feat: Implement OpenAI proxy with streaming support

- Add main proxy endpoint (api/v1/messages.js)
- Add token validation via GATEWAY_TOKEN
- Add model mapping via MODEL_MAP env var
- Support full SSE streaming in Anthropic format
- Add package.json with openai dependency
- Add vercel.json for routing config
- Update README with Quick Start guide
- Consolidate memory to .claude/memory/

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

.claude/memory/MEMORY.md

@@ -1,3 +1,4 @@
 # Project Memory Index
 
 - [Memory Saving Rules](memory_saving_rules.md) — How to save memories in this project
+- [Implementation Plan](implementation_plan.md) — Architecture and design decisions for Claude Central Gateway

.claude/memory/implementation_plan.md

@@ -0,0 +1,47 @@
+---
+name: Implementation Plan
+description: Architecture and design decisions for Claude Central Gateway
+type: project
+---
+
+## Claude Central Gateway - Implementation
+
+**Why:** A lightweight proxy for Claude Code that routes requests to third-party API providers, deployable to Vercel without needing a VPS.
+
+### Architecture
+
+```
+Claude Code → Gateway (Vercel) → OpenAI API
+                ↓
+         Validate token
+         Transform request
+         Stream response
+```
+
+### Key Decisions
+
+- **Language**: Node.js with JavaScript (no TypeScript)
+- **Deployment**: Vercel serverless functions
+- **Providers**: OpenAI first (via official SDK), others in TODO
+- **Config**: Environment variables only (no database)
+- **Auth**: Single shared token (user's `ANTHROPIC_AUTH_TOKEN` must match `GATEWAY_TOKEN`)
+- **Streaming**: Full streaming support
+- **Model mapping**: Via `MODEL_MAP` env var (format: `claude:openai,claude2:openai2`)
+
+### Environment Variables
+
+| Variable | Description |
+|----------|-------------|
+| `GATEWAY_TOKEN` | Shared token for authentication |
+| `OPENAI_API_KEY` | OpenAI API key |
+| `MODEL_MAP` | Model name mapping (optional) |
+
+### File Structure
+
+```
+api/v1/messages.js  - Main proxy handler
+package.json        - Dependencies (openai SDK)
+vercel.json         - Routing config
+```
+
+### How to apply: When adding new providers or modifying the gateway, follow the established pattern in `api/v1/messages.js` for request/response transformation.