Not really, no.
I rather think you are talking about Dr. Martha McClintock's study of menstrual synchrony, back in 1971.
But plenty of studies since then have doisagreed.
It was your terming of it as 'proven' that got me, because that is not so. It;s not proven by a long way.
In my old socal group at school, the women's periods were staggered in the MOST awkward way. And they never got synchronous. And they met all the time.
If that theory were fully true, then technically all girls at a shcool would have periods at the same time!
Not that McClintock ever said that; her study was of women living together, not meeting regularly.