feat: Support continuous conversation for Claude memory

Author: andreyvelich

README.md

@@ -5,6 +5,7 @@ Jupyter AI integration with Claude Code persona for enhanced development capabil
 ## Features
 
 - **Claude Code Integration**: Full Claude Code persona for Jupyter AI
+- **Continuous Conversation**: Maintains conversation context across multiple messages
 - **Development Tools**: Access to Claude Code's built-in development tools
 - **Seamless Integration**: Works with existing Jupyter AI workflow
 - **Template Management**: Interactive task progress tracking and updates
@@ -55,6 +56,30 @@ This will start JupyterLab with the Jupyter AI extension and Claude Code persona
 3. Select "Claude" persona
 4. Interact with Claude Code's development tools
 
+#### Continuous Conversation
+
+The Claude Code persona now supports continuous conversation, which maintains context across multiple messages in a chat session. This allows Claude to:
+- Remember previous questions and answers
+- Build upon earlier context in the conversation
+- Provide more coherent multi-turn interactions
+
+**Session Management:**
+
+The persona automatically manages conversation sessions. Each time you send a message, it's added to the ongoing conversation context. If you want to reset the conversation and start fresh, you can programmatically call:
+
+```python
+# From within the ClaudeCodePersona instance
+await persona.reset_conversation()
+```
+
+This will clear the conversation history and start a new session with the next message.
+
+**How it works:**
+
+- The first message automatically creates a new `ClaudeSDKClient` session
+- Subsequent messages reuse the same client to maintain conversation context
+- The client persists until you explicitly reset it or the JupyterLab session ends
+
 ### Build the Package
 
 The package is automatically installed in editable mode during `pixi install`. To manually build: