feat(joinir): error_tags freeze_with_hint

- Add freeze_with_hint(tag, msg, hint) API
- Format: "[joinir/<tag>] <msg>  Hint: <hint>"
- Panic on empty hint (must provide actionable suggestion)
- Keep existing freeze() for backward compatibility

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

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

src/mir/join_ir/lowering/error_tags.rs

@@ -34,6 +34,27 @@ pub fn freeze(diagnostic: &str) -> String {
     format!("[joinir/freeze] {}", diagnostic)
 }
 
+/// Create error message with hint (Phase 109)
+///
+/// Format: "[joinir/<category>/<tag>] <msg>  Hint: <hint>"
+///
+/// # Panics
+/// Panics if hint is empty (must provide actionable fix suggestion)
+///
+/// # Example
+/// ```rust,ignore
+/// return Err(freeze_with_hint(
+///     "phase107/balanced_depth_scan/missing_tail_inc",
+///     "tail increment not found",
+///     "add 'i = i + 1' at top-level"
+/// ));
+/// // Output: "[joinir/phase107/balanced_depth_scan/missing_tail_inc] tail increment not found  Hint: add 'i = i + 1' at top-level"
+/// ```
+pub fn freeze_with_hint(tag: &str, msg: &str, hint: &str) -> String {
+    assert!(!hint.is_empty(), "hint must not be empty (tag: {})", tag);
+    format!("[joinir/{}] {}  Hint: {}", tag, msg, hint)
+}
+
 /// ExitLine contract violation - Phase 81+ exit metadata contract broken
 ///
 /// Used when exit line reconnection or exit PHI construction violates
@@ -133,4 +154,22 @@ mod tests {
         assert!(err.contains("[joinir/lowering/boundary]"));
         assert!(err.contains("Invalid block"));
     }
+
+    #[test]
+    fn test_freeze_with_hint_format() {
+        let result = freeze_with_hint(
+            "phase107/balanced_depth_scan/missing_tail_inc",
+            "tail increment not found",
+            "add 'i = i + 1' at top-level",
+        );
+        assert!(result.contains("[joinir/phase107/balanced_depth_scan/missing_tail_inc]"));
+        assert!(result.contains("Hint:"));
+        assert!(result.contains("add 'i = i + 1'"));
+    }
+
+    #[test]
+    #[should_panic(expected = "hint must not be empty")]
+    fn test_freeze_with_hint_empty_hint_panics() {
+        freeze_with_hint("test/tag", "message", "");
+    }
 }