This sentence is from a book well-known to many learners of Japanese, a compilation of Japanese short stories. It comes with partial translations and grammar notes by the editor. This story is 川上弘美の神様. But I'm not convinced by either the translation or the grammar note. The translation says
- ところで At any rate
- わかったのである it became clear
The grammar note says that
"のである makes the statement preceding it more emphatic and sets us up for the paragraphs that follow. [It] often lends an explanatory feel to the sentence it ends; here, it indicates that the narrator has reached a conclusion, and that the evidence on which that conclusion is based is about to be presented. [...]"
(In bold are the parts that I "agree" with, in italics my disagreement)
I've never heard that のである by itself announces anything about to be said. Quite on the contrary, I've always seen it as a way to explain the situation.
On top of that, translating ところで as "at any rate" makes sense in context (indeed, that sentence is the transition from the narrator wondering how considerate a bear offering soba to their neighbors might feel obligated to be, considering they're a bear, to how they themself learnt they are related to that bear.), but is weird and seems over-translated. It is supposed to be "by the way", literally "(this) (place/situation) (and)...".
So I'm wondering if, actually, ところで and わかったのである, put together, take some particular meaning.