diff --git a/.github/workflows/update-ty.yml b/.github/workflows/update-ty.yml
new file mode 100644
index 0000000..a813965
--- /dev/null
+++ b/.github/workflows/update-ty.yml
@@ -0,0 +1,103 @@
+name: Update ty Version Monthly
+
+on:
+  schedule:
+    # Run on the 1st of every month at 00:00 UTC
+    - cron: '0 0 1 * *'
+  workflow_dispatch:  # Allow manual triggering
+
+jobs:
+  update-ty:
+    runs-on: ubuntu-latest
+    permissions:
+      contents: write
+      pull-requests: write
+
+    steps:
+      - name: Checkout repository
+        uses: actions/checkout@v7
+
+      - name: Get latest ty version
+        run: |
+          LATEST_VERSION=$(curl -s https://pypi.org/pypi/ty/json | jq -r '.info.version')
+          echo "TY_VERSION=$LATEST_VERSION" >> $GITHUB_ENV
+          echo "Latest ty version: $LATEST_VERSION"
+
+          if grep -q '"ty==' pyproject.toml; then
+            CURRENT_VERSION=$(grep '"ty==' pyproject.toml | sed -E 's/.*ty==([0-9]+\.[0-9]+\.[0-9]+).*/\1/')
+            echo "CURRENT_VERSION=$CURRENT_VERSION" >> $GITHUB_ENV
+            echo "Current ty version: $CURRENT_VERSION"
+
+            if [ "$LATEST_VERSION" = "$CURRENT_VERSION" ]; then
+              echo "Already using the latest version of ty. No updates needed."
+              echo "NEEDS_UPDATE=false" >> $GITHUB_ENV
+            else
+              echo "NEEDS_UPDATE=true" >> $GITHUB_ENV
+            fi
+          else
+            echo "No ty version found in pyproject.toml"
+            echo "NEEDS_UPDATE=true" >> $GITHUB_ENV
+          fi
+
+      - name: Update ty version in pyproject.toml
+        if: env.NEEDS_UPDATE == 'true'
+        run: |
+          sed -i -E 's/"ty==([0-9]+\.[0-9]+\.[0-9]+)"/"ty==${{ env.TY_VERSION }}"/' pyproject.toml
+
+      - name: Update ty version in prek.toml
+        if: env.NEEDS_UPDATE == 'true'
+        run: |
+          sed -i -E '/repo = "https:\/\/github.com\/astral-sh\/ty-pre-commit"/,/^rev = / s/^rev = "v[0-9]+\.[0-9]+\.[0-9]+"/rev = "v${{ env.TY_VERSION }}"/' prek.toml
+
+      - name: Install the latest version of uv
+        if: env.NEEDS_UPDATE == 'true'
+        uses: astral-sh/setup-uv@v7
+
+      - name: Update the lockfile
+        if: env.NEEDS_UPDATE == 'true'
+        run: |
+          uv lock
+
+      - name: Run ty on the project
+        # ty is pre-1.0 and new releases often add diagnostics; a failure opens
+        # the PR as a draft instead of aborting the update.
+        if: env.NEEDS_UPDATE == 'true'
+        run: |
+          set +e
+          uv run --group dev ty check
+          if [ $? -ne 0 ]; then
+            echo "TY_CHECK_FAILED=true" >> $GITHUB_ENV
+          else
+            echo "TY_CHECK_FAILED=false" >> $GITHUB_ENV
+          fi
+
+      - name: Create Pull Request
+        if: env.NEEDS_UPDATE == 'true'
+        uses: peter-evans/create-pull-request@v8
+        with:
+          token: ${{ secrets.GITHUB_TOKEN }}
+          # open in draft mode if ty check failed
+          draft: ${{ env.TY_CHECK_FAILED }}
+          commit-message: "chore(deps-dev): update ty from ${{ env.CURRENT_VERSION }} to ${{ env.TY_VERSION }}"
+          title: "chore(deps-dev): update ty from ${{ env.CURRENT_VERSION }} to ${{ env.TY_VERSION }}"
+          body: |
+            ## ty Version Update
+
+            This PR updates the ty version from ${{ env.CURRENT_VERSION }} to ${{ env.TY_VERSION }}.
+
+            Changes:
+            - Updated version in `pyproject.toml`
+            - Updated version in `prek.toml`
+            - Regenerated `uv.lock`
+
+            ${{ env.TY_CHECK_FAILED == 'true' && '⚠️ **WARNING**: `ty check` reports new diagnostics with this version. A maintainer should fix them before merging.' || '`ty check` passes with this version.' }}
+
+            This PR was created automatically by a GitHub Actions workflow.
+          branch: chore-deps-update-ty-${{ env.TY_VERSION }}
+          delete-branch: true
+          labels: |
+            dependencies
+          add-paths: |
+            pyproject.toml
+            prek.toml
+            uv.lock
diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md
index 2daf540..ee689cb 100644
--- a/CONTRIBUTING.md
+++ b/CONTRIBUTING.md
@@ -43,7 +43,7 @@ All of these must pass before a pull request can be merged;
 ```bash
 uv run ruff check src/ tests/       # lint
 uv run ruff format --check src/ tests/
-uv run ty check src/                # type check
+uv run ty check                     # type check src/ and tests/
 uv run pytest -m "not slow"         # fast test suite
 uv run pytest                       # full suite, including slow tests
 ```
diff --git a/pyproject.toml b/pyproject.toml
index ea2e7a9..5dcf6a2 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -279,4 +279,4 @@ python-version = "3.11"
 allowed-unresolved-imports = ["cupy"]
 
 [tool.ty.src]
-include = ["src/src_method"]
+include = ["src/src_method", "tests"]
diff --git a/src/src_method/_validation.py b/src/src_method/_validation.py
index 5fbf893..ed8cbbb 100644
--- a/src/src_method/_validation.py
+++ b/src/src_method/_validation.py
@@ -19,7 +19,7 @@
 __all__ = ["validate_chi_out", "validate_cutoff", "validate_open_boundary"]
 
 
-def validate_chi_out(chi_out: int) -> None:
+def validate_chi_out(chi_out: object) -> int:
     """Reject a non-integer or non-positive output bond dimension.
 
     Any `numbers.Integral` is accepted, so NumPy integers pass; `bool` does not.
@@ -27,6 +27,9 @@ def validate_chi_out(chi_out: int) -> None:
     Args:
         chi_out: The requested output bond dimension.
 
+    Returns:
+        ``chi_out`` as a plain `int`.
+
     Raises:
         TypeError: If `chi_out` is not an integer.
         ValueError: If `chi_out` is not positive.
@@ -37,6 +40,7 @@ def validate_chi_out(chi_out: int) -> None:
     if chi_out < 1:
         msg = f"chi_out must be positive, got {chi_out!r}."
         raise ValueError(msg)
+    return int(chi_out)
 
 
 def validate_cutoff(cutoff: float) -> None:
diff --git a/src/src_method/apply.py b/src/src_method/apply.py
index 534c00d..7ea086e 100644
--- a/src/src_method/apply.py
+++ b/src/src_method/apply.py
@@ -16,13 +16,14 @@
 if TYPE_CHECKING:
     from collections.abc import Sequence
 
+    import numpy as np
     from numpy.typing import DTypeLike, NDArray
 
 
 def apply(
     left_tensor: Sequence[NDArray],
     right_tensor: Sequence[NDArray],
-    chi_out: int,
+    chi_out: int | np.integer,
     *,
     cutoff: float = 0.0,
     dtype: DTypeLike | None = None,
diff --git a/src/src_method/compress.py b/src/src_method/compress.py
index bdff465..ef37d84 100644
--- a/src/src_method/compress.py
+++ b/src/src_method/compress.py
@@ -15,12 +15,13 @@
 if TYPE_CHECKING:
     from collections.abc import Sequence
 
+    import numpy as np
     from numpy.typing import DTypeLike, NDArray
 
 
 def compress(
     tensor: Sequence[NDArray],
-    chi_out: int,
+    chi_out: int | np.integer,
     *,
     cutoff: float = 0.0,
     dtype: DTypeLike | None = None,
diff --git a/src/src_method/stack.py b/src/src_method/stack.py
index a7f7ace..9b32baa 100644
--- a/src/src_method/stack.py
+++ b/src/src_method/stack.py
@@ -23,6 +23,7 @@
 if TYPE_CHECKING:
     from collections.abc import Sequence
 
+    import numpy as np
     from numpy.typing import DTypeLike, NDArray
 
 logger = logging.getLogger(__name__)
@@ -35,7 +36,7 @@
 
 def src(
     *trains: Sequence[NDArray],
-    chi_out: int,
+    chi_out: int | np.integer,
     cutoff: float = 0.0,
     dtype: DTypeLike | None = None,
     seed: int | None = None,
@@ -95,7 +96,7 @@ def src(
             not recognised.
         ImportError: If ``device="gpu"`` but cupy is not installed.
     """
-    validate_chi_out(chi_out)
+    chi_out = validate_chi_out(chi_out)
     validate_cutoff(cutoff)
     xp = get_xp(device)
     prng = default_rng(seed)