feat: Add polecat agent bead lifecycle (gt-rxa7v)

Create ephemeral agent beads for ZFC-compliant polecat state tracking.

- Add AgentFields struct and helpers to beads package
  - CreateAgentBead: Creates agent bead with role_type/rig/agent_state
  - UpdateAgentState: Updates agent_state and hook_bead fields
  - DeleteAgentBead: Hard-deletes ephemeral agent bead
  - GetAgentBead: Retrieves and parses agent bead

- Integrate lifecycle in polecat manager:
  - Add(): Creates gt-polecat-<rig>-<name> bead with state=spawning
  - Recreate(): Deletes old bead, creates fresh with state=spawning
  - RemoveWithOptions(): Deletes agent bead on nuke

This enables Witness to read polecat state from beads instead of
tmux scraping. State updates (spawning→working→done) are done by
polecats via bd agent state (separate beads CLI enhancement).

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

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

internal/polecat/manager.go

@@ -82,6 +82,12 @@ func (m *Manager) assigneeID(name string) string {
 	return fmt.Sprintf("%s/%s", m.rig.Name, name)
 }
 
+// agentBeadID returns the agent bead ID for a polecat.
+// Format: "gt-polecat-<rig>-<name>" (e.g., "gt-polecat-gastown-Toast")
+func (m *Manager) agentBeadID(name string) string {
+	return fmt.Sprintf("gt-polecat-%s-%s", m.rig.Name, name)
+}
+
 // repoBase returns the git directory and Git object to use for worktree operations.
 // Prefers the shared bare repo (.repo.git) if it exists, otherwise falls back to mayor/rig.
 // The bare repo architecture allows all worktrees (refinery, polecats) to share branch visibility.
@@ -155,6 +161,19 @@ func (m *Manager) Add(name string) (*Polecat, error) {
 		fmt.Printf("Warning: could not set up shared beads: %v\n", err)
 	}
 
+	// Create agent bead for ZFC compliance (self-report state).
+	// State starts as "spawning" - will be updated to "working" when Claude starts.
+	agentID := m.agentBeadID(name)
+	_, err = m.beads.CreateAgentBead(agentID, agentID, &beads.AgentFields{
+		RoleType:   "polecat",
+		Rig:        m.rig.Name,
+		AgentState: "spawning",
+	})
+	if err != nil {
+		// Non-fatal - log warning but continue
+		fmt.Printf("Warning: could not create agent bead: %v\n", err)
+	}
+
 	// Return polecat with derived state (no issue assigned yet = idle)
 	// State is derived from beads, not stored in state.json
 	now := time.Now()
@@ -228,6 +247,15 @@ func (m *Manager) RemoveWithOptions(name string, force, nuclear bool) error {
 	m.namePool.Release(name)
 	_ = m.namePool.Save()
 
+	// Delete agent bead (non-fatal: may not exist or beads may not be available)
+	agentID := m.agentBeadID(name)
+	if err := m.beads.DeleteAgentBead(agentID); err != nil {
+		// Only log if not "not found" - it's ok if it doesn't exist
+		if !errors.Is(err, beads.ErrNotFound) {
+			fmt.Printf("Warning: could not delete agent bead %s: %v\n", agentID, err)
+		}
+	}
+
 	return nil
 }
 
@@ -286,6 +314,14 @@ func (m *Manager) Recreate(name string, force bool) (*Polecat, error) {
 		}
 	}
 
+	// Delete old agent bead before recreation (non-fatal)
+	agentID := m.agentBeadID(name)
+	if err := m.beads.DeleteAgentBead(agentID); err != nil {
+		if !errors.Is(err, beads.ErrNotFound) {
+			fmt.Printf("Warning: could not delete old agent bead %s: %v\n", agentID, err)
+		}
+	}
+
 	// Remove the worktree (use force for git worktree removal)
 	if err := repoGit.WorktreeRemove(polecatPath, true); err != nil {
 		// Fall back to direct removal
@@ -313,6 +349,16 @@ func (m *Manager) Recreate(name string, force bool) (*Polecat, error) {
 		fmt.Printf("Warning: could not set up shared beads: %v\n", err)
 	}
 
+	// Create fresh agent bead for ZFC compliance
+	_, err = m.beads.CreateAgentBead(agentID, agentID, &beads.AgentFields{
+		RoleType:   "polecat",
+		Rig:        m.rig.Name,
+		AgentState: "spawning",
+	})
+	if err != nil {
+		fmt.Printf("Warning: could not create agent bead: %v\n", err)
+	}
+
 	// Return fresh polecat
 	now := time.Now()
 	return &Polecat{