diff --git a/stdlib/@tests/stubtest_allowlists/py310.txt b/stdlib/@tests/stubtest_allowlists/py310.txt
index d2d31ee8ef53..73bc3da9eb6e 100644
--- a/stdlib/@tests/stubtest_allowlists/py310.txt
+++ b/stdlib/@tests/stubtest_allowlists/py310.txt
@@ -295,3 +295,9 @@ typing_extensions\.Annotated  # Undocumented implementation details
 # (Remove once 3.10.17 becomes available for all platforms)
 (email._header_value_parser.get_encoded_word)?
 (email._header_value_parser.make_quoted_pairs)?
+
+# These methods have no default implementation for Python < 3.13.
+_pickle.Pickler.persistent_id
+_pickle.Unpickler.persistent_load
+pickle.Pickler.persistent_id
+pickle.Unpickler.persistent_load
diff --git a/stdlib/@tests/stubtest_allowlists/py311.txt b/stdlib/@tests/stubtest_allowlists/py311.txt
index 92a7543862d7..655e603c06d1 100644
--- a/stdlib/@tests/stubtest_allowlists/py311.txt
+++ b/stdlib/@tests/stubtest_allowlists/py311.txt
@@ -259,3 +259,9 @@ typing_extensions\.Annotated  # Undocumented implementation details
 # (Remove once 3.11.12 becomes available for all platforms)
 (email._header_value_parser.get_encoded_word)?
 (email._header_value_parser.make_quoted_pairs)?
+
+# These methods have no default implementation for Python < 3.13.
+_pickle.Pickler.persistent_id
+_pickle.Unpickler.persistent_load
+pickle.Pickler.persistent_id
+pickle.Unpickler.persistent_load
diff --git a/stdlib/@tests/stubtest_allowlists/py312.txt b/stdlib/@tests/stubtest_allowlists/py312.txt
index aaea7009760b..3222fed0d8aa 100644
--- a/stdlib/@tests/stubtest_allowlists/py312.txt
+++ b/stdlib/@tests/stubtest_allowlists/py312.txt
@@ -228,3 +228,9 @@ sunau.Au_write.initfp
 threading.Lock  # Factory function at runtime, but that wouldn't let us use it in type hints
 types.SimpleNamespace.__init__  # class doesn't accept positional arguments but has default C signature
 typing_extensions\.Annotated  # Undocumented implementation details
+
+# These methods have no default implementation for Python < 3.13.
+_pickle.Pickler.persistent_id
+_pickle.Unpickler.persistent_load
+pickle.Pickler.persistent_id
+pickle.Unpickler.persistent_load
diff --git a/stdlib/@tests/stubtest_allowlists/py39.txt b/stdlib/@tests/stubtest_allowlists/py39.txt
index 04e9978a1ed6..a912b6f85b5b 100644
--- a/stdlib/@tests/stubtest_allowlists/py39.txt
+++ b/stdlib/@tests/stubtest_allowlists/py39.txt
@@ -245,3 +245,9 @@ typing_extensions\.Annotated  # Undocumented implementation details
 # Incompatible changes introduced in Python 3.9.22
 # (Remove once 3.9.22 becomes available for all platforms)
 (email._header_value_parser.get_encoded_word)?
+
+# These methods have no default implementation for Python < 3.13.
+_pickle.Pickler.persistent_id
+_pickle.Unpickler.persistent_load
+pickle.Pickler.persistent_id
+pickle.Unpickler.persistent_load
diff --git a/stdlib/_pickle.pyi b/stdlib/_pickle.pyi
index 50bbb6bc16cd..8e8afb600efa 100644
--- a/stdlib/_pickle.pyi
+++ b/stdlib/_pickle.pyi
@@ -1,4 +1,3 @@
-import sys
 from _typeshed import ReadableBuffer, SupportsWrite
 from collections.abc import Callable, Iterable, Iterator, Mapping
 from pickle import PickleBuffer as PickleBuffer
@@ -75,10 +74,9 @@ class Pickler:
     def memo(self, value: PicklerMemoProxy | dict[int, tuple[int, Any]]) -> None: ...
     def dump(self, obj: Any, /) -> None: ...
     def clear_memo(self) -> None: ...
-    if sys.version_info >= (3, 13):
-        def persistent_id(self, obj: Any, /) -> Any: ...
-    else:
-        persistent_id: Callable[[Any], Any]
+
+    # this method has no default implementation for Python < 3.13
+    def persistent_id(self, obj: Any, /) -> Any: ...
 
 @type_check_only
 class UnpicklerMemoProxy:
@@ -101,7 +99,6 @@ class Unpickler:
     def memo(self, value: UnpicklerMemoProxy | dict[int, tuple[int, Any]]) -> None: ...
     def load(self) -> Any: ...
     def find_class(self, module_name: str, global_name: str, /) -> Any: ...
-    if sys.version_info >= (3, 13):
-        def persistent_load(self, pid: Any, /) -> Any: ...
-    else:
-        persistent_load: Callable[[Any], Any]
+
+    # this method has no default implementation for Python < 3.13
+    def persistent_load(self, pid: Any, /) -> Any: ...