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.go

@@ -0,0 +1,71 @@
+package doctor
+
+import (
+	"os"
+	"path/filepath"
+)
+
+// TownGitCheck verifies that the town root directory is under version control.
+// Having the town harness in git is optional but recommended for:
+// - Backing up personal Gas Town configuration and operating history
+// - Tracking mail and coordination beads
+// - Easier federation across machines
+type TownGitCheck struct {
+	BaseCheck
+}
+
+// NewTownGitCheck creates a new town git version control check.
+func NewTownGitCheck() *TownGitCheck {
+	return &TownGitCheck{
+		BaseCheck: BaseCheck{
+			CheckName:        "town-git",
+			CheckDescription: "Verify town root is under version control",
+		},
+	}
+}
+
+// Run checks if the town root has a .git directory.
+func (c *TownGitCheck) Run(ctx *CheckContext) *CheckResult {
+	gitDir := filepath.Join(ctx.TownRoot, ".git")
+	info, err := os.Stat(gitDir)
+
+	if os.IsNotExist(err) {
+		return &CheckResult{
+			Name:    c.Name(),
+			Status:  StatusWarning,
+			Message: "Town root is not under version control",
+			Details: []string{
+				"Your town harness contains personal configuration and operating history",
+				"Version control makes it easier to backup and federate across machines",
+			},
+			FixHint: "Run 'git init' in your town root to initialize a repository",
+		}
+	}
+
+	if err != nil {
+		return &CheckResult{
+			Name:    c.Name(),
+			Status:  StatusError,
+			Message: "Failed to check town git status: " + err.Error(),
+		}
+	}
+
+	// Verify it's actually a directory (not a file named .git)
+	if !info.IsDir() {
+		return &CheckResult{
+			Name:    c.Name(),
+			Status:  StatusWarning,
+			Message: "Town root .git is not a directory",
+			Details: []string{
+				"Expected .git to be a directory, but it's a file",
+				"This may indicate a git worktree or submodule configuration",
+			},
+		}
+	}
+
+	return &CheckResult{
+		Name:    c.Name(),
+		Status:  StatusOK,
+		Message: "Town root is under version control",
+	}
+}