Fix spawn priming race: use deacon patrol instead of broken nudge (gt-6957)

- Remove 3-second sleep and NudgeSession from spawn.go
  (Claude takes 10-20s to initialize, message arrived too early)
- Add trigger-pending-spawns step to deacon patrol molecule
  (Deacon polls with WaitForClaudeReady, sends trigger when ready)
- SessionStart hook handles gt prime (internal, reliable)
- Deacon sends minimal 'Begin.' trigger to start polecat working

The spawn command now returns immediately after starting the session.
The deacon's patrol cycle will trigger the polecat when it's ready.

internal/beads/builtin_molecules.go

@@ -632,6 +632,31 @@ gt mail read <id>
 
 Callbacks may spawn new polecats, update issue state, or trigger other actions.
 
+## Step: trigger-pending-spawns
+Nudge newly spawned polecats that are ready for input.
+
+When polecats are spawned, their Claude session takes 10-20 seconds to initialize.
+The spawn command returns immediately without waiting. This step finds spawned
+polecats that are now ready and sends them a trigger to start working.
+
+` + "```" + `bash
+# For each rig with polecats
+for rig in gastown beads; do
+    gt polecats $rig
+    # For each working polecat, check if Claude is ready
+    # Use tmux capture-pane to look for "> " prompt
+done
+` + "```" + `
+
+For each ready polecat that hasn't been triggered yet:
+1. Send "Begin." to trigger UserPromptSubmit hook
+2. The hook injects mail, polecat sees its assignment
+3. Mark polecat as triggered in state
+
+Use WaitForClaudeReady from tmux package (polls for "> " prompt).
+Timeout: 60 seconds per polecat. If not ready, try again next cycle.
+Needs: inbox-check
+
 ## Step: health-scan
 Ping Witnesses and Refineries.
 
@@ -649,7 +674,7 @@ done
 ` + "```" + `
 
 Report any issues found. Restart unresponsive components if needed.
-Needs: inbox-check
+Needs: trigger-pending-spawns
 
 ## Step: plugin-run
 Execute registered plugins.

internal/cmd/spawn.go

@@ -7,7 +7,6 @@ import (
 	"os/exec"
 	"path/filepath"
 	"strings"
-	"time"
 
 	"github.com/spf13/cobra"
 	"github.com/steveyegge/gastown/internal/config"
@@ -354,41 +353,30 @@ func runSpawn(cmd *cobra.Command, args []string) error {
 	// Check if already running
 	running, _ := sessMgr.IsRunning(polecatName)
 	if running {
-		// Session already running - send notification to check inbox
-		fmt.Printf("Session already running, notifying to check inbox...\n")
-		time.Sleep(500 * time.Millisecond) // Brief pause for notification
+		fmt.Printf("Session already running\n")
 	} else {
 		// Start new session
 		fmt.Printf("Starting session for %s/%s...\n", rigName, polecatName)
 		if err := sessMgr.Start(polecatName, session.StartOptions{}); err != nil {
 			return fmt.Errorf("starting session: %w", err)
 		}
-		// Wait for Claude Code to fully initialize (banner, prompt ready)
-		// 3 seconds is enough for the UI to stabilize
-		time.Sleep(3 * time.Second)
 	}
 
 	fmt.Printf("%s Session started. Attach with: %s\n",
 		style.Bold.Render("✓"),
 		style.Dim.Render(fmt.Sprintf("gt session at %s/%s", rigName, polecatName)))
 
-	// Send direct nudge to start working using reliable NudgeSession
-	// The polecat has a work assignment in its inbox; just tell it to check
-	sessionName := sessMgr.SessionName(polecatName)
-	nudgeMsg := fmt.Sprintf("You have a work assignment. Run 'gt mail inbox' to see it, then start working on issue %s.", assignmentID)
-	if err := t.NudgeSession(sessionName, nudgeMsg); err != nil {
-		fmt.Printf("  %s\n", style.Dim.Render(fmt.Sprintf("Warning: could not nudge polecat: %v", err)))
-	} else {
-		fmt.Printf("  %s\n", style.Dim.Render("Polecat nudged to start working"))
-	}
+	// NOTE: We do NOT send a nudge here. Claude Code takes 10-20+ seconds to initialize,
+	// and sending keys before the prompt is ready causes them to be mangled.
+	// The Deacon will poll with WaitForClaudeReady and send a trigger when ready.
+	// The polecat's SessionStart hook runs gt prime, and work assignment is in its inbox.
 
-	// Notify Witness about the spawn - Witness will monitor startup and nudge when ready
-	// Note: If Witness is down, Deacon's health check will wake it and Witness will
-	// process the SPAWN message from its inbox on startup.
+	// Notify Witness about the spawn for monitoring
 	// Use town-level beads for cross-agent mail (gt-c6b: mail coordination uses town-level)
 	townRouter := mail.NewRouter(townRoot)
 	witnessAddr := fmt.Sprintf("%s/witness", rigName)
 	sender := detectSender()
+	sessionName := sessMgr.SessionName(polecatName)
 	spawnNotification := &mail.Message{
 		To:      witnessAddr,
 		From:    sender,
@@ -400,12 +388,9 @@ Issue: %s
 Session: %s
 Spawned by: %s
 
-Please monitor this polecat's startup. When Claude is ready (you can see the prompt
-in the tmux session), send a nudge to start working:
-
-    tmux send-keys -t %s "Check your inbox with 'gt mail inbox' and begin working." Enter
-
-The polecat has a work assignment in its inbox.`, polecatName, assignmentID, sessMgr.SessionName(polecatName), sender, sessMgr.SessionName(polecatName)),
+The Deacon will trigger this polecat when Claude is ready (WaitForClaudeReady).
+The polecat's SessionStart hook runs gt prime, and work assignment is in its inbox.
+Monitor for stuck/idle state after a few minutes.`, polecatName, assignmentID, sessionName, sender),
 	}
 
 	if err := townRouter.Send(spawnNotification); err != nil {