diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index a62665c..8bdc8dc 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -1,5 +1,5 @@
 default_language_version:
-  python: python3.11
+  python: python3.12
 
 repos:
   - repo: local
diff --git a/README.md b/README.md
index 7919805..aaf4949 100644
--- a/README.md
+++ b/README.md
@@ -4,14 +4,14 @@
 [![Checked with mypy](https://www.mypy-lang.org/static/mypy_badge.svg)](https://mypy-lang.org/)
 [![Code style: black](https://img.shields.io/badge/code%20style-black-000000.svg)](https://github.com/psf/black)
 [![License: MIT](https://img.shields.io/badge/License-MIT-yellow.svg)](./LICENSE)
-[![arXiv](https://img.shields.io/badge/arXiv-xxx.svg)](https://arxiv.org/abs/xxx)
+[![arXiv](https://img.shields.io/badge/arXiv-2509.15409-b31b1b.svg)](https://arxiv.org/abs/2509.15409)
 
 ## Overview
 
-FragmentRetro is a fragment-based retrosynthetic method with quadratic complexity, offering a scalable alternative to tree search and [DirectMultiStep](https://github.com/batistagroup/DirectMultiStep/tree/main). The preprint for this work was posted on [arXiv](https://arxiv.org/abs/xxx).
+FragmentRetro is a fragment-based retrosynthetic method with quadratic complexity, offering a scalable alternative to tree search and [DirectMultiStep](https://github.com/batistagroup/DirectMultiStep/tree/main). The preprint for this work was posted on [arXiv](https://arxiv.org/abs/2509.15409).
 
 See our [documentation](./docs/index.md) for installation, stock preprocessing, and usage examples.
 
 ## Licenses
 
-All code is licensed under MIT License. The content of the [pre-print on arXiv](https://arxiv.org/abs/xxx) is licensed under CC-BY 4.0.
+All code is licensed under MIT License. The content of the [pre-print on arXiv](https://arxiv.org/abs/2509.15409) is licensed under CC-BY 4.0.
diff --git a/docs/index.md b/docs/index.md
index 47e29e8..4784142 100644
--- a/docs/index.md
+++ b/docs/index.md
@@ -89,4 +89,4 @@ uv pip install -e ".[dev]"
 ## License
 
 - Code: MIT License
-- Paper content ([arXiv preprint](https://arxiv.org/abs/xxxxx)): CC-BY 4.0
+- Paper content ([arXiv preprint](https://arxiv.org/abs/2509.15409)): CC-BY 4.0
diff --git a/src/fragmentretro/substructure_matcher.py b/src/fragmentretro/substructure_matcher.py
index 66040e2..3dc5b6f 100644
--- a/src/fragmentretro/substructure_matcher.py
+++ b/src/fragmentretro/substructure_matcher.py
@@ -80,7 +80,7 @@ def convert_to_smarts(fragment_smiles: str) -> str:
         smarts = re.sub(r":\d+\]", "]", smarts)
         # sub [#0] with *, which is a wildcard for any atom
         smarts = re.sub(r"\[\d*\#0\]", "*", smarts)
-        return cast(str, smarts)
+        return smarts
 
     @staticmethod
     def addH_to_wildcard_neighbors(fragment_smarts: str) -> str: