diff --git a/docs/config-catalog.md b/docs/config-catalog.md
index 08423c351d..a74d1493a4 100644
--- a/docs/config-catalog.md
+++ b/docs/config-catalog.md
@@ -1968,8 +1968,8 @@ export interface Config {
    * requires the provider's `depthLimit` capability (mount fails loud
    * otherwise). The provider checks the calling agent's current depth at every
    * start; the tool remains model-visible so runtime policy owns rejection.
-   * `'provider-managed'` is for an out-of-process provider (ACP) whose
-   * recursion budget belongs to the child harness's own deployment.
+   * `'provider-managed'` is for an out-of-process provider whose recursion
+   * budget belongs to the child runtime or its own deployment.
    */
   maxDepth?: number | 'provider-managed'
 }
diff --git a/packages/subagent/subagent-codex/src/run.ts b/packages/subagent/subagent-codex/src/run.ts
index 27d01f6ac6..54a2bc1d79 100644
--- a/packages/subagent/subagent-codex/src/run.ts
+++ b/packages/subagent/subagent-codex/src/run.ts
@@ -150,7 +150,7 @@ export async function startCodexRun(
       )
     }
     if (runAbort.signal.aborted) {
-      throw new Error('subagent-codex: request was aborted before app-server startup')
+      throw new Error('subagent-codex: request was aborted before run publication')
     }
     throw thrownError(error)
   }
diff --git a/packages/subagent/subagent-codex/tests/subagent-codex.spec.ts b/packages/subagent/subagent-codex/tests/subagent-codex.spec.ts
index 7d550d42cb..181ddb919e 100644
--- a/packages/subagent/subagent-codex/tests/subagent-codex.spec.ts
+++ b/packages/subagent/subagent-codex/tests/subagent-codex.spec.ts
@@ -939,7 +939,7 @@ describe('run lifecycle and quiescence', () => {
     const threadStart = await child.peer.nextMethod('thread/start')
     child.peer.respond(threadStart, { thread: { id: 'thread-1', ephemeral: true } })
     controller.abort('startup race')
-    await expect(starting).rejects.toThrow('aborted before app-server startup')
+    await expect(starting).rejects.toThrow('aborted before run publication')
     expect(child.terminate).toHaveBeenCalledTimes(1)
   })
 
diff --git a/packages/subagent/tool-subagent/src/index.ts b/packages/subagent/tool-subagent/src/index.ts
index f95c5ad09d..67894c32cb 100644
--- a/packages/subagent/tool-subagent/src/index.ts
+++ b/packages/subagent/tool-subagent/src/index.ts
@@ -67,8 +67,8 @@ export interface Config {
    * requires the provider's `depthLimit` capability (mount fails loud
    * otherwise). The provider checks the calling agent's current depth at every
    * start; the tool remains model-visible so runtime policy owns rejection.
-   * `'provider-managed'` is for an out-of-process provider (ACP) whose
-   * recursion budget belongs to the child harness's own deployment.
+   * `'provider-managed'` is for an out-of-process provider whose recursion
+   * budget belongs to the child runtime or its own deployment.
    */
   maxDepth?: number | 'provider-managed'
 }