feat: real-time live data integration

- lib/live-data.ts: Shared TypeScript client for blackroad-live-data Worker
- components/live-stats.tsx: LiveStatsBar, RecentRepos, AgentStatusGrid components
- app/page.tsx: Import LiveStatsBar in main page header

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

app/api/conversations/route.ts

@@ -0,0 +1,78 @@
+import { NextResponse } from 'next/server';
+
+export const runtime = 'edge';
+
+// KV binding CONVERSATIONS_KV for persistence (set in wrangler/Vercel env)
+// eslint-disable-next-line @typescript-eslint/no-explicit-any
+declare const CONVERSATIONS_KV: any;
+
+export interface Message {
+  role: 'user' | 'assistant';
+  content: string;
+  ts: string;
+}
+
+export interface Conversation {
+  id: string;
+  title: string;
+  agent: string;
+  messages: Message[];
+  created_at: string;
+  updated_at: string;
+  preview: string;
+}
+
+// ── GET /api/conversations ──────────────────────────────────────────────────
+export async function GET(request: Request) {
+  const url = new URL(request.url);
+  const limit = Math.min(parseInt(url.searchParams.get('limit') || '50'), 200);
+  const agent = url.searchParams.get('agent') || null;
+
+  try {
+    if (typeof CONVERSATIONS_KV !== 'undefined') {
+      const raw = await CONVERSATIONS_KV.get('convs:index', 'json') as Conversation[] | null;
+      let convs = raw ?? [];
+      if (agent) convs = convs.filter(c => c.agent === agent);
+      return NextResponse.json({ conversations: convs.slice(0, limit), total: convs.length });
+    }
+  } catch { /* KV not available */ }
+
+  return NextResponse.json({ conversations: [], total: 0, source: 'empty' });
+}
+
+// ── POST /api/conversations ─────────────────────────────────────────────────
+export async function POST(request: Request) {
+  let body: Partial<Conversation & { message: string }>;
+  try { body = await request.json(); }
+  catch { return NextResponse.json({ error: 'Invalid JSON' }, { status: 400 }); }
+
+  const now = new Date().toISOString();
+  const firstMsg: Message | undefined = body.message
+    ? { role: 'user', content: body.message, ts: now }
+    : undefined;
+
+  const conv: Conversation = {
+    id:         `conv_${Date.now()}_${Math.random().toString(36).slice(2, 7)}`,
+    title:      body.title || (body.message ? body.message.slice(0, 60) : 'New conversation'),
+    agent:      body.agent || 'lucidia',
+    messages:   firstMsg ? [firstMsg] : [],
+    created_at: now,
+    updated_at: now,
+    preview:    body.message ? body.message.slice(0, 120) : '',
+  };
+
+  try {
+    if (typeof CONVERSATIONS_KV !== 'undefined') {
+      const existing = (await CONVERSATIONS_KV.get('convs:index', 'json') as Conversation[] | null) ?? [];
+      const updated = [conv, ...existing].slice(0, 1000);
+      await CONVERSATIONS_KV.put('convs:index', JSON.stringify(updated), {
+        expirationTtl: 60 * 60 * 24 * 365,
+      });
+      await CONVERSATIONS_KV.put(`conv:${conv.id}`, JSON.stringify(conv), {
+        expirationTtl: 60 * 60 * 24 * 365,
+      });
+    }
+  } catch { /* KV not bound — return conv without persisting */ }
+
+  return NextResponse.json(conv, { status: 201 });
+}