feat(doctor): Add rig-level health checks (gt-f9x.6)

Add 7 new checks for rig health when using `gt doctor --rig <name>`:

- rig-is-git-repo: Verify mayor/rig/ is a valid git clone
- git-exclude-configured: Check .git/info/exclude has Gas Town dirs (fixable)
- witness-exists: Verify witness/ structure exists (fixable)
- refinery-exists: Verify refinery/ structure exists (fixable)
- mayor-clone-exists: Verify mayor/rig/ clone exists (fixable)
- polecat-clones-valid: Verify polecat directories are valid clones
- beads-config-valid: Verify beads configuration works (fixable)

Checks are only registered when --rig flag is provided.

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

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

internal/cmd/doctor.go

@@ -37,6 +37,15 @@ Clone divergence checks:
   - persistent-role-branches Detect crew/witness/refinery not on main
   - clone-divergence         Detect clones significantly behind origin/main
 
+Rig checks (with --rig flag):
+  - rig-is-git-repo          Verify rig is a valid git repository
+  - git-exclude-configured   Check .git/info/exclude has Gas Town dirs (fixable)
+  - witness-exists           Verify witness/ structure exists (fixable)
+  - refinery-exists          Verify refinery/ structure exists (fixable)
+  - mayor-clone-exists       Verify mayor/rig/ clone exists (fixable)
+  - polecat-clones-valid     Verify polecat directories are valid clones
+  - beads-config-valid       Verify beads configuration (fixable)
+
 Routing checks (fixable):
   - routes-config            Check beads routing configuration
 
@@ -119,6 +128,11 @@ func runDoctor(cmd *cobra.Command, args []string) error {
 	d.Register(doctor.NewHookSingletonCheck())
 	d.Register(doctor.NewOrphanedAttachmentsCheck())
 
+	// Rig-specific checks (only when --rig is specified)
+	if doctorRig != "" {
+		d.RegisterAll(doctor.RigChecks()...)
+	}
+
 	// Run checks
 	var report *doctor.Report
 	if doctorFix {