feat(formula): Add check-timer-gates step to Witness patrol

Cross-rig change from beads Timer Gates feature (bd-kbfn).
Adds timer gate expiration check to patrol loop.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

.beads/formulas/mol-witness-patrol.formula.toml

@@ -1,4 +1,4 @@
-description = "Per-rig worker monitor patrol loop.\n\nThe Witness is the Pit Boss for your rig. You watch polecats, nudge them toward\ncompletion, verify clean git state before kills, and escalate stuck workers.\n\n**You do NOT do implementation work.** Your job is oversight, not coding.\n\n## Design Philosophy\n\nThis patrol follows Gas Town principles:\n- **Discovery over tracking**: Observe reality each cycle, don't maintain state\n- **Events over state**: POLECAT_DONE mail triggers cleanup wisps\n- **Cleanup wisps as finalizers**: Pending cleanups are wisps, not queue entries\n- **Task tool for parallelism**: Subagents inspect polecats, not molecule arms\n\n## Patrol Shape (Linear, Deacon-style)\n\n```\ninbox-check ─► process-cleanups ─► check-refinery ─► survey-workers\n                                                            │\n         ┌──────────────────────────────────────────────────┘\n         ▼\n  check-swarm ─► ping-deacon ─► patrol-cleanup ─► context-check ─► loop-or-exit\n```\n\nNo dynamic arms. No fanout gates. No persistent nudge counters.\nState is discovered each cycle from reality (tmux, beads, mail)."
+description = "Per-rig worker monitor patrol loop.\n\nThe Witness is the Pit Boss for your rig. You watch polecats, nudge them toward\ncompletion, verify clean git state before kills, and escalate stuck workers.\n\n**You do NOT do implementation work.** Your job is oversight, not coding.\n\n## Design Philosophy\n\nThis patrol follows Gas Town principles:\n- **Discovery over tracking**: Observe reality each cycle, don't maintain state\n- **Events over state**: POLECAT_DONE mail triggers cleanup wisps\n- **Cleanup wisps as finalizers**: Pending cleanups are wisps, not queue entries\n- **Task tool for parallelism**: Subagents inspect polecats, not molecule arms\n\n## Patrol Shape (Linear, Deacon-style)\n\n```\ninbox-check ─► process-cleanups ─► check-refinery ─► survey-workers\n                                                            │\n         ┌──────────────────────────────────────────────────┘\n         ▼\n  check-timer-gates ─► check-swarm ─► ping-deacon ─► patrol-cleanup ─► context-check ─► loop-or-exit\n```\n\nNo dynamic arms. No fanout gates. No persistent nudge counters.\nState is discovered each cycle from reality (tmux, beads, mail)."
 formula = 'mol-witness-patrol'
 version = 2
 
@@ -25,10 +25,16 @@ id = 'survey-workers'
 needs = ['check-refinery']
 title = 'Inspect all active polecats'
 
+[[steps]]
+description = "Check for expired timer gates and escalate as needed.\n\nTimer gates are async wait conditions with a timeout. When the timeout expires,\nthe gate should be escalated to the overseer for human intervention.\n\n**Step 1: Run timer gate check**\n```bash\nbd gate check --type=timer --escalate\n```\n\nThis command:\n1. Finds all open gate issues with await_type=timer\n2. Checks if `now > created_at + timeout`\n3. Escalates expired gates via `gt escalate` (HIGH severity)\n4. Reports summary of gate status\n\n**Step 2: Review output**\n\nIf expired gates were found and escalated:\n- The escalation creates an audit trail bead\n- Overseer will be notified via mail\n- Gate remains open until manually resolved\n\nIf no expired gates:\n- Continue patrol normally\n\n**Note**: Timer gates do NOT auto-close on expiration. They escalate.\nThis ensures human oversight of timeout conditions.\n\n**Parallelism**: This is a single command, no parallel execution needed."
+id = 'check-timer-gates'
+needs = ['survey-workers']
+title = 'Check timer gates for expiration'
+
 [[steps]]
 description = "If Mayor started a batch (SWARM_START), check if all polecats have completed.\n\n**Step 1: Find active swarm tracking wisps**\n```bash\nbd list --wisp --labels=swarm --status=open\n```\nIf no active swarm, skip this step.\n\n**Step 2: Count completed polecats for this swarm**\n\nExtract from wisp labels: swarm_id, total, completed, start timestamp.\nCheck how many cleanup wisps have been closed for this swarm's polecats.\n\n**Step 3: If all complete, notify Mayor**\n```bash\ngt mail send mayor/ -s \"SWARM_COMPLETE: <swarm_id>\" -m \"All <total> polecats merged.\nDuration: <minutes> minutes\nSwarm: <swarm_id>\"\n\n# Close the swarm tracking wisp\nbd close <swarm-wisp-id> --reason \"All polecats merged\"\n```\n\nNote: Runs every patrol cycle. Notification sent exactly once when all complete."
 id = 'check-swarm-completion'
-needs = ['survey-workers']
+needs = ['check-timer-gates']
 title = 'Check if active swarm is complete'
 
 [[steps]]