Loki is working on illusions.

With the healing spells all done to her satisfaction she spent a good deal of time trying to figure out what the best unison of simplicity (in spell construction), subtlety (in varying likely degrees of company) and versatility (in use) might be. Turning into a bird would be great fun, but useful only in a handful of situations; she thinks it might take as long as a millennium to work out how to teleport with all the safeties she'd like; and either one would be worthless unless she could cover her escape or saved it only for unlikely last resorts -

But illusions? If she can get general-purpose illusions working, in at least vision and sound if not touch or smell, she will be able to do anything else she likes and cover it up in front of anyone who looks. Either the doing or that it's her - she could look like a boy if she liked, go out among strangers, use her healing spells. (There are other healing spells but she thinks that building her own from the very tiniest building blocks all the way up must get better results; she is not comparatively impressed with the results of the others.) It will be useful against any wild monster she fights (without witnesses) that tracks by sight or hearing; she will be able to render herself invisible by the same principles, make it look like she's elsewhere while she nimbly relocates.

It will be disastrously complicated, if not as bad as teleporting, but - unlike things like the grace spell, which had to be cast exactly once and entire, or the healing spells, which she completed without ever needing them badly enough to take the risk, the illusions could be useful even in their most basic components. She can use pieces she invented for the healing spells to build in a concept of what living things are like and how they move for the illusion spell and she won't have to animate illusory doubles or decoys walking and turning their heads correctly on the fly in her head. (Although she will have to work out how to incorporate clothes before that will be suitable for use among people.) Invisibility should be fairly straightforward, too. And once she has all that she'll fill in the gaps until she can make anything look like anything from thin air to a scale model of the entire World Tree.

She plots out the course of her work and starts.

It's not long before she can change her face enough that - given that she's still a slip of a girl with no telltale development, anyway - she will be mistaken for an unremarkable (and, on a whim, redheaded) boy, not a princess, if she goes out.

She is then distracted for several months while she sneaks into every single lecture in a particular series about magic theory. It's interesting, or she'd stop going, but she tears herself away from excursions to the school when the series is over rather than picking up another one. She has been nearly missed at home once or twice and cannot explain. The way everyone who was not educated in ecstatic atomized summary by the Tesseract performs magic is not enough like her own methods for her to take their concepts wholesale.

(But by this time she's very keen on how it feels to go out and be seen as a boy. She doesn't so much want to be called "you there, young man" as she wants the legitimization of a hidden fraction of herself that comes with it. She'd certainly be tired of "you there, young man" if that were all she ever heard - but centuries of what is and is not womanly being made crushingly relevant to her make it a welcome distraction. So she still changes herself and she still disappears into the city around the palace, just when she wants to go for walks.

She turns outright invisible, once she can, when she wants to go into a hospital and repair the sick and hurt.)

She gets better at the illusions. She can do clothes, although the design will tend to be plain unless she has planning time or is copying something she's seen. Once she can do clothes she can cloak herself in the illusion of someone who is not only maler than herself but also taller. (Being "excuse me, sir" is a new thrill on a pattern that's become old and comfortable.) Later she can do free-formed pictures, in three dimensions as long as she's paying attention. There is still work to be done (she could decrease pinpoint size for better image resolution, she would like more of the object permanence to handle itself once she's set up an illusion of a solid, invisibility should automatically extend if she picks something up instead of her having to think about it every time) but the basics are handled.

She locks herself in her bathroom and fills the air with swimming penguins and laughs, because -

Heimdall - never - says - a - word.

She must know. There is no way she doesn't, now; the other spells could have been missed, written off in the vast confusion of the cosmos. This is unmissable, it's been going on for so long, Heimdall has to have seen. Loki has no way to tell without asking if it's tacit approval, or if everyone has culturally taboo habits in private and Heimdall operates under a general policy of quiet, or if she's getting special treatment because she is a princess which somehow doesn't extend to Odin having privileged access to the information, or what. Whatever it is? Heimdall never tells. Heimdall sees and she is silent.

---

She's gotten a bit older.

She hasn't been neglecting her practice too much, despite intensive research on the illusion spell.

She's at a good stopping place; she can stand to put it down for a while.

It's probably about time she went and killed something menacing to enter adult society, isn't it.