Monsters (or youma) are real and there are Spirit World Warriors who put them down. Kuriyama Mirai  is a Spirit World Warrior from a cursed clan that hunts using blood magic, and is something of an outcast from both magical and mundane society. By “blood magic” I mean that Mirai can summon a nasty sword  from her blood .
Kanbara Akihito is an immortal half youma who starts off as Mirai’s practice for hunting youma (since she can’t actually kill him), and this quickly develops into a sort of partnership to actually hunt youma.
The first six episodes follow a familiar pattern:
- Introduce the two leads
- Introduce the supporting cast
- Explore the main characters, introduce (or suggest) key plot elements such as why Mirai is likely to be a Defrosting Ice Queen (or similar) over the course of the series & hint at the actual villains (this was a two part story)
- A Day in the Limelight episode for Mitsuki
- Start showing the process of the Defrosting Ice Queen connecting to a group of friends.
At this stage I would be expecting two to three more Limelight episodes with Hiromi and then Ayaka being the most likely candidates. I’m not sure who the focus character for the third Limelight episode is likely to be.
The remaining 4 episodes are likely to tackle the core plot elements: the developing Mirai/Akihito relationship and what’s really going on in the world.
The episodes so far have generally been well scripted to achieve their aims within the formula, usually with some misdirection to make what’s happening slightly less obvious.
The two part sequence exploring Mirai and Akihito (Moonlight Purple and Bitter Orange ) uses some astonishing action sequences to cover the infodump and the growing connection between the two. In some respects the major sequence was reminiscent of the battles in in Puella Magi Madoka Magica, and certainly matched them for spectacle.
Mirai’s increasing connection to the Literary Club is buried beneath the gloriously funny parodies that make up Shocking Pink, but is still there if you’re watching for it .
Most of the characters are engaging, well realised, and interact in interesting (if occasionally questionable) ways. Overt fanservice has been kept to a reasonable minimum , albeit that Akihito’s glasses fetish and Hiromi’s sister complex are more than a little creepy .
The Interim Verdict
Beyond the Boundary is, despite the formulaic structure, a fun series to watch with interesting characters and occasionally superb scripting of individual episodes.
Unless it pulls off some major surprises in the remaining episodes, Beyond the Boundary will be a good but not great anime.
Overall Beyond the Boundary is definitely worth following and, barring a major stuff-up of some sort, is a series that I’ll enjoy watching to the end of the season.
UPDATE: I’ve added a link in the footnotes to a post on Illogical Zen that looks at the Shinto implications of blood magic, and I forgot to put in the opening credits:
 I have to use the northern hemisphere designations for the seasons. This occasionally annoys me, particularly during bushfire season in Australia.
 The other Fall 2013 shows that I’m currently following are Nagi no Asakura, Gingitsune, and Arpeggio of Blue Steel.
 There have been blog posts exploring the nasty implications of using blood like this in Shintoism. If I find a good one I’ll link to it, but it isn’t a topic I know well enough to tackle myself. If you know of such a blog post, please provide a link to it in the comments. UPDATE: This post by Illogical Zen is a good place to start.