diff --git a/pytools/persistent_dict.py b/pytools/persistent_dict.py
index de0b5fe4..050e0be0 100644
--- a/pytools/persistent_dict.py
+++ b/pytools/persistent_dict.py
@@ -244,8 +244,18 @@ def __call__(self, key: Any) -> str:
     # understandably don't like it.
 
     def update_for_type(self, key_hash: Hash, key: type) -> None:
-        key_hash.update(
-            f"{key.__module__}.{key.__qualname__}.{key.__name__}".encode())
+        try:
+            module = sys.modules[key.__module__]
+            resolved = module
+            for attr in key.__qualname__.split("."):
+                resolved = getattr(resolved, attr)  # pyright: ignore[reportAny]
+            if resolved is key:
+                # Globally accessible: hash based on name
+                self.rec(key_hash, f"{key.__module__}.{key.__qualname__}")
+            else:
+                raise ValueError(f"Cannot hash function-local class '{key}'")
+        except (KeyError, AttributeError):
+            raise ValueError(f"Cannot hash function-local class '{key}'") from None
 
     update_for_ABCMeta = update_for_type
 
diff --git a/pytools/test/test_persistent_dict.py b/pytools/test/test_persistent_dict.py
index 2cdd2a7c..e06c0978 100644
--- a/pytools/test/test_persistent_dict.py
+++ b/pytools/test/test_persistent_dict.py
@@ -503,8 +503,6 @@ def test_ABC_hashing() -> None:  # noqa: N802
     class MyABC(ABC):  # noqa: B024
         pass
 
-    assert keyb(MyABC) != keyb(ABC)
-
     with pytest.raises(TypeError):
         keyb(MyABC())
 
@@ -515,19 +513,29 @@ class MyABC2(MyABC):
         def update_persistent_hash(self, key_hash, key_builder):
             key_builder.rec(key_hash, 42)
 
-    assert keyb(MyABC2) != keyb(MyABC)
     assert keyb(MyABC2())
 
     class MyABC3(metaclass=ABCMeta):  # noqa: B024
         def update_persistent_hash(self, key_hash, key_builder):
             key_builder.rec(key_hash, 42)
 
-    assert keyb(MyABC3) != keyb(MyABC) != keyb(MyABC3())
+    assert keyb(MyABC3())
+
+
+class WithoutUpdateMethodGlobal:
+    pass
 
 
 def test_class_hashing() -> None:
     keyb = KeyBuilder()
 
+    assert keyb(WithoutUpdateMethodGlobal) == keyb(WithoutUpdateMethodGlobal)
+    assert keyb(WithoutUpdateMethodGlobal) == "49c4673089d30507"
+
+    with pytest.raises(TypeError):
+        # does not have update_persistent_hash() = > will raise
+        keyb(WithoutUpdateMethodGlobal())
+
     class WithUpdateMethod:
         def update_persistent_hash(self, key_hash, key_builder):
             # Only called for instances of this class, not for the class itself
@@ -540,15 +548,11 @@ class TagClass(Tag):
     class TagClass2(Tag):
         pass
 
-    assert keyb(WithUpdateMethod) != keyb(WithUpdateMethod())
-    assert keyb(TagClass) != keyb(TagClass())
-    assert keyb(TagClass2) != keyb(TagClass2())
+    assert keyb(WithUpdateMethod()) == keyb(WithUpdateMethod())
 
-    assert keyb(TagClass) != keyb(TagClass2)
     assert keyb(TagClass()) != keyb(TagClass2())
 
     assert keyb(TagClass()) == "7b3e4e66503438f6"
-    assert keyb(TagClass2) == "690b86bbf51aad83"
 
     @tag_dataclass
     class TagClass3(Tag):