I don't know. "Beginningless." The only thing similar I can remember in the scriptures was when the Buddha was asked what was the Beginning of time. He was also asked things like: is the world eternal or not eternal, does the Buddha exist or not exist after death, or does he both exist and not exist after death, and similar wild questions. The Buddha wouldn't answer them. He said, "I make no comment on that". He was the wisest man in the Universe, right? Yet he wouldn't answer these questions. Why? He would reply, "I make no comments on that, because it does not lead to purification of the mind and heart. It does not lead to deep happiness. It does not lead ultimately to enlightenment". He would then teach the Four Noble Truths.
Once, when a person asked if the Buddha knows the beginning of time, it is recorded, he shut his eyes, then opened them and replied similar to this, "I can see back 70,000 eons and I cannot find the beginning of time." So as far as "beginningless," it's not even an issue within Theravadin Buddhism, rather the purification of the heart by the practice of the Four Noble Truths. That's our practice.