fix(kanban): persist _recent_worker_exits across gateway restarts

agent/prompt_builder.py

@@ -319,7 +319,32 @@ def _strip_yaml_frontmatter(content: str) -> str:
     "specialist profile.\n"
     "- Do not call `delegate_task` as a board substitute. `delegate_task` is "
     "for short reasoning subtasks inside your own run; board tasks are for "
-    "cross-agent handoffs that outlive one API loop."
+    "cross-agent handoffs that outlive one API loop.\n"
+    "\n"
+    "## Sweeper idempotency contract\n"
+    "The worktree-sweeper auto-pushes branches, opens PRs, and completes ready "
+    "worktree cards on the ops board. Recognise its side effects so neither you "
+    "nor a re-sweep double-processes a card. Three equivalent sticky markers — "
+    "any one present means the card has already been swept; do NOT re-push, do "
+    "NOT open a new PR, do NOT re-complete:\n"
+    "\n"
+    "1. **Sentinel comment** on the card matching\n"
+    "   `sweeper:auto-pushed:\\d{10,}:https://github\\.com/.+/pull/\\d+` "
+    "— written via `hermes_comment` immediately before the sweeper calls "
+    "`kanban_complete`.\n"
+    "2. **PR URL in card body** matching "
+    "`https://github\\.com/[^\\s)]+/pull/\\d+` — set by previous sweeps or by "
+    "operators completing the card with the PR URL inline.\n"
+    "3. **`PR: <URL>` line** in the most recent completion summary — the sweeper "
+    "always appends this as the final line of the `kanban_complete` summary so "
+    "subsequent sweeps can grep for it.\n"
+    "\n"
+    "Original spec called for an `auto-pushed` tag; the kanban schema has no "
+    "tags column, so the sentinel comment is the live durable marker. Treat any "
+    "future `auto-pushed` tag as an ADDITIONAL valid signal, not a replacement. "
+    "Branch-cleanliness checks, push, PR creation, and the status=ready→done "
+    "transition are the sweeper's job — your job is the implementation work "
+    "that precedes them."
 )
 
 TOOL_USE_ENFORCEMENT_GUIDANCE = (