diff --git a/suitesparse.sh b/suitesparse.sh
index ad05bbf..aab7fd3 100755
--- a/suitesparse.sh
+++ b/suitesparse.sh
@@ -27,6 +27,20 @@ if [ -z "${NPROC}" ]; then
 fi
 
 cmake_params=()
+
+# Fail the build if OpenMP is missing instead of silently producing a serial
+# library. GraphBLAS only warns and carries on, so a serial build stays
+# invisible until someone measures it: conda-forge's graphblas 10.5.0 shipped
+# that way on osx-arm64 while still depending on llvm-openmp. The matching
+# runtime check on the built wheel is tests/test_package.py::test_openmp.
+cmake_params+=(-DSUITESPARSE_USE_OPENMP=ON)
+cmake_params+=(-DSUITESPARSE_USE_STRICT=ON)
+# STRICT makes any requested-but-missing feature fatal, and SuiteSparsePolicy
+# defaults both of these to ON, so they must be turned off explicitly or the
+# configure step dies on "CUDA required for SuiteSparse but not found".
+cmake_params+=(-DSUITESPARSE_USE_CUDA=OFF)
+cmake_params+=(-DSUITESPARSE_USE_FORTRAN=OFF)
+
 if [ -n "${BREW_LIBOMP}" ]; then
     # macOS OpenMP flags.
     # FindOpenMP doesn't find brew's libomp, so set the necessary configs manually.
diff --git a/suitesparse_graphblas/__init__.py b/suitesparse_graphblas/__init__.py
index 895a66f..7d08d23 100644
--- a/suitesparse_graphblas/__init__.py
+++ b/suitesparse_graphblas/__init__.py
@@ -24,6 +24,15 @@
     ) from exc
 del importlib, platform
 
+# The SuiteSparse:GraphBLAS C library this binding was built against, as
+# (major, minor, sub). ``__version__`` is the version of *this package*,
+# which should normally match.
+libgraphblas_version = (
+    lib.GxB_IMPLEMENTATION_MAJOR,
+    lib.GxB_IMPLEMENTATION_MINOR,
+    lib.GxB_IMPLEMENTATION_SUB,
+)
+
 # It is strongly recommended to use the non-variadic version of functions to be
 # compatible with the most number of architectures. For example, you should use
 # GxB_Matrix_Option_get_INT32 instead of GxB_Matrix_Option_get.
diff --git a/suitesparse_graphblas/tests/test_package.py b/suitesparse_graphblas/tests/test_package.py
index 77086a6..b0e2d32 100644
--- a/suitesparse_graphblas/tests/test_package.py
+++ b/suitesparse_graphblas/tests/test_package.py
@@ -1,5 +1,7 @@
+import pytest
+
 import suitesparse_graphblas
-from suitesparse_graphblas import ffi, lib  # noqa: F401
+from suitesparse_graphblas import ffi, lib
 
 
 def test_matrix_existence():
@@ -12,3 +14,55 @@ def test_version():
     version = suitesparse_graphblas.__version__
     version = [int(x) for x in version.split("+")[0].split(".")]
     assert version > [9, 4, 4, 0]
+
+
+def test_openmp():
+    # GraphBLAS only warns at configure time when OpenMP is missing and still
+    # builds a working, but serial, library, so a serial build is invisible
+    # from the outside: conda-forge's graphblas 10.5.0 shipped that way on
+    # osx-arm64. Wheels build GraphBLAS from source in suitesparse.sh, where
+    # macOS has to point CMake at Homebrew's libomp by hand, so the same slip
+    # is possible here.
+    val_ptr = ffi.new("int32_t*")
+    info = lib.GrB_Global_get_INT32(lib.GrB_GLOBAL, val_ptr, lib.GxB_LIBRARY_OPENMP)
+    assert info == lib.GrB_SUCCESS
+    assert val_ptr[0], "libgraphblas was built without OpenMP"
+
+
+def test_libgraphblas_version_matches_the_loaded_library():
+    """The GraphBLAS this extension was compiled against must be the one it loads.
+
+    ``libgraphblas_version`` reads cffi ``#define`` constants, which are
+    resolved when the C extension is compiled against a particular
+    GraphBLAS.h. The values below come from the shared library actually loaded
+    at runtime. When those disagree, every cffi call is reading a struct laid
+    out by a different build -- a mismatch that surfaces later as an
+    unexplained ``GrB_OUT_OF_MEMORY`` or a crash, never as an import error.
+    """
+    val_ptr = ffi.new("int32_t*")
+    runtime = []
+    for field in (
+        lib.GrB_LIBRARY_VER_MAJOR,
+        lib.GrB_LIBRARY_VER_MINOR,
+        lib.GrB_LIBRARY_VER_PATCH,
+    ):
+        assert lib.GrB_Global_get_INT32(lib.GrB_GLOBAL, val_ptr, field) == lib.GrB_SUCCESS
+        runtime.append(val_ptr[0])
+    assert tuple(runtime) == suitesparse_graphblas.libgraphblas_version
+
+
+def test_version_tracks_libgraphblas():
+    """A released version's first three parts are the SuiteSparse:GraphBLAS version.
+
+    That convention is what lets a caller infer the library version from the
+    package version, and it only holds for a release: between releases the
+    version reports the previous tag, which is why ``libgraphblas_version``
+    exists and why anything gating on a library feature should read that
+    instead. Skipped on a development build rather than asserted, since
+    disagreeing there is the expected state, not a defect.
+    """
+    version = suitesparse_graphblas.__version__
+    if "+" in version:
+        pytest.skip(f"development build between releases: {version}")
+    parts = tuple(int(x) for x in version.split(".")[:3])
+    assert parts == suitesparse_graphblas.libgraphblas_version