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Yes, C11 is fine, scikit-learn builds successfully under the free-threaded build with this PR checked out.

To be clear, the specific issue we're working around is there's a static_assert in an internal CPython header that cython includes to get at the internals of the python frame object in a build configuration that is triggered in the free-threaded build. static_assert was introduced in C11, so compiling in C99 mode leads to an error for cython code that triggers including the internal header. In principle, CPython could switch the static_assert to Py_BUILD_ASSERT, which does compile under C99. It's all kind of murky though because cython is using an internal header but they are only doing that because there's no public way to get at the relevant information they need.

That said, all the compilers Python supports should also build with the C11 standard, so it should be safe to update this as long as pyiodide is OK with it.

Thanks very much for taking the time to write this explanation @ngoldbaum.