chore: add agent chat example

examples/agent-chat/README.md

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+# Agent Sync Chat
+
+A modern real-time chat application with AI integration, built using ActorCore, TypeScript, and Next.js.
+
+## Features
+
+- Real-time messaging using ActorCore's actor model
+- Claude AI integration for intelligent chat assistance
+- Multiple chat rooms with isolated actor states
+- Real-time user presence and typing indicators
+- Modern, responsive UI with Tailwind CSS
+- Persistent message storage using ActorCore's state management
+- Fast and efficient message delivery through WebSocket
+- Mobile-friendly design with animations
+
+## Architecture
+
+The application uses ActorCore's actor model for real-time communication:
+
+- Each chat room is an isolated actor instance
+- Messages are broadcasted using ActorCore's event system
+- User state is managed through actor connections
+- Claude AI integration runs in a separate service
+- Frontend uses React with Next.js for optimal performance
+
+## Technologies
+
+- [ActorCore](https://github.com/rivet-gg/actorcore) - Actor model framework for real-time applications
+- [TypeScript](https://www.typescriptlang.org/) - Type-safe JavaScript
+- [Next.js](https://nextjs.org/) - React framework for production
+- [Anthropic Claude API](https://www.anthropic.com/claude) - AI language model
+- [Tailwind CSS](https://tailwindcss.com/) - Utility-first CSS framework
+
+## Prerequisites
+
+- Node.js 18+ and yarn
+- Anthropic API key for Claude integration
+
+## Installation
+
+1. Clone the repository:
+```bash
+git clone https://github.com/yourusername/agentsyncchat.git
+cd agentsyncchat
+```
+
+2. Install dependencies:
+```bash
+# Install root dependencies
+yarn install
+
+# Install frontend dependencies
+cd frontend && yarn install
+```
+
+3. Configure environment variables:
+
+Create a `.env` file in the root directory:
+```env
+PORT=3000
+ANTHROPIC_API_KEY=your_api_key_here
+```
+
+Create a `.env.local` file in the `frontend` directory:
+```env
+NEXT_PUBLIC_API_URL=http://localhost:3000
+```
+
+4. Start the development servers:
+
+```bash
+# Start the backend server
+yarn dev
+
+# In a new terminal, start the frontend
+cd frontend && yarn dev
+```
+
+The application will be available at:
+- Frontend: http://localhost:3001
+- Backend: http://localhost:3000
+
+## Project Structure
+
+```
+├── src/                    # Backend source code
+│   ├── index.ts           # Main entry point and server setup
+│   ├── chat-room.ts       # Chat room actor implementation
+│   ├── claude-service.ts  # Claude AI integration service
+│   ├── client.ts         # ActorCore client configuration
+│   └── web-server-actor.ts# Web server actor implementation
+│
+├── frontend/              # Frontend application
+│   ├── app/              # Next.js app directory
+│   │   └── page.tsx      # Main chat interface
+│   ├── public/           # Static assets
+│   └── package.json      # Frontend dependencies
+│
+└── package.json          # Backend dependencies
+```
+
+## Actor Implementation
+
+The chat system uses ActorCore's actor model:
+
+- Each chat room is an isolated actor instance
+- Messages are handled through RPC calls
+- State is automatically persisted between calls
+- Events are used for real-time updates
+- Typing indicators use ActorCore's event system
+
+## Development
+
+- Use `yarn check-types` to verify TypeScript types
+- The frontend auto-reloads when you make changes
+- The backend uses `tsx watch` for automatic reloading
+- Follow ActorCore's development guide for best practices
+
+## Troubleshooting
+
+Common issues and solutions:
+
+1. Port conflicts:
+```bash
+# Check for processes using ports
+lsof -i :3000,3001
+
+# Kill the processes if needed
+kill -9 <PID>
+```
+
+2. TypeScript errors:
+```bash
+# Run type checking
+yarn check-types
+
+# Clean and rebuild
+yarn clean && yarn build
+```
+
+## Contributing
+
+1. Fork the repository
+2. Create your feature branch (`git checkout -b feature/amazing-feature`)
+3. Follow ActorCore development guidelines
+4. Run tests and type checks
+5. Commit your changes (`git commit -m 'Add feature'`)
+6. Push to the branch (`git push origin feature/amazing-feature`)
+7. Open a Pull Request
+
+## License
+
+MIT
+
+## Security
+
+- Never commit API keys or sensitive data
+- Use environment variables for configuration
+- Follow ActorCore's security guidelines
+- Validate all user inputs
+- Use appropriate CORS settings 

examples/agent-chat/frontend/.eslintrc.json

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+{
+  "extends": [
+    "next/core-web-vitals",
+    "next/typescript"
+  ]
+}

examples/agent-chat/frontend/.gitignore

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+# See https://help.github.com/articles/ignoring-files/ for more about ignoring files.
+
+# dependencies
+/node_modules
+/.pnp
+.pnp.*
+.yarn/*
+!.yarn/patches
+!.yarn/plugins
+!.yarn/releases
+!.yarn/versions
+
+# testing
+/coverage
+
+# next.js
+/.next/
+/out/
+
+# production
+/build
+
+# misc
+.DS_Store
+*.pem
+
+# debug
+npm-debug.log*
+yarn-debug.log*
+yarn-error.log*
+.pnpm-debug.log*
+
+# env files (can opt-in for committing if needed)
+.env*
+
+# vercel
+.vercel
+
+# typescript
+*.tsbuildinfo
+next-env.d.ts

examples/agent-chat/frontend/README.md

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+This is a [Next.js](https://nextjs.org) project bootstrapped with [`create-next-app`](https://nextjs.org/docs/app/api-reference/cli/create-next-app).
+
+## Getting Started
+
+First, run the development server:
+
+```bash
+npm run dev
+# or
+yarn dev
+# or
+pnpm dev
+# or
+bun dev
+```
+
+Open [http://localhost:3000](http://localhost:3000) with your browser to see the result.
+
+You can start editing the page by modifying `app/page.tsx`. The page auto-updates as you edit the file.
+
+This project uses [`next/font`](https://nextjs.org/docs/app/building-your-application/optimizing/fonts) to automatically optimize and load [Geist](https://vercel.com/font), a new font family for Vercel.
+
+## Learn More
+
+To learn more about Next.js, take a look at the following resources:
+
+- [Next.js Documentation](https://nextjs.org/docs) - learn about Next.js features and API.
+- [Learn Next.js](https://nextjs.org/learn) - an interactive Next.js tutorial.
+
+You can check out [the Next.js GitHub repository](https://github.com/vercel/next.js) - your feedback and contributions are welcome!
+
+## Deploy on Vercel
+
+The easiest way to deploy your Next.js app is to use the [Vercel Platform](https://vercel.com/new?utm_medium=default-template&filter=next.js&utm_source=create-next-app&utm_campaign=create-next-app-readme) from the creators of Next.js.
+
+Check out our [Next.js deployment documentation](https://nextjs.org/docs/app/building-your-application/deploying) for more details.

examples/agent-chat/frontend/app/globals.css

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+@import "tailwindcss";
+
+@theme {
+  --font-sans: var(--font-geist-sans);
+  --font-mono: var(--font-geist-mono);
+}
+
+:root {
+  --background: #ffffff;
+  --foreground: #171717;
+}
+
+@media (prefers-color-scheme: dark) {
+  :root {
+    --background: #0a0a0a;
+    --foreground: #ededed;
+  }
+}
+
+body {
+  color: var(--foreground);
+  background: var(--background);
+  font-family: Arial, Helvetica, sans-serif;
+}

examples/agent-chat/frontend/app/layout.tsx

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+import type { Metadata } from "next";
+import { Geist, Geist_Mono } from "next/font/google";
+import "./globals.css";
+
+const geistSans = Geist({
+  variable: "--font-geist-sans",
+  subsets: ["latin"],
+});
+
+const geistMono = Geist_Mono({
+  variable: "--font-geist-mono",
+  subsets: ["latin"],
+});
+
+export const metadata: Metadata = {
+  title: "Create Next App",
+  description: "Generated by create next app",
+};
+
+export default function RootLayout({
+  children,
+}: Readonly<{
+  children: React.ReactNode;
+}>) {
+  return (
+    <html lang="en">
+      <body
+        className={`${geistSans.variable} ${geistMono.variable} antialiased`}
+      >
+        {children}
+      </body>
+    </html>
+  );
+}