Test the initialize entry adapter forms

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

tests/unit/test_refinement_three_level_multipatch.py

@@ -313,3 +313,20 @@ class ConstructorAndSchedule(unittest.TestCase):
 
 if __name__=='__main__':
     unittest.main()
+
+
+class InitialLevels(unittest.TestCase):
+    """initialize() entry adapter: positional per-level arrays or the legacy names, never both."""
+
+    def test_forms(self):
+        a, b, c = object(), object(), object()
+        f = host._initial_levels
+        self.assertEqual(f((a, b), None, None, None), (a, b))
+        self.assertEqual(f((a, b, c), None, None, None), (a, b, c))
+        self.assertEqual(f((a, b), None, None, c), (a, b, c))      # old initialize(c, f, child_g=g)
+        self.assertEqual(f((), a, b, None), (a, b))
+        self.assertEqual(f((), a, b, c), (a, b, c))
+        for args in (((a,), None, None, c), ((a, b, c), None, None, c), ((a,), a, b, None),
+                     ((), a, None, None), ((), None, b, c)):
+            with self.subTest(args=args), self.assertRaises(TypeError):
+                f(*args)