What is the origin relatioinship between the Cursed Blood Clan and the Kyoukai no Kanata?


Watching the movie, it seems like there is some relationship between the
Cursed Blood Clan (CBC) (Kuriyama's) and the Kyoukai no Kanana (KnK) Youmu's
origin.

And I am not talking about the **romantic** relationsip between Mirai and
Akihito. About the origins of them both.

It is shown that

> Akihito and Mirai's mothers were close enough that Kuriyama could ask to be
> reforged into a ring upon her death.

So, what is the rellationship?

> Was the CBC involved in creating KnK?

