fix(doctor): add role beads check with shared definitions (#378)

Role beads (hq-*-role) are templates that define role characteristics.
They are created during gt install but creation may fail silently.
Without role beads, agents fall back to defaults.

Changes:
- Add beads.AllRoleBeadDefs() as single source of truth for role bead definitions
- Update gt install to use shared definitions
- Add doctor check that detects missing role beads (warning, not error)
- Doctor --fix creates missing role beads

Fixes #371

Co-authored-by: julianknutsen <julianknutsen@users.noreply.github>
Co-authored-by: Claude Opus 4.5 <noreply@anthropic.com>

internal/doctor/role_beads_check_test.go

@@ -0,0 +1,68 @@
+package doctor
+
+import (
+	"os"
+	"path/filepath"
+	"testing"
+
+	"github.com/steveyegge/gastown/internal/beads"
+)
+
+func TestRoleBeadsCheck_Run(t *testing.T) {
+	t.Run("no town beads returns warning", func(t *testing.T) {
+		tmpDir := t.TempDir()
+		// Create minimal town structure without .beads
+		if err := os.MkdirAll(filepath.Join(tmpDir, "mayor"), 0755); err != nil {
+			t.Fatal(err)
+		}
+
+		check := NewRoleBeadsCheck()
+		ctx := &CheckContext{TownRoot: tmpDir}
+		result := check.Run(ctx)
+
+		// Without .beads directory, all role beads are "missing"
+		expectedCount := len(beads.AllRoleBeadDefs())
+		if result.Status != StatusWarning {
+			t.Errorf("expected StatusWarning, got %v: %s", result.Status, result.Message)
+		}
+		if len(result.Details) != expectedCount {
+			t.Errorf("expected %d missing role beads, got %d: %v", expectedCount, len(result.Details), result.Details)
+		}
+	})
+
+	t.Run("check is fixable", func(t *testing.T) {
+		check := NewRoleBeadsCheck()
+		if !check.CanFix() {
+			t.Error("RoleBeadsCheck should be fixable")
+		}
+	})
+}
+
+func TestRoleBeadsCheck_usesSharedDefs(t *testing.T) {
+	// Verify the check uses beads.AllRoleBeadDefs()
+	roleDefs := beads.AllRoleBeadDefs()
+
+	if len(roleDefs) < 7 {
+		t.Errorf("expected at least 7 role beads, got %d", len(roleDefs))
+	}
+
+	// Verify key roles are present
+	expectedIDs := map[string]bool{
+		"hq-mayor-role":    false,
+		"hq-deacon-role":   false,
+		"hq-witness-role":  false,
+		"hq-refinery-role": false,
+	}
+
+	for _, role := range roleDefs {
+		if _, exists := expectedIDs[role.ID]; exists {
+			expectedIDs[role.ID] = true
+		}
+	}
+
+	for id, found := range expectedIDs {
+		if !found {
+			t.Errorf("expected role %s not found in AllRoleBeadDefs()", id)
+		}
+	}
+}