feat(doctor): add town-git check for version control

Checks whether the town root (~/gt) is under git version control.
Having the town harness in git is optional but recommended for:
- Backing up personal Gas Town configuration and history
- Tracking mail and coordination beads
- Easier federation across machines

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

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

internal/doctor/town_git_check_test.go

@@ -0,0 +1,88 @@
+package doctor
+
+import (
+	"os"
+	"path/filepath"
+	"testing"
+)
+
+func TestNewTownGitCheck(t *testing.T) {
+	check := NewTownGitCheck()
+
+	if check.Name() != "town-git" {
+		t.Errorf("expected name 'town-git', got %q", check.Name())
+	}
+
+	if check.Description() == "" {
+		t.Error("expected non-empty description")
+	}
+
+	if check.CanFix() {
+		t.Error("expected CanFix() to return false")
+	}
+}
+
+func TestTownGitCheck_NoGitDir(t *testing.T) {
+	// Create temp directory without .git
+	tmpDir, err := os.MkdirTemp("", "town-git-test-*")
+	if err != nil {
+		t.Fatalf("failed to create temp dir: %v", err)
+	}
+	defer os.RemoveAll(tmpDir)
+
+	ctx := &CheckContext{TownRoot: tmpDir}
+	check := NewTownGitCheck()
+	result := check.Run(ctx)
+
+	if result.Status != StatusWarning {
+		t.Errorf("expected StatusWarning, got %v", result.Status)
+	}
+
+	if result.FixHint == "" {
+		t.Error("expected non-empty FixHint")
+	}
+}
+
+func TestTownGitCheck_WithGitDir(t *testing.T) {
+	// Create temp directory with .git
+	tmpDir, err := os.MkdirTemp("", "town-git-test-*")
+	if err != nil {
+		t.Fatalf("failed to create temp dir: %v", err)
+	}
+	defer os.RemoveAll(tmpDir)
+
+	gitDir := filepath.Join(tmpDir, ".git")
+	if err := os.Mkdir(gitDir, 0755); err != nil {
+		t.Fatalf("failed to create .git dir: %v", err)
+	}
+
+	ctx := &CheckContext{TownRoot: tmpDir}
+	check := NewTownGitCheck()
+	result := check.Run(ctx)
+
+	if result.Status != StatusOK {
+		t.Errorf("expected StatusOK, got %v", result.Status)
+	}
+}
+
+func TestTownGitCheck_GitIsFile(t *testing.T) {
+	// Create temp directory with .git as a file (worktree case)
+	tmpDir, err := os.MkdirTemp("", "town-git-test-*")
+	if err != nil {
+		t.Fatalf("failed to create temp dir: %v", err)
+	}
+	defer os.RemoveAll(tmpDir)
+
+	gitFile := filepath.Join(tmpDir, ".git")
+	if err := os.WriteFile(gitFile, []byte("gitdir: /some/path"), 0644); err != nil {
+		t.Fatalf("failed to create .git file: %v", err)
+	}
+
+	ctx := &CheckContext{TownRoot: tmpDir}
+	check := NewTownGitCheck()
+	result := check.Run(ctx)
+
+	if result.Status != StatusWarning {
+		t.Errorf("expected StatusWarning for .git file, got %v", result.Status)
+	}
+}