diff --git a/src/async_kernel/compat/json.py b/src/async_kernel/compat/json.py
index 9e78bfff..3e57e0d7 100644
--- a/src/async_kernel/compat/json.py
+++ b/src/async_kernel/compat/json.py
@@ -9,9 +9,31 @@
 if TYPE_CHECKING:
     from collections.abc import Callable
 
-    pack_json_bytes: Callable[[Any], bytes]
-    pack_json_str: Callable[[Any], str]
-    unpack_json: Callable[[str | bytes], Any]
+    from jupyter_client.jsonutil import json_default
+
+    def pack_json_bytes(obj: Any, /, default: Callable[[Any], Any] | None = json_default) -> bytes:
+        """
+        Pack obj into json serialized bytes.
+
+        Args:
+            data: The data to serialize.
+            default: A function that should return a serializable version of obj or raise TypeError.
+        """
+        ...
+
+    def pack_json_str(obj: Any, /, default: Callable[[Any], Any] | None = json_default) -> str:
+        """
+        Pack obj into json serialized string.
+
+        Args:
+            data: The data to serialize.
+            default: A function that should return a serializable version of obj or raise TypeError.
+        """
+        ...
+
+    def unpack_json(data: str | bytes, /) -> Any:
+        "Deserialize data in a Python object."
+        ...
 
 
 if importlib.util.find_spec("jupyter_client"):
@@ -19,11 +41,11 @@
 
     from jupyter_client.jsonutil import json_default
 
-    def _jc_pack_bytes(data: Any) -> bytes:
-        return json.dumps(data, default=json_default).encode()
+    def _jc_pack_bytes(obj: Any, default: Callable[[Any], Any] | None = json_default) -> bytes:
+        return json.dumps(obj, default=default).encode()
 
-    def _jc_pack_str(data: Any) -> str:
-        return json.dumps(data, default=json_default)
+    def _jc_pack_str(obj: Any, default: Callable[[Any], Any] | None = json_default) -> str:
+        return json.dumps(obj, allow_nan=False, default=default)
 
     pack_json_bytes, pack_json_str, unpack_json = _jc_pack_bytes, _jc_pack_str, json.loads
 
@@ -36,10 +58,10 @@ def _jc_pack_str(data: Any) -> str:
 
     ORJSON_OPTION = orjson.OPT_SERIALIZE_NUMPY | orjson.OPT_NAIVE_UTC | orjson.OPT_UTC_Z
 
-    def _oj_pack_bytes(data) -> bytes:
-        return orjson.dumps(data, default=json_default, option=ORJSON_OPTION)
+    def _oj_pack_bytes(obj: Any, default: Callable[[Any], Any] | None = json_default) -> bytes:
+        return orjson.dumps(obj, default=default, option=ORJSON_OPTION)
 
-    def _oj_pack_str(data) -> str:
-        return orjson.dumps(data, default=json_default, option=ORJSON_OPTION).decode()
+    def _oj_pack_str(obj: Any, default: Callable[[Any], Any] | None = json_default) -> str:
+        return orjson.dumps(obj, default=default, option=ORJSON_OPTION).decode()
 
     pack_json_bytes, pack_json_str, unpack_json = _oj_pack_bytes, _oj_pack_str, orjson.loads