Refactor Deacon patrol to detect→dispatch pattern (gt-0x5og.4)

Major changes to mol-deacon-patrol.formula.toml v4:
- Add DOG_DONE message handling in inbox-check step
- Add dog-pool-maintenance step for idle dog availability
- Change orphan-check to detect-only (dispatches to dogs via sling)
- Change session-gc to detect-only (dispatches to dogs via sling)

The Deacon now stays lightweight by detecting issues and dispatching
heavy work to dogs rather than executing inline. This prevents context
bloat and keeps patrol cycles fast.

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

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

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

@@ -12,7 +12,7 @@ Witnesses detect it and escalate to the Mayor.
 The Deacon's agent bead last_activity timestamp is updated during each patrol
 cycle. Witnesses check this timestamp to verify health."""
 formula = "mol-deacon-patrol"
-version = 3
+version = 4
 
 [[steps]]
 id = "inbox-check"
@@ -55,6 +55,19 @@ Archive after processing:
 gt mail archive <message-id>
 ```
 
+**DOG_DONE messages**:
+Dogs report completion after infrastructure tasks (orphan-scan, session-gc, etc.).
+Subject format: `DOG_DONE <hostname>`
+Body contains: task name, counts, status.
+```bash
+# Parse the report, log metrics if needed
+gt mail read <id>
+# Archive after noting completion
+gt mail archive <message-id>
+```
+Dogs return to idle automatically. The report is informational - no action needed
+unless the dog reports errors that require escalation.
+
 Callbacks may spawn new polecats, update issue state, or trigger other actions.
 
 **Hygiene principle**: Archive messages after they're fully processed.
@@ -318,51 +331,104 @@ Plugins marked parallel: true can run concurrently using Task tool subagents. Se
 Skip this step if ~/gt/plugins/ does not exist or is empty."""
 
 [[steps]]
-id = "orphan-check"
-title = "Find abandoned work"
+id = "dog-pool-maintenance"
+title = "Maintain dog pool"
 needs = ["health-scan"]
 description = """
-Find abandoned work.
-
-Scan for orphaned state:
-- Issues marked in_progress with no active polecat
-- Polecats that stopped responding mid-work
-- Merge queue entries with no polecat owner
-- Wisp sessions that outlived their spawner
+Ensure dog pool has available workers for dispatch.
 
+**Step 1: Check dog pool status**
 ```bash
-bd list --status=in_progress
-gt polecats --all --orphan
+gt dog status
+# Shows idle/working counts
 ```
 
-For each orphan:
-- Check if polecat session still exists
-- If not, mark issue for reassignment or retry
-- File incident beads if data loss occurred"""
+**Step 2: Ensure minimum idle dogs**
+If idle count is 0 and working count is at capacity, consider spawning:
+```bash
+# If no idle dogs available
+gt dog add <name>
+# Names: alpha, bravo, charlie, delta, etc.
+```
+
+**Step 3: Retire stale dogs (optional)**
+Dogs that have been idle for >24 hours can be removed to save resources:
+```bash
+gt dog status <name>
+# Check last_active timestamp
+# If idle > 24h: gt dog remove <name>
+```
+
+**Pool sizing guidelines:**
+- Minimum: 1 idle dog always available
+- Maximum: 4 dogs total (balance resources vs throughput)
+- Spawn on demand when pool is empty
+
+**Exit criteria:** Pool has at least 1 idle dog."""
+
+[[steps]]
+id = "orphan-check"
+title = "Detect abandoned work"
+needs = ["dog-pool-maintenance"]
+description = """
+**DETECT ONLY** - Check for orphaned state and dispatch to dog if found.
+
+**Step 1: Quick orphan scan**
+```bash
+# Check for in_progress issues with dead assignees
+bd list --status=in_progress --json | head -20
+```
+
+For each in_progress issue, check if assignee session exists:
+```bash
+tmux has-session -t <session> 2>/dev/null && echo "alive" || echo "orphan"
+```
+
+**Step 2: If orphans detected, dispatch to dog**
+```bash
+# Sling orphan-scan formula to an idle dog
+gt sling mol-orphan-scan deacon/dogs --var scope=town
+```
+
+**Important:** Do NOT fix orphans inline. Dogs handle recovery.
+The Deacon's job is detection and dispatch, not execution.
+
+**Step 3: If no orphans detected**
+Skip dispatch - nothing to do.
+
+**Exit criteria:** Orphan scan dispatched to dog (if needed)."""
 
 [[steps]]
 id = "session-gc"
-title = "Clean dead sessions"
+title = "Detect cleanup needs"
 needs = ["orphan-check"]
 description = """
-Clean dead sessions and orphaned state.
-
-Run `gt doctor --fix` to handle all cleanup:
+**DETECT ONLY** - Check if cleanup is needed and dispatch to dog.
 
+**Step 1: Preview cleanup needs**
 ```bash
-# Preview what needs cleaning
 gt doctor -v
-
-# Fix everything
-gt doctor --fix
+# Check output for issues that need cleaning
 ```
 
-This handles:
-- **orphan-sessions**: Kill orphaned tmux sessions (gt-* not matching valid patterns)
-- **orphan-processes**: Kill orphaned Claude processes (no tmux parent)
-- **wisp-gc**: Garbage collect abandoned wisps (>1h old)
+**Step 2: If cleanup needed, dispatch to dog**
+```bash
+# Sling session-gc formula to an idle dog
+gt sling mol-session-gc deacon/dogs --var mode=conservative
+```
 
-All cleanup is handled by doctor checks - no need to run separate commands."""
+**Important:** Do NOT run `gt doctor --fix` inline. Dogs handle cleanup.
+The Deacon stays lightweight - detection only.
+
+**Step 3: If nothing to clean**
+Skip dispatch - system is healthy.
+
+**Cleanup types (for reference):**
+- orphan-sessions: Dead tmux sessions
+- orphan-processes: Orphaned Claude processes
+- wisp-gc: Old wisps past retention
+
+**Exit criteria:** Session GC dispatched to dog (if needed)."""
 
 [[steps]]
 id = "log-maintenance"