We are currently solving the following issue within our repository. Here is the issue text:
--- BEGIN ISSUE ---
behaviors with decorated mixin methods cannot be pickled
### Version of Awkward Array

main

### Description and code to reproduce

The mixin machinery introduces a closure, which `pickle` can't serialise.

--- END ISSUE ---

Below are some code segments, each from a relevant file. One or more of these files may contain bugs.
--- BEGIN FILES ---
Path: `src/awkward/behaviors/mixins.py`
Content:
```
1 # BSD 3-Clause License; see https://github.com/scikit-hep/awkward-1.0/blob/main/LICENSE
2 
3 
4 import sys
5 
6 import awkward as ak
7 
8 
9 def mixin_class(registry, name=None):
10     """
11     Args:
12         registry (dict): The destination behavior mapping registry. Typically,
13             this would be the global registry #ak.behavior, but one may wish
14             to register methods in an alternative way.
15         name (str): The name to assign to the behaviour class.
16 
17     This decorator can be used to register a behavior mixin class.
18 
19     Any inherited behaviors will automatically be made available to the decorated
20     class.
21 
22     See the "Mixin decorators" section of #ak.behavior for further details.
23     """
24 
25     def register(cls):
26         cls_name = cls.__name__
27         if name is None:
28             behavior_name = cls_name
29         else:
30             behavior_name = name
31 
32         record = type(
33             cls_name + "Record",
34             (cls, ak.highlevel.Record),
35             {"__module__": cls.__module__},
36         )
37         setattr(sys.modules[cls.__module__], cls_name + "Record", record)
38         registry[behavior_name] = record
39         array = type(
40             cls_name + "Array",
41             (cls, ak.highlevel.Array),
42             {"__module__": cls.__module__},
43         )
44         setattr(sys.modules[cls.__module__], cls_name + "Array", array)
45         registry["*", behavior_name] = array
46         for basecls in cls.mro():
47             for method in basecls.__dict__.values():
48                 if hasattr(method, "_awkward_mixin"):
49                     ufunc, rhs, transpose = method._awkward_mixin
50                     if rhs is None:
51                         registry.setdefault((ufunc, behavior_name), method)
52                         continue
53                     for rhs_name in list(rhs) + [behavior_name]:
54                         registry.setdefault((ufunc, behavior_name, rhs_name), method)
55                         if transpose is not None and rhs_name != behavior_name:
56                             registry.setdefault(
57                                 (ufunc, rhs_name, behavior_name), transpose
58                             )
59                     if basecls.__name__ in rhs:
60                         rhs.add(behavior_name)
61         return cls
62 
63     return register
64 
65 
66 def mixin_class_method(ufunc, rhs=None, *, transpose=True):
67     """
68     Args:
69         ufunc (numpy.ufunc): A universal function (or NEP18 callable) that is
70             hooked in Awkward Array, i.e. it can be the first argument of a behavior.
71         rhs (Set[type] or None): Set of right-hand side argument types, optional
72             if wrapping a unary function. The left-hand side is expected to
73             always be `self` of the parent class.
74         transpose (bool): If true, automatically create a transpose signature
75             (only makes sense for binary ufuncs).
76 
77     This decorator can be used to register a mixin class method.
78 
79     Using this decorator ensures that derived classes that are declared with the
80     #ak.mixin_class decorator will also have the behaviors that this class has.
81     """
82 
83     def register(method):
84         if not isinstance(rhs, (set, type(None))):
85             raise ak._errors.wrap_error(
86                 ValueError("expected a set of right-hand-side argument types")
87             )
88         if transpose and rhs is not None:
89 
90             def transposed(left, right):
91                 return method(right, left)
92 
93             # make a copy of rhs, we will edit it later
94             method._awkward_mixin = (ufunc, set(rhs), transposed)
95         else:
96             method._awkward_mixin = (ufunc, rhs, None)
97         return method
98 
99     return register
100
```
--- END FILES ---

Please first localize the bug based on the issue statement, and then generate a patch according to the `git diff` format fenced by three backticks.

Here is an example:

```diff
diff --git a/examples/server_async.py b/examples/server_async.py
--- a/examples/server_async.py
+++ b/examples/server_async.py
@@ -313,4 +313,4 @@
 
 
 if __name__ == "__main__":
-    asyncio.run(run_async_server("."), debug=True)
+    asyncio.run(run_async_server(), debug=True)
diff --git a/examples/server_sync.py b/examples/server_sync.py
--- a/examples/server_sync.py
+++ b/examples/server_sync.py
@@ -313,5 +313,5 @@
 
 
 if __name__ == "__main__":
-    server = run_sync_server(".")
+    server = run_sync_server()
     server.shutdown()

```

diff --git a/src/awkward/behaviors/mixins.py b/src/awkward/behaviors/mixins.py
--- a/src/awkward/behaviors/mixins.py
+++ b/src/awkward/behaviors/mixins.py
@@ -1,6 +1,7 @@
 # BSD 3-Clause License; see https://github.com/scikit-hep/awkward-1.0/blob/main/LICENSE
 
 
+import functools
 import sys
 
 import awkward as ak
@@ -63,6 +64,10 @@
     return register
 
 
+def _call_transposed(func, left, right):
+    return func(right, left)
+
+
 def mixin_class_method(ufunc, rhs=None, *, transpose=True):
     """
     Args:
@@ -70,7 +75,8 @@
             hooked in Awkward Array, i.e. it can be the first argument of a behavior.
         rhs (Set[type] or None): Set of right-hand side argument types, optional
             if wrapping a unary function. The left-hand side is expected to
-            always be `self` of the parent class.
+            always be `self` of the parent class. The current class is implicitly
+            included in this set.
         transpose (bool): If true, automatically create a transpose signature
             (only makes sense for binary ufuncs).
 
@@ -86,12 +92,13 @@
                 ValueError("expected a set of right-hand-side argument types")
             )
         if transpose and rhs is not None:
-
-            def transposed(left, right):
-                return method(right, left)
-
             # make a copy of rhs, we will edit it later
-            method._awkward_mixin = (ufunc, set(rhs), transposed)
+            # use partial & a module-scoped function so that this is pickleable
+            method._awkward_mixin = (
+                ufunc,
+                set(rhs),
+                functools.partial(_call_transposed, method),
+            )
         else:
             method._awkward_mixin = (ufunc, rhs, None)
         return method

{"golden_diff": "diff --git a/src/awkward/behaviors/mixins.py b/src/awkward/behaviors/mixins.py\n--- a/src/awkward/behaviors/mixins.py\n+++ b/src/awkward/behaviors/mixins.py\n@@ -1,6 +1,7 @@\n # BSD 3-Clause License; see https://github.com/scikit-hep/awkward-1.0/blob/main/LICENSE\n \n \n+import functools\n import sys\n \n import awkward as ak\n@@ -63,6 +64,10 @@\n     return register\n \n \n+def _call_transposed(func, left, right):\n+    return func(right, left)\n+\n+\n def mixin_class_method(ufunc, rhs=None, *, transpose=True):\n     \"\"\"\n     Args:\n@@ -70,7 +75,8 @@\n             hooked in Awkward Array, i.e. it can be the first argument of a behavior.\n         rhs (Set[type] or None): Set of right-hand side argument types, optional\n             if wrapping a unary function. The left-hand side is expected to\n-            always be `self` of the parent class.\n+            always be `self` of the parent class. The current class is implicitly\n+            included in this set.\n         transpose (bool): If true, automatically create a transpose signature\n             (only makes sense for binary ufuncs).\n \n@@ -86,12 +92,13 @@\n                 ValueError(\"expected a set of right-hand-side argument types\")\n             )\n         if transpose and rhs is not None:\n-\n-            def transposed(left, right):\n-                return method(right, left)\n-\n             # make a copy of rhs, we will edit it later\n-            method._awkward_mixin = (ufunc, set(rhs), transposed)\n+            # use partial & a module-scoped function so that this is pickleable\n+            method._awkward_mixin = (\n+                ufunc,\n+                set(rhs),\n+                functools.partial(_call_transposed, method),\n+            )\n         else:\n             method._awkward_mixin = (ufunc, rhs, None)\n         return method\n", "issue": "behaviors with decorated mixin methods cannot be pickled\n### Version of Awkward Array\n\nmain\n\n### Description and code to reproduce\n\nThe mixin machinery introduces a closure, which `pickle` can't serialise.\n", "before_files": [{"content": "# BSD 3-Clause License; see https://github.com/scikit-hep/awkward-1.0/blob/main/LICENSE\n\n\nimport sys\n\nimport awkward as ak\n\n\ndef mixin_class(registry, name=None):\n    \"\"\"\n    Args:\n        registry (dict): The destination behavior mapping registry. Typically,\n            this would be the global registry #ak.behavior, but one may wish\n            to register methods in an alternative way.\n        name (str): The name to assign to the behaviour class.\n\n    This decorator can be used to register a behavior mixin class.\n\n    Any inherited behaviors will automatically be made available to the decorated\n    class.\n\n    See the \"Mixin decorators\" section of #ak.behavior for further details.\n    \"\"\"\n\n    def register(cls):\n        cls_name = cls.__name__\n        if name is None:\n            behavior_name = cls_name\n        else:\n            behavior_name = name\n\n        record = type(\n            cls_name + \"Record\",\n            (cls, ak.highlevel.Record),\n            {\"__module__\": cls.__module__},\n        )\n        setattr(sys.modules[cls.__module__], cls_name + \"Record\", record)\n        registry[behavior_name] = record\n        array = type(\n            cls_name + \"Array\",\n            (cls, ak.highlevel.Array),\n            {\"__module__\": cls.__module__},\n        )\n        setattr(sys.modules[cls.__module__], cls_name + \"Array\", array)\n        registry[\"*\", behavior_name] = array\n        for basecls in cls.mro():\n            for method in basecls.__dict__.values():\n                if hasattr(method, \"_awkward_mixin\"):\n                    ufunc, rhs, transpose = method._awkward_mixin\n                    if rhs is None:\n                        registry.setdefault((ufunc, behavior_name), method)\n                        continue\n                    for rhs_name in list(rhs) + [behavior_name]:\n                        registry.setdefault((ufunc, behavior_name, rhs_name), method)\n                        if transpose is not None and rhs_name != behavior_name:\n                            registry.setdefault(\n                                (ufunc, rhs_name, behavior_name), transpose\n                            )\n                    if basecls.__name__ in rhs:\n                        rhs.add(behavior_name)\n        return cls\n\n    return register\n\n\ndef mixin_class_method(ufunc, rhs=None, *, transpose=True):\n    \"\"\"\n    Args:\n        ufunc (numpy.ufunc): A universal function (or NEP18 callable) that is\n            hooked in Awkward Array, i.e. it can be the first argument of a behavior.\n        rhs (Set[type] or None): Set of right-hand side argument types, optional\n            if wrapping a unary function. The left-hand side is expected to\n            always be `self` of the parent class.\n        transpose (bool): If true, automatically create a transpose signature\n            (only makes sense for binary ufuncs).\n\n    This decorator can be used to register a mixin class method.\n\n    Using this decorator ensures that derived classes that are declared with the\n    #ak.mixin_class decorator will also have the behaviors that this class has.\n    \"\"\"\n\n    def register(method):\n        if not isinstance(rhs, (set, type(None))):\n            raise ak._errors.wrap_error(\n                ValueError(\"expected a set of right-hand-side argument types\")\n            )\n        if transpose and rhs is not None:\n\n            def transposed(left, right):\n                return method(right, left)\n\n            # make a copy of rhs, we will edit it later\n            method._awkward_mixin = (ufunc, set(rhs), transposed)\n        else:\n            method._awkward_mixin = (ufunc, rhs, None)\n        return method\n\n    return register\n", "path": "src/awkward/behaviors/mixins.py"}], "after_files": [{"content": "# BSD 3-Clause License; see https://github.com/scikit-hep/awkward-1.0/blob/main/LICENSE\n\n\nimport functools\nimport sys\n\nimport awkward as ak\n\n\ndef mixin_class(registry, name=None):\n    \"\"\"\n    Args:\n        registry (dict): The destination behavior mapping registry. Typically,\n            this would be the global registry #ak.behavior, but one may wish\n            to register methods in an alternative way.\n        name (str): The name to assign to the behaviour class.\n\n    This decorator can be used to register a behavior mixin class.\n\n    Any inherited behaviors will automatically be made available to the decorated\n    class.\n\n    See the \"Mixin decorators\" section of #ak.behavior for further details.\n    \"\"\"\n\n    def register(cls):\n        cls_name = cls.__name__\n        if name is None:\n            behavior_name = cls_name\n        else:\n            behavior_name = name\n\n        record = type(\n            cls_name + \"Record\",\n            (cls, ak.highlevel.Record),\n            {\"__module__\": cls.__module__},\n        )\n        setattr(sys.modules[cls.__module__], cls_name + \"Record\", record)\n        registry[behavior_name] = record\n        array = type(\n            cls_name + \"Array\",\n            (cls, ak.highlevel.Array),\n            {\"__module__\": cls.__module__},\n        )\n        setattr(sys.modules[cls.__module__], cls_name + \"Array\", array)\n        registry[\"*\", behavior_name] = array\n        for basecls in cls.mro():\n            for method in basecls.__dict__.values():\n                if hasattr(method, \"_awkward_mixin\"):\n                    ufunc, rhs, transpose = method._awkward_mixin\n                    if rhs is None:\n                        registry.setdefault((ufunc, behavior_name), method)\n                        continue\n                    for rhs_name in list(rhs) + [behavior_name]:\n                        registry.setdefault((ufunc, behavior_name, rhs_name), method)\n                        if transpose is not None and rhs_name != behavior_name:\n                            registry.setdefault(\n                                (ufunc, rhs_name, behavior_name), transpose\n                            )\n                    if basecls.__name__ in rhs:\n                        rhs.add(behavior_name)\n        return cls\n\n    return register\n\n\ndef _call_transposed(func, left, right):\n    return func(right, left)\n\n\ndef mixin_class_method(ufunc, rhs=None, *, transpose=True):\n    \"\"\"\n    Args:\n        ufunc (numpy.ufunc): A universal function (or NEP18 callable) that is\n            hooked in Awkward Array, i.e. it can be the first argument of a behavior.\n        rhs (Set[type] or None): Set of right-hand side argument types, optional\n            if wrapping a unary function. The left-hand side is expected to\n            always be `self` of the parent class. The current class is implicitly\n            included in this set.\n        transpose (bool): If true, automatically create a transpose signature\n            (only makes sense for binary ufuncs).\n\n    This decorator can be used to register a mixin class method.\n\n    Using this decorator ensures that derived classes that are declared with the\n    #ak.mixin_class decorator will also have the behaviors that this class has.\n    \"\"\"\n\n    def register(method):\n        if not isinstance(rhs, (set, type(None))):\n            raise ak._errors.wrap_error(\n                ValueError(\"expected a set of right-hand-side argument types\")\n            )\n        if transpose and rhs is not None:\n            # make a copy of rhs, we will edit it later\n            # use partial & a module-scoped function so that this is pickleable\n            method._awkward_mixin = (\n                ufunc,\n                set(rhs),\n                functools.partial(_call_transposed, method),\n            )\n        else:\n            method._awkward_mixin = (ufunc, rhs, None)\n        return method\n\n    return register\n", "path": "src/awkward/behaviors/mixins.py"}]}