: stacks.StateUnhealthy}); strings.Contains(got, "URL-NOT-PUBLISHED") {
+		t.Errorf("not-deployed must NOT show the indicator, got %q", got)
+	}
+}
diff --git a/controller/internal/web/templates/dashboard.html b/controller/internal/web/templates/dashboard.html
index 5b40e88..046d736 100644
--- a/controller/internal/web/templates/dashboard.html
+++ b/controller/internal/web/templates/dashboard.html
@@ -149,6 +149,7 @@
         <div class="stack-actions">
             <span class="stack-state-label">{{stateLabel .State}}</span>
             {{if .Orphaned}}<span class="badge badge-orphaned">Elavult</span>{{end}}
+            {{if and .Deployed (routeUnpublished .State)}}<span class="badge badge-route-unpublished" title="A proxy (Traefik) csak egészséges konténerhez publikál nyilvános útvonalat. Amíg az alkalmazás nem egészséges, az URL 404-et ad, pedig a konténer fut.">⚠ URL nem elérhető</span>{{end}}
 
             {{if .Protected}}
                 <span class="badge badge-protected">Védett</span>
diff --git a/controller/internal/web/templates/stacks.html b/controller/internal/web/templates/stacks.html
index 840495b..9c468f4 100644
--- a/controller/internal/web/templates/stacks.html
+++ b/controller/internal/web/templates/stacks.html
@@ -30,6 +30,9 @@
                     <a class="subdomain-link" href="https://{{$subdomain}}.{{$.Domain}}" target="_blank">
                         {{$subdomain}}.{{$.Domain}} ↗
                     </a>
+                    {{if and .Deployed (routeUnpublished .State)}}
+                    <span class="route-unpublished" title="A proxy (Traefik) csak egészséges konténerhez publikál nyilvános útvonalat. Amíg az alkalmazás nem egészséges, az URL nem érhető el (404), pedig a konténer fut.">⚠ URL nem elérhető – útvonal nincs publikálva</span>
+                    {{end}}
                     {{end}}
                 </div>
             </div>
diff --git a/controller/internal/web/templates/style.css b/controller/internal/web/templates/style.css
index 422858d..767e1ed 100644
--- a/controller/internal/web/templates/style.css
+++ b/controller/internal/web/templates/style.css
@@ -1249,6 +1249,20 @@ a.stat-card:hover {
     color: var(--orange);
 }
 
+/* F5: an unhealthy/restarting deployed app has its public route withheld by Traefik (404 at the URL). */
+.badge-route-unpublished {
+    background: var(--orange-bg);
+    color: var(--orange);
+    white-space: nowrap;
+}
+.route-unpublished {
+    display: inline-block;
+    margin-top: 2px;
+    font-size: 0.8em;
+    color: var(--orange);
+    white-space: nowrap;
+}
+
 /* Delete modal */
 .modal-overlay {
     position: fixed;