Make Codex conversation history readable on mobile when the host computer is offline

What feature would you like to see?

Please sync the conversational layer of Codex threads to the cloud so that the latest exchanges remain readable in the ChatGPT mobile app even when the host computer is turned off.

This request is not about running Codex remotely while the computer is offline. The local machine can remain required for code execution, file access, terminal commands, tests, and other agent actions.

The requested mobile experience is:

• Codex threads remain visible and readable in the ChatGPT mobile app after the desktop host disconnects or powers off.
• The latest user prompts, Codex responses, decisions, test results, and change summaries remain available.
• The thread clearly shows that the host computer is offline and execution is unavailable.
• The user can review the work and draft or queue the next instruction from mobile.
• When the desktop reconnects, the same thread resumes with its local environment and execution capabilities.

Why this matters

My concrete use case is commuting. I work extensively with Codex in the evening and spend around two hours per day on public transport. That time could be used productively to review the previous session, understand what Codex changed, inspect its conclusions, and prepare the next instructions.

Remote Control is useful while the host is online, but requiring the computer to remain powered on makes simple review unnecessarily dependent on a live connection. The conversation and execution layers should be separated:

• Conversation/history: cloud-synced and readable across desktop, web, and mobile.
• Execution/local context: available only when the relevant host is connected.

This would provide genuine continuity between desktop development sessions and mobile review time without introducing the security or infrastructure implications of executing local work while the computer is off.

Expected behavior

1. Finish a Codex session on desktop.
2. Shut down the computer.
3. Open ChatGPT on mobile during the commute.
4. Open the same Codex thread and read its latest content in a read-only/offline-host state.
5. Draft or queue the next message.
6. Reconnect the desktop later and continue the same thread with local execution restored.

Additional information

The current official product documentation states that Codex history remains separate from ChatGPT history and that supported desktop Codex chats are accessed through the mobile Remote tab. This request is specifically to persist the latest thread content for review when the desktop host is offline, without requiring cloud execution of the local project.