I hope this is not a double post...

Should I use "at the time" or "at that time" - when I want to express something that was known during the time when the events occured.

For example

Bonco presents the facts known at the time about Fiolo and their interpretation by various authors.

Here I mean "at the time" as "at the moment that Bonco wrote it".

I hope this is not a double post.

Should I use "at the time" or "at that time" when I want to express something that was known during the time when the events occurred?

Bonco presents the facts known at the time about Fiolo and their interpretation by various authors.

Here I mean "at the time" as "at the moment that Bonco wrote it."