> But during the Dark Ages, there were NO places in Europe where science or scholarship really flourished.

That seems different from what you originally argued but either way, that's also not really accurate. I'm going to assume you're referring to "Western Europe" here since you're clearly aware of Eastern Roman/Byzantine empire still existing, but that still leaves Al-Andalus, the Carolingian Renaissance, agricultural advancements like the three-field system, wheelbarrows, multiple types of milling technology, and during the latter end you start getting advanced compasses, bells, mechnical watches, and other metallurgy.

Where all of these done in one or two specific places? No, continuing to ignore Byzantium here, but there was a still a variety of advancements happening all the time without which the Renaissance couldn't have happened.

> It should have started around the time of the move of the Roman capital to Constantinople. By the time of the fall of Rome, the Darkening had been in full swing.

I mean, you can think that but that's not how or what the term "The Dark Ages" usually refers to. It sounds like you have your own constructed time period in mind and I'm not interested in discussing something I'm not aware of.

> If you want a precise date, I propose the date of murder of Hypatia in 415 AD.

A very pointed date to choose.