[Mangaka-chan]

Oh boy, did we get a lot of plot this week!

Spoiler for Spoilers for epi. 7 and some thoughts:

My guess right now is that maybe the Nase clan is saving the Hollow Shadow core in order to boost the power of Izumi's weapon, much like how Sakura had been feeding her borrowed scythe with the youmu cores she's gathered. That would help hold back Fijimu, who looks to be pretty damn strong in his own right. If Fijimu intends to absorb the titular youmu Beyond the Boundary then Izumi would certainly need to also boost her own powers with Hollow Shadow if she wants to defeat him.

The question is, what does Akihito have to do with all this? Is his youmu core (I assume even a half youmu has one) somehow more valuable? Given what we've seen of his youmu power when it awakens that seems plausible. But because he is still half human and has no conscious control over his youmu self when it awakens the Nase and the Society can't easily justify killing him, even if Akihito's dream and a flashback from an earlier episode suggests he had killed someone in the past. But if his youmu side is weakened by the lull and his human side is placed into dormancy then they might have an excuse and an opportunity to kill him during the Lull. Izumi might need Mirai's power to get the job done, and that's why she intervened when the Inami clan initially wanted to execute Mirai for Yui's death.