Keep Claude commands out of subagents

SUBAGENTS.md

@@ -66,8 +66,12 @@ transcript is still being written to and its process is the session's to stop.
 
 ## Lifecycle, as events in the subagent's transcript
 
-1. Created on the first child line for an unseen parent id (or, when the
-   parent Task call was seen, at that call). First lines written:
+1. Created when the parent Task/Agent call is seen. A current Claude CLI's
+   `task_started` with `task_type: local_agent` is a recovery source when an
+   adopted stream begins after that call. A bare `parent_tool_use_id` is not
+   enough: other operations can also parent nested lines, and treating one as
+   proof created false subagents named after their first subcommand.
+   First lines written:
    `Status Running`, then `UserMessage { text: <the Task's prompt> }` when
    the prompt is known -- it genuinely is the subagent's first user turn.
 2. Every child line is translated by that subagent's own `Translator`
@@ -75,12 +79,13 @@ transcript is still being written to and its process is the session's to stop.
    content-block index, and parallel subagents interleave).
 3. **What ends a subagent is the CLI's own task lifecycle**, on top-level
    `system` lines that carry no `parent_tool_use_id`: `task_started`
-   (`task_id`, `tool_use_id`, `is_backgrounded`, the prompt), `task_progress`
-   repeatedly, then `task_updated` (`patch.status`, naming the *task* only)
-   and `task_notification` (`tool_use_id`, `status`, and `summary` -- the
-   agent's own report). `translate_task` keeps the `task_id -> tool_use_id`
-   mapping from the first so the update can be attributed, records the
-   summary as the subagent's closing text, and writes `Status Exited`. A
+   (`task_id`, `tool_use_id`, `task_type`, `is_backgrounded`, the prompt),
+   `task_progress` repeatedly, then `task_updated` (`patch.status`, naming the
+   *task* only) and `task_notification` (`tool_use_id`, `status`, and `summary`
+   -- the agent's own report). `translate_task` keeps the
+   `task_id -> tool_use_id` mapping from the first so the update can be
+   attributed, records the summary as the subagent's closing text, and writes
+   `Status Exited`. A
    `completed` update is deliberately not the end: its notification carries
    the summary and would otherwise land after the ending. Any other terminal
    status ends it from the update, since the failure to avoid is a subagent
@@ -175,11 +180,11 @@ its last status stays `Running`, which the list reports as **unknown**
 rather than as running (see the wire shape) until then.
 
 Title: for Claude, the Task call's `description` input, then
-` (<subagent_type>)` when one is given; falling back to the tool's name when
-the child arrives before (or without) the parent call being seen. For Codex,
-the first lifecycle record uses the spawned thread's name or the last segment
-of `agentPath`, with underscores shown as spaces, then falls back to
-`subagent`.
+` (<subagent_type>)` when one is given; falling back to `Task` when the
+description is absent. An adopted current CLI can recover the same fields from
+its `local_agent` lifecycle record. For Codex, the first lifecycle record uses
+the spawned thread's name or the last segment of `agentPath`, with underscores
+shown as spaces, then falls back to `subagent`.
 
 ## Server layout