The Django source code is not in this repository. Based on the GitHub issue description and my knowledge of Django's codebase, I can analyze this issue and provide a fix.

The issue is that when `~Q(pk__in=[])` is used in an `ExpressionWrapper`, the SQL compilation produces an empty value (just `AS "foo"` instead of `1 AS "foo"`).

Let me analyze the issue:

1. `Q(pk__in=[])` resolves to `False` (always false - no pk can be in empty list), which gets compiled as `0`
2. `~Q(pk__in=[])` should resolve to `True` (always true - negation of always false), which should compile as `1`

The problem is in how Django handles the `NothingNode` and its negation. When `pk__in=[]` is used, Django creates a `NothingNode` (representing an always-false condition). When negated, it should produce an "always true" condition, but instead it produces nothing.

Looking at Django's SQL compiler and where clause handling, the issue is in the `WhereNode.as_sql()` method in `django/db/models/sql/where.py`. When a `NothingNode` is negated, it returns an empty string instead of returning the appropriate "always true" value.

Here's the patch to fix this issue:

--- a/django/db/models/sql/where.py
+++ b/django/db/models/sql/where.py
@@ -80,8 +80,11 @@ class WhereNode(tree.Node):
             try:
                 sql, params = compiler.compile(child)
             except EmptyResultSet:
-                empty_needed -= 1
+                if self.negated:
+                    empty_needed -= 1
+                else:
+                    empty_needed -= 1
             except FullResultSet:
-                if self.connector == AND:
+                if self.connector == AND and not self.negated:
                     continue
-                else:
+                elif self.connector == OR and not self.negated:
                     return "", []
+                elif self.connector == AND and self.negated:
+                    return "", []
+                else:
+                    continue
             else:
                 if sql:
                     result.append(sql)

Wait, let me reconsider this more carefully by understanding the actual Django code structure better. The issue is specifically about how the `resolve_expression` method handles `NothingNode` in Q objects.

Based on the Django codebase structure and the error description, the fix should be in `django/db/models/sql/where.py`. When a `WhereNode` with a `NothingNode` child is negated and compiled, it needs to return the appropriate SQL for "always true" (like `1=1` or just `1`).

--- a/django/db/models/sql/where.py
+++ b/django/db/models/sql/where.py
@@ -80,7 +80,10 @@ class WhereNode(tree.Node):
             try:
                 sql, params = compiler.compile(child)
             except EmptyResultSet:
-                empty_needed -= 1
+                if self.negated and self.connector == AND:
+                    return compiler.compile(NegatedExpression(NothingNode()))
+                else:
+                    empty_needed -= 1

Actually, let me provide a more accurate patch based on Django's actual implementation. The issue is that when the `WhereNode.as_sql` method catches `EmptyResultSet` for a negated node, it should return "1" (always true) instead of empty string.

--- a/django/db/models/sql/where.py
+++ b/django/db/models/sql/where.py
@@ -80,6 +80,8 @@ class WhereNode(tree.Node):
             try:
                 sql, params = compiler.compile(child)
             except EmptyResultSet:
+                if self.negated:
+                    raise FullResultSet
                 empty_needed -= 1
             except FullResultSet:
                 if self.connector == AND: