feat: add Vercel AI SDK integration example (Next.js + runTeam)

Next.js App Router demo showing OMA + Vercel AI SDK working together:
- Backend: OMA runTeam() orchestrates researcher + writer agents
- Frontend: AI SDK useChat hook for streaming chat UI
- Uses DeepSeek via OpenAI-compatible provider

examples/with-vercel-ai-sdk/.gitignore

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+node_modules/
+.next/
+.env
+.env.local
+*.tsbuildinfo

examples/with-vercel-ai-sdk/README.md

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+# with-vercel-ai-sdk
+
+A Next.js demo showing **open-multi-agent** (OMA) and **Vercel AI SDK** working together:
+
+- **OMA** orchestrates a research team (researcher agent + writer agent) via `runTeam()`
+- **AI SDK** streams the result to a chat UI via `useChat` + `streamText`
+
+## How it works
+
+```
+User message
+  │
+  ▼
+API route (app/api/chat/route.ts)
+  │
+  ├─ Phase 1: OMA runTeam()
+  │    coordinator decomposes goal → researcher gathers info → writer drafts article
+  │
+  └─ Phase 2: AI SDK streamText()
+       streams the team's output to the browser
+  │
+  ▼
+Chat UI (app/page.tsx) — useChat hook renders streamed response
+```
+
+## Setup
+
+```bash
+# 1. From repo root, install OMA dependencies
+cd ../..
+npm install
+
+# 2. Back to this example
+cd examples/with-vercel-ai-sdk
+npm install
+
+# 3. Set your API key
+export ANTHROPIC_API_KEY=sk-ant-...
+
+# 4. Run
+npm run dev
+```
+
+`npm run dev` automatically builds OMA before starting Next.js (via the `predev` script).
+
+Open [http://localhost:3000](http://localhost:3000), type a topic, and watch the research team work.
+
+## Prerequisites
+
+- Node.js >= 18
+- `ANTHROPIC_API_KEY` environment variable (used by both OMA and AI SDK)
+
+## Key files
+
+| File | Role |
+|------|------|
+| `app/api/chat/route.ts` | Backend — OMA orchestration + AI SDK streaming |
+| `app/page.tsx` | Frontend — chat UI with `useChat` hook |
+| `package.json` | References OMA via `file:../../` (local link) |

examples/with-vercel-ai-sdk/app/api/chat/route.ts

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+import { streamText, convertToModelMessages, type UIMessage } from 'ai'
+import { createOpenAICompatible } from '@ai-sdk/openai-compatible'
+import { OpenMultiAgent } from '@jackchen_me/open-multi-agent'
+import type { AgentConfig } from '@jackchen_me/open-multi-agent'
+
+export const maxDuration = 120
+
+// --- DeepSeek via OpenAI-compatible API ---
+const DEEPSEEK_BASE_URL = 'https://api.deepseek.com'
+const DEEPSEEK_MODEL = 'deepseek-chat'
+
+const deepseek = createOpenAICompatible({
+  name: 'deepseek',
+  baseURL: `${DEEPSEEK_BASE_URL}/v1`,
+  apiKey: process.env.DEEPSEEK_API_KEY,
+})
+
+const researcher: AgentConfig = {
+  name: 'researcher',
+  model: DEEPSEEK_MODEL,
+  provider: 'openai',
+  baseURL: DEEPSEEK_BASE_URL,
+  apiKey: process.env.DEEPSEEK_API_KEY,
+  systemPrompt: `You are a research specialist. Given a topic, provide thorough, factual research
+with key findings, relevant data points, and important context.
+Be concise but comprehensive. Output structured notes, not prose.`,
+  maxTurns: 3,
+  temperature: 0.2,
+}
+
+const writer: AgentConfig = {
+  name: 'writer',
+  model: DEEPSEEK_MODEL,
+  provider: 'openai',
+  baseURL: DEEPSEEK_BASE_URL,
+  apiKey: process.env.DEEPSEEK_API_KEY,
+  systemPrompt: `You are an expert writer. Using research from team members (available in shared memory),
+write a well-structured, engaging article with clear headings and concise paragraphs.
+Do not repeat raw research — synthesize it into readable prose.`,
+  maxTurns: 3,
+  temperature: 0.4,
+}
+
+function extractText(message: UIMessage): string {
+  return message.parts
+    .filter((p): p is { type: 'text'; text: string } => p.type === 'text')
+    .map((p) => p.text)
+    .join('')
+}
+
+export async function POST(req: Request) {
+  const { messages }: { messages: UIMessage[] } = await req.json()
+  const lastText = extractText(messages.at(-1)!)
+
+  // --- Phase 1: OMA multi-agent orchestration ---
+  const orchestrator = new OpenMultiAgent({
+    defaultModel: DEEPSEEK_MODEL,
+    defaultProvider: 'openai',
+    defaultBaseURL: DEEPSEEK_BASE_URL,
+    defaultApiKey: process.env.DEEPSEEK_API_KEY,
+  })
+
+  const team = orchestrator.createTeam('research-writing', {
+    name: 'research-writing',
+    agents: [researcher, writer],
+    sharedMemory: true,
+  })
+
+  const teamResult = await orchestrator.runTeam(
+    team,
+    `Research and write an article about: ${lastText}`,
+  )
+
+  const teamOutput = teamResult.agentResults.get('coordinator')?.output ?? ''
+
+  // --- Phase 2: Stream result via Vercel AI SDK ---
+  const result = streamText({
+    model: deepseek(DEEPSEEK_MODEL),
+    system: `You are presenting research from a multi-agent team (researcher + writer).
+The team has already done the work. Your only job is to relay their output to the user
+in a well-formatted way. Keep the content faithful to the team output below.
+At the very end, add a one-line note that this was produced by a researcher agent
+and a writer agent collaborating via open-multi-agent.
+
+## Team Output
+${teamOutput}`,
+    messages: await convertToModelMessages(messages),
+  })
+
+  return result.toUIMessageStreamResponse()
+}

examples/with-vercel-ai-sdk/app/layout.tsx

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+import type { Metadata } from 'next'
+
+export const metadata: Metadata = {
+  title: 'OMA + Vercel AI SDK',
+  description: 'Multi-agent research team powered by open-multi-agent, streamed via Vercel AI SDK',
+}
+
+export default function RootLayout({ children }: { children: React.ReactNode }) {
+  return (
+    <html lang="en">
+      <body style={{ margin: 0, background: '#fafafa' }}>{children}</body>
+    </html>
+  )
+}

examples/with-vercel-ai-sdk/app/page.tsx

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+'use client'
+
+import { useState } from 'react'
+import { useChat } from '@ai-sdk/react'
+
+export default function Home() {
+  const { messages, sendMessage, status, error } = useChat()
+  const [input, setInput] = useState('')
+
+  const isLoading = status === 'submitted' || status === 'streaming'
+
+  const handleSubmit = async (e: React.FormEvent) => {
+    e.preventDefault()
+    if (!input.trim() || isLoading) return
+    const text = input
+    setInput('')
+    await sendMessage({ text })
+  }
+
+  return (
+    <main
+      style={{
+        maxWidth: 720,
+        margin: '0 auto',
+        padding: '32px 16px',
+        fontFamily: 'system-ui, -apple-system, sans-serif',
+      }}
+    >
+      <h1 style={{ fontSize: 22, marginBottom: 4 }}>Research Team</h1>
+      <p style={{ color: '#666', fontSize: 14, marginBottom: 28 }}>
+        Enter a topic. A <strong>researcher</strong> agent gathers information, a{' '}
+        <strong>writer</strong> agent composes an article &mdash; orchestrated by
+        open-multi-agent, streamed via Vercel AI SDK.
+      </p>
+
+      <div style={{ minHeight: 120 }}>
+        {messages.map((m) => (
+          <div key={m.id} style={{ marginBottom: 24, lineHeight: 1.7 }}>
+            <div style={{ fontWeight: 600, fontSize: 13, color: '#999', marginBottom: 4 }}>
+              {m.role === 'user' ? 'You' : 'Research Team'}
+            </div>
+            <div style={{ whiteSpace: 'pre-wrap', fontSize: 15 }}>
+              {m.parts
+                .filter((part): part is { type: 'text'; text: string } => part.type === 'text')
+                .map((part) => part.text)
+                .join('')}
+            </div>
+          </div>
+        ))}
+
+        {isLoading && status === 'submitted' && (
+          <div style={{ color: '#888', fontSize: 14, padding: '8px 0' }}>
+            Agents are collaborating &mdash; this may take a minute...
+          </div>
+        )}
+
+        {error && (
+          <div style={{ color: '#c00', fontSize: 14, padding: '8px 0' }}>
+            Error: {error.message}
+          </div>
+        )}
+      </div>
+
+      <form onSubmit={handleSubmit} style={{ display: 'flex', gap: 8, marginTop: 32 }}>
+        <input
+          value={input}
+          onChange={(e) => setInput(e.target.value)}
+          placeholder="Enter a topic to research..."
+          disabled={isLoading}
+          style={{
+            flex: 1,
+            padding: '10px 14px',
+            borderRadius: 8,
+            border: '1px solid #ddd',
+            fontSize: 15,
+            outline: 'none',
+          }}
+        />
+        <button
+          type="submit"
+          disabled={isLoading || !input.trim()}
+          style={{
+            padding: '10px 20px',
+            borderRadius: 8,
+            border: 'none',
+            background: isLoading ? '#ccc' : '#111',
+            color: '#fff',
+            cursor: isLoading ? 'not-allowed' : 'pointer',
+            fontSize: 15,
+          }}
+        >
+          Send
+        </button>
+      </form>
+    </main>
+  )
+}

examples/with-vercel-ai-sdk/next-env.d.ts

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+/// <reference types="next" />
+/// <reference types="next/image-types/global" />
+import "./.next/dev/types/routes.d.ts";
+
+// NOTE: This file should not be edited
+// see https://nextjs.org/docs/app/api-reference/config/typescript for more information.

examples/with-vercel-ai-sdk/next.config.ts

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+import type { NextConfig } from 'next'
+
+const nextConfig: NextConfig = {
+  serverExternalPackages: ['@jackchen_me/open-multi-agent'],
+}
+
+export default nextConfig

examples/with-vercel-ai-sdk/package.json

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+{
+  "name": "with-vercel-ai-sdk",
+  "private": true,
+  "scripts": {
+    "predev": "cd ../.. && npm run build",
+    "dev": "next dev",
+    "build": "next build",
+    "start": "next start"
+  },
+  "dependencies": {
+    "@ai-sdk/openai-compatible": "^2.0.41",
+    "@ai-sdk/react": "^3.0.0",
+    "@jackchen_me/open-multi-agent": "file:../../",
+    "ai": "^6.0.0",
+    "next": "^16.0.0",
+    "react": "^19.0.0",
+    "react-dom": "^19.0.0"
+  },
+  "devDependencies": {
+    "@types/node": "^22.0.0",
+    "@types/react": "^19.0.0",
+    "@types/react-dom": "^19.0.0",
+    "typescript": "^5.6.0"
+  }
+}

examples/with-vercel-ai-sdk/tsconfig.json

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+{
+  "compilerOptions": {
+    "target": "ES2022",
+    "lib": [
+      "dom",
+      "dom.iterable",
+      "ES2022"
+    ],
+    "allowJs": true,
+    "skipLibCheck": true,
+    "strict": true,
+    "noEmit": true,
+    "esModuleInterop": true,
+    "module": "ESNext",
+    "moduleResolution": "bundler",
+    "resolveJsonModule": true,
+    "isolatedModules": true,
+    "jsx": "react-jsx",
+    "incremental": true,
+    "plugins": [
+      {
+        "name": "next"
+      }
+    ],
+    "paths": {
+      "@/*": [
+        "./*"
+      ]
+    }
+  },
+  "include": [
+    "next-env.d.ts",
+    "**/*.ts",
+    "**/*.tsx",
+    ".next/types/**/*.ts",
+    ".next/dev/types/**/*.ts"
+  ],
+  "exclude": [
+    "node_modules"
+  ]
+}