Witches
Witches are monsters that used to be magical girls. The act of turning into a Witch is called "witching out". It occurs when a Soul Gem turns completely black from corruption, and transforms into a Grief Seed. Soul Gem corruption is caused by either emotional lability, or by spending magical reserves.
When this happens, the Seed loses its bond to the human body, and starts creating a new one, that of a monster, refelecting the former magical girl's mind in some fashion. Sometimes, the human body is used as a part of the Witch's body, sometimes it disappears, and sometimes a dead body is left behind on the spot.
The Witch also creates a world in her own, surreal image, on the immaterial plane, called a Barrier. If the Witch is fully matured, she will usually divide the Barrier into two or more parts. Typically a central part, in which she resides, and the Labyrinth, which revolves around her. Most full-fledged Barriers can be only entered from their corners, giving any visitor the whole Labyrinth to go through.
A Labyrinth may be populated by Familiars, who are the Witch's servants. They can be her slaves or her tormentors, but their main purpose is bringing her food(humans from the outside), and feeding themselves as well. Though humans are always killed in feeding, it is not necessary for Witches to consume human flesh. They sometimes do - it generally makes them more ferocious. The presence of a Witch clouds the mortal minds, and Familiars can easily charm mundane humans and bring them in. A charmed human carries a mark called "Witch's Kiss", each Witch having her own design for it.
It's possible, if a lengthy matter, for a Familiar to grow into a full-fledged Witch themselves, if they are very successful at what they do. It's not clear how much effort this takes, and whether they would resemble their creator or not. In the case that it happens, though, they create their own Grief Seed, looking the same as one that used to be a Soul Gem, which can then also be collected upon their defeat. A Witch is technically still alive within the Seed, and if left alone and not handed to an Incubator, can be eventually reborn from it.
Witches are hunted and Grief Seeds are collected for two reasons, first being that each can be used to clean a Soul Gem once. More importantly, though, a Grief Seed holds untold amounts of condensed energy, which the Incubators can extract from it. Some of the more powerful Grief Seeds hold as much energy as a small star. This energy is then used to fuel the universe, and stave off the heat death.
Originally, this procedure is the sole reason for Incubators to create magical girls in the first place. It is not specified how many other planets and intelligent races in the universe host this cycle, but humans are noted to be exceptionally emotional.
The individual power of a Witch depends on several rather complicated factors, emotionality being the main one, but it suffices to say that special people become special Witches. The Witches are ranked by power, or threat level:
CHARLIE - Normal Witches. Can be solo'd by a competent middle-ranking Magical Girl, or a newbie squad.
BETA - Stronger Witches, possibly with familiars. Needs a competent squad, maybe two.
ALPHA - Witches with Familiars, the kind that's consumed human flesh already. May have intelligence. Needs at least three squads. Can be solo'd by Rank Leader. Instead of a Grief Seed, they have what is called a Witch Core or Grief Core. Those can be used to cleanse Grief Seeds, and thus also Soul Gems repeatedly, and are extremely valuable an asset for any Officio to own.
ALPHA PLUS - Alpha, but with witch-familiars and/or slave Witches. Needs specialists/killsquads led by Rank Leader.
OMEGA - Walpurgisnacht.
OMEGA PLUS - Geheimnisnacht.
Recently, more pressing concerns brought the Incubators on Earth to instead use magical girls as a work force - servants and soldiers, organized in the Officio Assassinorum system.
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