feat(formula): add checksum-based auto-update for embedded formulas

Adds infrastructure to automatically update embedded formulas when
the binary is upgraded, while preserving user customizations.

Changes:
- Add CheckFormulaHealth() to detect outdated/modified/missing formulas
- Add UpdateFormulas() to safely update formulas via gt doctor --fix
- Track installed formula checksums in .beads/formulas/.installed.json
- Add FormulaCheck to gt doctor with auto-fix capability
- Compute checksums at runtime from embedded files (no build-time manifest)

Update scenarios:
- Outdated (embedded changed, user unchanged): Update automatically
- Modified (user customized): Skip with warning
- Missing (user deleted): Reinstall with message
- New (never installed): Install

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

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

internal/doctor/formula_check.go

@@ -0,0 +1,123 @@
+package doctor
+
+import (
+	"fmt"
+	"strings"
+
+	"github.com/steveyegge/gastown/internal/formula"
+)
+
+// FormulaCheck verifies that embedded formulas are up-to-date.
+// It detects outdated formulas (binary updated), missing formulas (user deleted),
+// and modified formulas (user customized). Can auto-fix outdated and missing.
+type FormulaCheck struct {
+	FixableCheck
+}
+
+// NewFormulaCheck creates a new formula check.
+func NewFormulaCheck() *FormulaCheck {
+	return &FormulaCheck{
+		FixableCheck: FixableCheck{
+			BaseCheck: BaseCheck{
+				CheckName:        "formulas",
+				CheckDescription: "Check embedded formulas are up-to-date",
+			},
+		},
+	}
+}
+
+// Run checks if formulas need updating.
+func (c *FormulaCheck) Run(ctx *CheckContext) *CheckResult {
+	report, err := formula.CheckFormulaHealth(ctx.TownRoot)
+	if err != nil {
+		return &CheckResult{
+			Name:    c.Name(),
+			Status:  StatusWarning,
+			Message: fmt.Sprintf("Could not check formulas: %v", err),
+		}
+	}
+
+	// All good
+	if report.Outdated == 0 && report.Missing == 0 && report.Modified == 0 && report.New == 0 {
+		return &CheckResult{
+			Name:    c.Name(),
+			Status:  StatusOK,
+			Message: fmt.Sprintf("%d formulas up-to-date", report.OK),
+		}
+	}
+
+	// Build details
+	var details []string
+	var needsFix bool
+
+	for _, f := range report.Formulas {
+		switch f.Status {
+		case "outdated":
+			details = append(details, fmt.Sprintf("  %s: update available", f.Name))
+			needsFix = true
+		case "missing":
+			details = append(details, fmt.Sprintf("  %s: missing (will reinstall)", f.Name))
+			needsFix = true
+		case "modified":
+			details = append(details, fmt.Sprintf("  %s: locally modified (skipping)", f.Name))
+		case "new":
+			details = append(details, fmt.Sprintf("  %s: new formula available", f.Name))
+			needsFix = true
+		}
+	}
+
+	// Determine status
+	status := StatusOK
+	if needsFix {
+		status = StatusWarning
+	}
+
+	// Build message
+	var parts []string
+	if report.Outdated > 0 {
+		parts = append(parts, fmt.Sprintf("%d outdated", report.Outdated))
+	}
+	if report.Missing > 0 {
+		parts = append(parts, fmt.Sprintf("%d missing", report.Missing))
+	}
+	if report.New > 0 {
+		parts = append(parts, fmt.Sprintf("%d new", report.New))
+	}
+	if report.Modified > 0 {
+		parts = append(parts, fmt.Sprintf("%d modified", report.Modified))
+	}
+
+	message := fmt.Sprintf("Formulas: %s", strings.Join(parts, ", "))
+
+	result := &CheckResult{
+		Name:    c.Name(),
+		Status:  status,
+		Message: message,
+		Details: details,
+	}
+
+	if needsFix {
+		result.FixHint = "Run 'gt doctor --fix' to update formulas"
+	}
+
+	return result
+}
+
+// Fix updates outdated and missing formulas.
+func (c *FormulaCheck) Fix(ctx *CheckContext) error {
+	updated, skipped, reinstalled, err := formula.UpdateFormulas(ctx.TownRoot)
+	if err != nil {
+		return err
+	}
+
+	// Log what was done (caller will re-run check to show new status)
+	if updated > 0 || reinstalled > 0 || skipped > 0 {
+		// The doctor framework will re-run the check after fix
+		// so we don't need to log here
+		_ = updated
+		_ = reinstalled
+		_ = skipped
+	}
+
+	return nil
+}