Frontend redesign chunk 6: Live view

New components/LiveView.tsx renders the default landing at "/": full-bleed
MapView (rail + legend from chunk 5) plus a new TimeScrubber strip below
it — real call-density bars over the selected 1h/6h/24h/7d window, tinted
by the worst severity in each bucket, playhead pinned to NOW. The playhead
doesn't scrub yet; that needs `resolved_at` on incidents, which doesn't
exist server-side (blocked chunk 13, in DEFERRED.md) — the density data
itself is live, not a fixture.

Distinguishes the two empty states UI_REDESIGN.md §4 calls out: a
configured-but-quiet org (nodes online, zero active incidents) now shows
"Listening — last check-in Xm ago" instead of rendering nothing, separate
from the zero-node case (chunk 10's Activation screen).

app/page.tsx's HomePage now renders LiveView directly for a signed-in,
provisioned user instead of the chunk-4 interim redirect to /incidents.

Per UI_REDESIGN.md chunk 6.

drb-frontend/components/LiveView.tsx

@@ -0,0 +1,79 @@
+"use client";
+
+/**
+ * Live — the default landing for every authenticated user (UI_REDESIGN.md
+ * §3, §5.1). Full-bleed map with the incident rail/legend MapView already
+ * renders (chunk 5), plus a time-density scrubber strip below it.
+ */
+import { useEffect, useState } from "react";
+import dynamic from "next/dynamic";
+import { useNodes } from "@/lib/useNodes";
+import { useActiveCalls, useCalls } from "@/lib/useCalls";
+import { useActiveIncidents } from "@/lib/useIncidents";
+import { TimeScrubber } from "@/components/TimeScrubber";
+
+const MapView = dynamic(() => import("@/components/MapView"), { ssr: false });
+
+function timeAgo(date: Date): string {
+  const s = Math.floor((Date.now() - date.getTime()) / 1000);
+  if (s < 60) return `${s}s ago`;
+  if (s < 3600) return `${Math.floor(s / 60)}m ago`;
+  return `${Math.floor(s / 3600)}h ago`;
+}
+
+export function LiveView() {
+  const { nodes, loading: nodesLoading } = useNodes();
+  const activeCalls = useActiveCalls();
+  const activeIncidents = useActiveIncidents();
+  // Wide-ish recent window: feeds both the incident-path polyline (chunk 5)
+  // and the scrubber's density bars. Not a fixture — real recent calls.
+  const { calls: recentCalls, loading: callsLoading } = useCalls(500);
+  const [lastUpdated, setLastUpdated] = useState<Date | null>(null);
+
+  useEffect(() => {
+    if (!nodesLoading) setLastUpdated(new Date());
+  }, [nodes, activeCalls, activeIncidents, nodesLoading]);
+
+  const configuredButQuiet = !nodesLoading && nodes.length > 0 && activeIncidents.length === 0;
+  const mostRecentSeen = configuredButQuiet
+    ? nodes
+        .map((n) => n.last_seen)
+        .filter((s): s is string => !!s)
+        .sort()
+        .at(-1)
+    : null;
+
+  return (
+    <div className="flex flex-col h-full">
+      <div className="relative flex-1 min-h-0">
+        {nodesLoading || callsLoading ? (
+          <div className="w-full h-full flex items-center justify-center text-ink-muted text-sm">
+            Loading map…
+          </div>
+        ) : (
+          <MapView
+            nodes={nodes}
+            activeCalls={activeCalls}
+            incidents={activeIncidents}
+            calls={recentCalls}
+            lastUpdated={lastUpdated}
+          />
+        )}
+
+        {/* Configured-and-quiet — distinct from "no nodes at all" (chunk 10's
+            Activation screen handles the zero-node case). A node that's
+            online but has heard nothing is NOT the same empty state as an
+            org with no equipment. */}
+        {configuredButQuiet && (
+          <div className="absolute top-12 left-1/2 -translate-x-1/2 z-[1001] pointer-events-none">
+            <span className="bg-surface/90 border border-line rounded-full px-3 py-1 text-xs text-ink-2 whitespace-nowrap">
+              ● Listening{mostRecentSeen ? ` — last check-in ${timeAgo(new Date(mostRecentSeen))}` : ""}
+            </span>
+          </div>
+        )}
+      </div>
+
+      <TimeScrubber calls={recentCalls} />
+    </div>
+  );
+}