Note for those unfamiliar: "Assiti Shards" is a universe created by Eric Flint which is designed to serve as a basis for several distinct series of alternate history/fiction books. The most famous/notable of those is the "1632"/"Ring of Fire" series.
The common concept uniting the different series is the titular "Assiti Shards". To quote from Wikipedia:
The Assiti Shards work by displacing bits of the world into other times and places, exchanging it with that which was there. These "shards", according to the fictional universe backstory, are waste byproduct of artworks created by the sophisticated and curious alien race known as the Assiti. The various stories involve shards striking the Earth and timeshifting characters into different periods and places.
As a note, the shards themselves play very little role, at least in 1632 series - they merely serve as a brief couple-pages-long explanation/method for setting up the series universe and don't play any subsequent role beyond backstory explanation.
QUESTION: Are there any commonalities (e.g. references to common characters, in-book events, etc...) between the different SERIES of books in the Assiti Shards universe, aside from the shard-based time displacement origins of each series?
Note: I personally don't care if the answer contains any spoilers.