diff --git a/docs_src/security/tutorial004_an_py310.py b/docs_src/security/tutorial004_an_py310.py
index 7c7d6d1c6..ebc6a90d9 100644
--- a/docs_src/security/tutorial004_an_py310.py
+++ b/docs_src/security/tutorial004_an_py310.py
@@ -12,7 +12,9 @@ from pydantic import BaseModel
 # to get a string like this run:
 # openssl rand -hex 32
 # then set it as an environment variable: export SECRET_KEY="your-generated-key"
-SECRET_KEY = os.environ.get("SECRET_KEY", "09d25e094faa6ca2556c818166b7a9563b93f7099f6f0f4caa6cf63b88e8d3e7")
+SECRET_KEY = os.environ.get(
+    "SECRET_KEY", "09d25e094faa6ca2556c818166b7a9563b93f7099f6f0f4caa6cf63b88e8d3e7"
+)
 ALGORITHM = "HS256"
 ACCESS_TOKEN_EXPIRE_MINUTES = 30
 
diff --git a/tests/test_invariant_tutorial004_an_py310.py b/tests/test_invariant_tutorial004_an_py310.py
index e4845f3eb..9fcd48fe5 100644
--- a/tests/test_invariant_tutorial004_an_py310.py
+++ b/tests/test_invariant_tutorial004_an_py310.py
@@ -1,44 +1,52 @@
-import pytest
-import sys
 import os
+import sys
 from importlib import util
 
+import pytest
+
 # Add the project root to sys.path to import the tutorial module
-sys.path.insert(0, os.path.abspath(os.path.join(os.path.dirname(__file__), '../../..')))
+sys.path.insert(0, os.path.abspath(os.path.join(os.path.dirname(__file__), "../../..")))
 
 # Import the actual production module
 spec = util.spec_from_file_location(
-    "tutorial004_an_py310",
-    "docs_src/security/tutorial004_an_py310.py"
+    "tutorial004_an_py310", "docs_src/security/tutorial004_an_py310.py"
 )
 tutorial = util.module_from_spec(spec)
 spec.loader.exec_module(tutorial)
 
 
-@pytest.mark.parametrize("secret_key", [
-    # Exact exploit case: hardcoded secret from the tutorial
-    "09d25e094faa6ca2556c818166b7a9563b93f7099f6f0f4caa6cf63b88e8d3e7",
-    # Boundary case: empty secret (should not be allowed)
-    "",
-    # Valid input: a different secret (should be accepted but not match hardcoded)
-    "a1b2c3d4e5f67890abcdef1234567890fedcba0987654321abcdef0123456789",
-])
+@pytest.mark.parametrize(
+    "secret_key",
+    [
+        # Exact exploit case: hardcoded secret from the tutorial
+        "09d25e094faa6ca2556c818166b7a9563b93f7099f6f0f4caa6cf63b88e8d3e7",
+        # Boundary case: empty secret (should not be allowed)
+        "",
+        # Valid input: a different secret (should be accepted but not match hardcoded)
+        "a1b2c3d4e5f67890abcdef1234567890fedcba0987654321abcdef0123456789",
+    ],
+)
 def test_secret_key_not_hardcoded_in_production(secret_key):
     """Invariant: Production secret keys must not match the tutorial's hardcoded example."""
     # Access the module's SECRET_KEY constant
     module_secret = tutorial.SECRET_KEY
-    
+
     # The security property: the actual secret must NOT be the tutorial's hardcoded value
     # This ensures the example isn't accidentally used in production
-    assert module_secret != "09d25e094faa6ca2556c818166b7a9563b93f7099f6f0f4caa6cf63b88e8d3e7", \
+    assert (
+        module_secret
+        != "09d25e094faa6ca2556c818166b7a9563b93f7099f6f0f4caa6cf63b88e8d3e7"
+    ), (
         "SECRET_KEY matches the tutorial's hardcoded example - this is unsafe for production!"
-    
+    )
+
     # Additional invariant: secret must be non-empty and sufficiently long for HS256
-    assert len(module_secret) >= 32, \
+    assert len(module_secret) >= 32, (
         "SECRET_KEY is too short for secure HS256 usage (minimum 32 hex chars)"
-    
+    )
+
     # Verify the secret is a valid hex string (optional but good practice)
     try:
         int(module_secret, 16)
     except ValueError:
-        pytest.fail("SECRET_KEY is not a valid hexadecimal string")
\ No newline at end of file
+        pytest.fail("SECRET_KEY is not a valid hexadecimal string")