Let Codex on macOS send a notification to ChatGPT on iPhone when explicitly asked

Core request

I want to be able to tell Codex on my Mac:

Notify me on my phone when this is done.

Codex should then send a notification through the ChatGPT app on my iPhone when it reaches that point.

The notification should tell me something useful about the result, not merely say that an unspecified task finished. For example:

Codex finished the report
The report is ready and the source check passed.

Tapping it should open the relevant Codex task.

Why I want this

I want to know when something is done, and I want to know something about it.

Currently I have to keep opening Codex on my phone, wait for the slow Remote screen to load, find and click the right thread, and inspect it to learn whether anything happened. I do not want to repeatedly poll the app while a task runs on my Mac.

This is primarily a small, explicit agent capability: when I ask Codex to notify me, it can send a useful notification to the ChatGPT mobile app associated with my account.

Minimum expected behavior

1. The user explicitly asks Codex on macOS to notify them at some point.
2. Codex can invoke a first-party “send notification to my ChatGPT mobile app” capability.
3. The iPhone receives a concise notification saying what happened.
4. Tapping it opens the correct Codex task.

Possible extensions

The following could be useful later, but they are extensions rather than the core request:

• automatic opt-in notifications for task or turn completion;
• failures;
• approval or permission requests;
• scheduled automation completion or failure;
• per-task or per-automation notification controls;
• privacy controls for lock-screen content.

Related issues

• #20930 concerns missing desktop turn-completion notifications for remote projects. This request is specifically about first-party delivery to the ChatGPT iOS app.
• #14813 concerns external notify hooks. This request should not require Pushover, Slack, email, shell hooks, or another third-party service.
• #22773 contains broader Remote Control reliability reports, including delayed or absent mobile push.

No account identifiers, private task content, thread IDs, or local paths are included in this public request.