docs: add Claude Code integration instructions to README

README.md

@@ -70,6 +70,58 @@ uv run mnemosyne
 
 Point your LLM client (e.g., Claude Code) to the proxy URL (e.g., `http://127.0.0.1:8080/v1`).
 
+## Claude Code Integration
+
+Mnemosyne works with [Claude Code](https://docs.anthropic.com/en/docs/claude-code) out of the box. Claude Code uses the Anthropic SDK internally, which respects the `ANTHROPIC_BASE_URL` environment variable.
+
+### Quick Start
+
+```bash
+ANTHROPIC_BASE_URL=http://127.0.0.1:8080 claude
+```
+
+### Permanent Setup
+
+Add to your shell profile (`~/.zshrc`, `~/.bashrc`, etc.):
+
+```bash
+export ANTHROPIC_BASE_URL=http://127.0.0.1:8080
+```
+
+All Claude Code sessions will then route through Mnemosyne automatically.
+
+### Authentication
+
+Claude Code normally authenticates via Anthropic OAuth. When routing through Mnemosyne, there are two options:
+
+1. **OAuth passthrough** (recommended): Mnemosyne forwards OAuth credentials to Anthropic transparently. No extra configuration needed — just run `claude` as usual.
+
+2. **API key**: Set `ANTHROPIC_API_KEY` directly and Mnemosyne will forward it:
+   ```bash
+   export ANTHROPIC_API_KEY=sk-ant-...
+   export ANTHROPIC_BASE_URL=http://127.0.0.1:8080
+   ```
+
+### Systemd Service
+
+To ensure Mnemosyne is always running when Claude Code starts, install the systemd user service:
+
+```bash
+cp mnemosyne.service ~/.config/systemd/user/
+systemctl --user enable mnemosyne.service
+systemctl --user start mnemosyne.service
+```
+
+### Verifying the Connection
+
+While Claude Code is running, check the dashboard at `http://127.0.0.1:8080/dashboard` or query the API:
+
+```bash
+curl -s http://127.0.0.1:8080/api/sessions | python3 -m json.tool
+```
+
+You should see an active session with incoming/outgoing byte counts.
+
 ## API Reference
 
 * `/api/sessions`: List active conversation sessions.