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Currently, signalmodule.c tracks the "main thread" and the "main interpreter":
 main_thread = PyThread_get_thread_ident();
 main_interp = _PyInterpreterState_Get();
This information is already tracked in the global _PyRuntime variable which is updated at fork by _PyRuntimeState_ReInitThreads() (called by PyOS_AfterFork_Child).
Attached PR removes main_thread and main_interp from signalmodule.c, to reuse _PyRuntime. It should help to ensure that Python remains consistent (less risk of inconsistency if one variable is updated, but not the other).
By the way, _PyInterpreterState_DeleteExceptMain() is called before _PyRuntimeState_ReInitThreads(). _PyInterpreterState_DeleteExceptMain() acquires runtime->interpreters.mutex, whereas this lock is reset by _PyRuntimeState_ReInitThreads(). Maybe I introduced this bug recently when I refactored code, I don't know. But it sounds like a bug as well.
Note: PyOS_AfterFork_Child() doesn't update runtime->interpreters->main, but os.fork() raises a RuntimeError if it's not called from the main interpreter. So it's fine.

New changeset d8613dc86f4c7acd3e2598095c466fe9dc0ad27c by Victor Stinner in branch 'master':
bpo-37031: Reuse _PyRuntime.main_thread in signalmodule.c (GH-13538)
https://github.com/python/cpython/commit/d8613dc86f4c7acd3e2598095c466fe9dc0ad27c

New changeset b49858b4b7b4c9d85ef6946ad020f83e4fa1caa7 by Victor Stinner in branch 'master':
bpo-37031: Fix PyOS_AfterFork_Child() (GH-13537)
https://github.com/python/cpython/commit/b49858b4b7b4c9d85ef6946ad020f83e4fa1caa7