diff --git a/.basedpyright/baseline.json b/.basedpyright/baseline.json
index a7c4183e..cef291cd 100644
--- a/.basedpyright/baseline.json
+++ b/.basedpyright/baseline.json
@@ -4129,30 +4129,6 @@
                     "lineCount": 1
                 }
             },
-            {
-                "code": "reportUnknownMemberType",
-                "range": {
-                    "startColumn": 15,
-                    "endColumn": 30,
-                    "lineCount": 1
-                }
-            },
-            {
-                "code": "reportAny",
-                "range": {
-                    "startColumn": 59,
-                    "endColumn": 63,
-                    "lineCount": 1
-                }
-            },
-            {
-                "code": "reportAny",
-                "range": {
-                    "startColumn": 67,
-                    "endColumn": 73,
-                    "lineCount": 1
-                }
-            },
             {
                 "code": "reportUnnecessaryComparison",
                 "range": {
@@ -6189,30 +6165,6 @@
                     "lineCount": 1
                 }
             },
-            {
-                "code": "reportUnknownVariableType",
-                "range": {
-                    "startColumn": 12,
-                    "endColumn": 16,
-                    "lineCount": 1
-                }
-            },
-            {
-                "code": "reportOperatorIssue",
-                "range": {
-                    "startColumn": 19,
-                    "endColumn": 77,
-                    "lineCount": 1
-                }
-            },
-            {
-                "code": "reportUnknownArgumentType",
-                "range": {
-                    "startColumn": 62,
-                    "endColumn": 66,
-                    "lineCount": 1
-                }
-            },
             {
                 "code": "reportPrivateImportUsage",
                 "range": {
@@ -9979,14 +9931,6 @@
                     "lineCount": 3
                 }
             },
-            {
-                "code": "reportUnknownArgumentType",
-                "range": {
-                    "startColumn": 29,
-                    "endColumn": 75,
-                    "lineCount": 1
-                }
-            },
             {
                 "code": "reportUnknownArgumentType",
                 "range": {
@@ -10043,14 +9987,6 @@
                     "lineCount": 1
                 }
             },
-            {
-                "code": "reportUnknownVariableType",
-                "range": {
-                    "startColumn": 8,
-                    "endColumn": 14,
-                    "lineCount": 1
-                }
-            },
             {
                 "code": "reportUnknownArgumentType",
                 "range": {
diff --git a/arraycontext/container/__init__.py b/arraycontext/container/__init__.py
index 620978ff..6b40db1c 100644
--- a/arraycontext/container/__init__.py
+++ b/arraycontext/container/__init__.py
@@ -89,6 +89,17 @@
 .. class:: SerializedContainer
 
     :canonical: arraycontext.SerializedContainer
+
+References
+----------
+
+.. class:: GenericAlias
+
+    See :class:`types.GenericAlias`.
+
+.. class:: UnionType
+
+    See :class:`types.UnionType`.
 """
 
 from __future__ import annotations
@@ -120,7 +131,6 @@
 
 from collections.abc import Hashable, Sequence
 from functools import singledispatch
-from types import GenericAlias, UnionType
 from typing import (
     TYPE_CHECKING,
     TypeAlias,
@@ -133,18 +143,23 @@
 import numpy as np
 from typing_extensions import TypeIs
 
-from pytools.obj_array import ObjectArrayND as ObjectArrayND
+from pytools.obj_array import ObjectArray, ObjectArrayND as ObjectArrayND
 
 from arraycontext.typing import (
+    ArithArrayContainer,
     ArrayContainer,
     ArrayContainerT,
     ArrayOrArithContainer,
     ArrayOrArithContainerOrScalar as ArrayOrArithContainerOrScalar,
     ArrayOrContainerOrScalar,
+    _UserDefinedArithArrayContainer,
+    _UserDefinedArrayContainer,
 )
 
 
 if TYPE_CHECKING:
+    from types import GenericAlias, UnionType
+
     from pymbolic.geometric_algebra import CoeffT, MultiVector
 
     from arraycontext.context import ArrayContext
@@ -217,17 +232,21 @@ def is_array_container_type(cls: type | GenericAlias | UnionType) -> bool:
         function will say that :class:`numpy.ndarray` is an array container
         type, only object arrays *actually are* array containers.
     """
-    if cls is ArrayContainer:
+    if cls is ArrayContainer or cls is ArithArrayContainer:
         return True
 
-    while isinstance(cls, GenericAlias):
-        cls = get_origin(cls)
+    origin = get_origin(cls)
+    if origin is not None:
+        cls = origin  # pyright: ignore[reportAny]
 
     assert isinstance(cls, type), (
         f"must pass a {type!r}, not a '{cls!r}'")
 
     return (
-            cls is ArrayContainer  # pyright: ignore[reportUnnecessaryComparison]
+            cls is ObjectArray
+            or cls is ArrayContainer  # pyright: ignore[reportUnnecessaryComparison]
+            or cls is _UserDefinedArrayContainer
+            or cls is _UserDefinedArithArrayContainer
             or (serialize_container.dispatch(cls)
                 is not serialize_container.__wrapped__))  # type:ignore[attr-defined]
 
diff --git a/arraycontext/container/dataclass.py b/arraycontext/container/dataclass.py
index d2487567..d0b5c6ec 100644
--- a/arraycontext/container/dataclass.py
+++ b/arraycontext/container/dataclass.py
@@ -66,6 +66,7 @@
 
 if TYPE_CHECKING:
     from collections.abc import Mapping, Sequence
+    from types import GenericAlias, UnionType
 
 
 T = TypeVar("T")
@@ -81,7 +82,7 @@ class _Field(NamedTuple):
     type: type
 
 
-def _is_array_or_container_type(tp: type, /) -> bool:
+def _is_array_or_container_type(tp: type | GenericAlias | UnionType, /) -> bool:
     if tp is np.ndarray:
         warn("Encountered 'numpy.ndarray' in a dataclass_array_container. "
              "This is deprecated and will stop working in 2026. "
diff --git a/arraycontext/context.py b/arraycontext/context.py
index 0625a752..0d61d59c 100644
--- a/arraycontext/context.py
+++ b/arraycontext/context.py
@@ -84,10 +84,6 @@
 
     A :class:`typing.ParamSpec` representing the arguments of a function
     being :meth:`ArrayContext.outline`\ d.
-
-References
-----------
-
 """
 
 from __future__ import annotations