Warning: Spoilers up until the end of the series will be left unmarked.
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Hatou "Gaku" Manabu
Yukari's friend and the protagonist of the story, affectionally referred to as Gaku-chan.
Hatou was kidnapped by the culprit of the Tokyo Dismemberment Killer case and her left arm was sawed off, but this was fixed by Yukari through using Hatou's cellphone as supplementary parts. This resulted in her left arm functioning like a typical left arm does, while also serving as a cellphone.
She receives a call from a voice she recognizes as her own, informing her of Yukari's upcoming demise. Realizing that she can use this to communicate with 'herself' in various parallel worlds, Hatou collects knowledge of all these versions of herself to find a way to keep Yukari safe.
- Abusive Parents: Uses her powers of being able to take control of anyone remotely related to 'her', Hatou manages to become Yukari's mother in one timeline. She becomes physically abusive to a young Yukari that doesn't want to suppress her powers, while also lovingly embracing her to keep her loyal.
- Ascended to a Higher Plane of Existence: Chapter 16 sees her understanding the Theory Of Everything and becoming a 'non-existent existence' that can observe the world without being a physical part of it, which allows her to prevent Yukari's death.
- Boyish Short Hair: Her 'present' form always has her hair cut in a styled bob, as she's most active with her naginata training, and it fits with her boyish and aggressive personality.
- Catchphrase: "I must act in imitation of light." or even "become light" itself.
- Cursed with Awesome: Her left hand works like a regular cellphone, which gives her the ability to call people with it. This includes communicating with parallel world versions of herself, allowing her to draw information from an infinite number of possible realities.
- Determinator: Intent on finding a way to keep Yukari safe and alive in a world, regardless of which reality it is. Her determination is so intense that she visually kills off the part of her mind that would consider giving up on saving Yukari.
- The Dulcinea Effect: Her main motivation for her actions, despite having been Yukari's friend for only a short time. Deconstructed by showing how far Hatou goes and how dehumanized she becomes in her desire to see Yukari alive.
- Girliness Upgrade: Any 'future' form of Hatou shown has her growing her hair out, with her personality also mellowing out, or becoming more manipulative, as she realizes more of her powers and the experience of her many parallel selves.
- Ignored Epiphany: Hatou eventually realizes the futility of the collective's goal, believing that the only reason they can use their powers and attempt to save Yukari is because Yukari died, meaning that keeping Yukari alive would mean that they wouldn't be able to do anything to begin with. This realization gets promptly ignored, literally killed off in a visual fashion, and then the collective continues on with its mission.
- Innocently Insensitive: The more often Hatou performs her leaping between various parallel worlds and timelines, she doesn't seem to realize that she's gone too far.
- One timeline has her kill Alice's abusive mother in front of her, but doesn't understand why Alice would hate her for 'freeing' her of this abuse.
- Another timeline has her bluntly tell an adult Alice that 'this world' has no meaning to her anymore, now that Alice has come to hate her so much that she'd want to kill Hatou, leading to her no longer being helpful to her goal.
- In-Universe Nickname
- 'Gaku' used by Yukari.
- 'Helmet Head' used exclusive by Tenjou, much to Hatou's annoyance.
- Insane Troll Logic: Invoked by her to fuel her powers.
- An infinite number of parallel worlds exists, with their own possibilities in them. This leads Hatou to deduct that there must be a universe where magic exists. When she finds it, she gains magical powers and becomes a magical girl.
- Hatou can communicate with any form of 'herself' in any kind of parallel world. As her parents make up her genetics, this makes them part of 'her', leading to her being able to take control of them. This gets extended to going further back on her family tree, to the point of being able to take control of a ton of people due to even distant ancestors. This does have limitations, as she cannot take control of people like Yukari and Alice, as she cannot see the world the way they do, and while she knows the physical information of what the person does, she doesn't understand why they do things.
- Killing Your Alternate Self
- The collective Hatou has one of its incarnations shoot the incarnation that thinks their mission is futile because there's no way to keep Yukari alive, after all, to give up on the very idea of giving up.
- Another timeline, where she takes control of other people even remotely related to 'her', Hatou kills that timeline's completely seperate-from-her entity of 'Hatou Manabu', to see if her existence was actually important to her mission.
- Logical Weakness: Her left arm functioning as a cellphone has its advantages, but she serves as its battery and easily tires from using it. She often eats sugary snacks while using it to keep her energy up.
- Magic Feather: Her cellphone upgrade turns out to be this. Hatou realizes that she's always had the ability to communicate with 'herself' in parallel worlds, just that the experience with her hand resulted in this power awakening.
- Magical Girl Warrior: Upon realizing that a universe where magic exists is a possibility, she finds the universe and gains magical powers, choosing to become Multiple Magical Girl Mana-chan! She uses her powers to slaughter all of the founding members and future executives of JAUNT, and founders of similar organizations that replace it in other timelines.
- Mental Time Travel: Her communication and leaping powers work this way, resulting in her retaining knowledge and experience any of her possible world selves have gained. This is also why Hatou dying in one world merely results in her leaping to another possible world.
- Please Kill Me if It Satisfies You: Nearly says this word for word when one timeline has Alice pointing a gun at her head, realizing that this attempt of a world has run its course and cannot help Hatou reach her goal of saving Yukari anymore, considering it useless. When Alice hesitates out of love, Hatou puts the gun to her own head and gives Alice the okay.
- Physical God: Can perform almost anything as the series goes on. She can perform magic, gain control of other people, even run the world as a non-existent existence.
- Super Power Lottery: Begins to extend the ability of her powers as she learns more about their possibilities.
- Ripple-Effect-Proof Memory: She can communicate with 'herself' in any parallel world that could possibly exist and retain her memories and experience.
- Multiple-Choice Past: Then chooses to use this knowledge to observe said possible worlds and make the correct choices to meet her desired outcome.
- Mental Time Travel: Upon giving up on the idea of linear timelines, she can leap to parallel worlds and change the past up to the point in time of gaining her powers.
- New Game Plus: Can invoke this by communicating with any past self of hers in a parallel world, giving them the knowledge and experience learned later on.
- Reality Warper: And finally realizes the extent her powers can take because they are based on her perception and belief. She manages to find possible worlds by treating each possibility as its own extending branch, leading to her finding a reality where magic exists because she believes it wouldn't be abnormal because of the amount of parallel universes.
- Thou Shalt Not Kill: Defies this in worlds where she chooses to kill Alice and any replacement JAUNT member sent to recruit Yukari.
- Took a Level in Badass: Invoked by taking on experience with her many parallel selves, all of them working together for one goal.
- Took a Level in Jerkass: Hatou was a very friendly girl, but as the series progresses and she becomes obsessed with finding any mean to have a world where Yukari doesn't die, she becomes manipulative and aggressive.
- Walking Spoiler: Little can be said about her, without showing in what direction the series goes.
- Yandere: Focused on Yukari and even says in one timeline that she won't 'let her go' this time around.
Marii Yukari
Yukari is the deuteragonist of the series.
She has purple eyes and a strange way of perceiving the world. All life forms, other than herself, appear as robots to her. This leads to her being able to fix things by taking them apart and putting them back together, just as one would for plastic models.
Yukari's powers allow her to see some things that others can't, which nets her the interest of organizations like JAUNT. She transfers out of school and joins JAUNT at the behest of Alice and encouragement of Hatou, but ends up dying in what gets claimed to be an accident.
- Alone in a Crowd: From her perspective, she's the only human being in a world full of robots. And while she looks like a normal human girl to others, she's never seen anyone that looks like herself, leading to her being uncertain about what she is herself.
- Awesomeness by Analysis: Her strange vision allows her to assess a person's abilities based on the components of their robot form.
- Brain in a Jar: Ends up as one after her initial death.
- Bus Crash: Leaves Japan to join JAUNT, but is reported to have died in an accident six months later.
- Childhood Friends
- The original timeline shows that she was this with Tenjou, until the incident with the jungle gym.
- Hatou manipulates events in some timelines, so that she's also a childhood friend of hers.
- The Cutie: Yukari is small, innocent, and super sweet. It's hard for anyone to dislike her upon knowing her.
- Deuteragonist: The second most important character to the story, though her appearance significantly reduces as the story focuses on Hatou's parallel world travelling.
- Gadgeteer Genius: Can analyze, build, and repair any type of machine, including turning plastic models into autonomous, functioning robots. Maybe.
- Genius Ditz: Often described as airheaded, but she's talented at building and fixing things.
- Hypocrite: Upon learning that Hatou became a non-existent existence to ensure that Yukari avoids her early death, Yukari tells her that only Yukari herself can decide her fate and that Hatou shouldn't enforce her will on what she thinks is best for Yukari. But Yukari has enforced her will upon people previously: using a cellphone to attach Hatou's severed arm back onto her body, using jungle gym parts to fix Tenjou's injuries from a fall, and disassembling the Tokyo Dismemberment Killer to fix her 'bug'. Her words to Hatou come across as more pretentious, like enforcing her will on people, no matter how well-intended, is alright.
- Just a Machine: There is no difference between humans and machines, as the former look like robots to her. Interestingly for this trope, instead of lessening the value of human life, this leads her to regard machines with the same value and importance as humans.
- Kill the Cutie: First killed off in Chapter 6, which begins to set the ball in motion for the second half of the series and her deaths in other worlds.
- Killed Offscreen: Majority of her deaths over the course of the series occur when Hatou isn't or can't be near her.
- Living Macguffin: Her importance to the plot ends up more based on Hatou's desire to prevent Yukari's death, rather than Yukari's own actions. Treating her like this is exactly why Hatou was never able to save Yukari permanently in previous attempts, as Yukari decides her own fate. Only when Hatou treats Yukari like her own person again and lets her make her own decisions, does this lead to Yukari making choices that prevent her death.
- The Lost Lenore: Her death is the driving force behind Hatou's actions.
- Magical Eye: Her purple-colored eyes have her see humans as robots. Turns out that her eyes are not magical in any way to why she sees the world this way.
- Meaningful Name: Her family name Marii comes from the 'Mary's Room' thought experiment. This experiment involved making people consider the feelings of a person, the eponymous Mary, who had only been fed information on colors besides black and white, up until the point they experience those colors themselves for the first time.
- Out of Focus: Despite being the deuteragonist of the story, she appears less and less after her first death in Chapter 6, as the focus shifts to the quantum physics and parallel world travelling performed by Hatou. It's easy to forget that the initial goal was to prevent Yukari's death by travelling to those worlds.
- Reality Warper: Her vision allows her to dismantle, reprogram, and rebuild human beings just like action figures and robots, with nary a drop of blood being spilled.
- P.O.V. Boy, Poster Girl: Featured prominently on the covers of the light novel, even being the sole character shown on the manga's first volume cover, but the main focus and action follows Hatou.
- Sacrificial Lion: Her death sets Hatou's quest in motion.
- Super-Empowering: Inadvertently allows Hatou's powers to manifest after implanting a cellphone into her hand.
- What Beautiful Eyes!: The purple qualia that the title refers to are Yukari's purple-colored eyes. Hatou's monologue near the end of the series details how mysterious and beautiful they are.
Tenjou Nanami
Tenjou used to be friends with Yukari.
She's taken to picking on Yukari in a way that even Hatou doesn't refer to bullying, but more an immature, childish way of interacting with each other. Even their classmates know to not interfere, as it isn't actually harmful. Yukari herself doesn't seem to mind how Tenjou treats her.
Tenjou warns Hatou about being friends with Yukari, citing that she'll eventually see how terrifying her viewpoint can make Yukari. She does mean well, as Tenjou still cares for Yukari, and hopes to keep Hatou from experiencing what she did.
- Demoted to Extra: Appears less during the second half of the series, as timelines shift more and more away from the original one.
- Foil: To Hatou. Both are Yukari's friends and know about how her eyes make her see the world, and both had severe injuries 'fixed' by her. But while Tenjou thinks that Yukari's sight means she sees humans as replaceable as robots, Hatou thinks it means that Yukari sees robots as precious as humans.
They also react differently to their respective 'fixings'. Tenjou was not only awake during her procedure, she goes on to use quantum physics as a way to explain worldviews, so she won't have to accept that her body is made up of jungle gym parts. Hatou slept through her procedure, and quickly came to accept her cellphone-imbued arm. - Jerk with a Heart of Gold: Teases Yukari and keeps up an abrasive attitude towards her, but does still care for her friend. It's just that her trauma gets coped with by acting this way towards Yukari.
- Meatgrinder Surgery: When playing on a rusted jungle gym as children, the structure broke and Tenjou sustained fatal injuries. Yukari wanted to save her friend and proceeded to use pieces of said jungle gym to 'fix' her injuries, all while Tenjou was awake and conscious.
- Secret Relationship: One timeline has her mention that she and Kasoku tried to keep their dating in their third-year a secret. Hatou points out that everyone knew they were.
- Trauma-Induced Amnesia: One timeline implies that Tenjou eventually did this to herself by 'reobserving her past' and forgetting that Yukari 'fixed' her injuries by using jungle gym parts, merely recalling her as being a quirky classmate.
- Wise Beyond Their Years: Very intelligent for her age, discussing quantum physics, the qualia, and the philosphical zombie with Hatou.
Alice Foyle
Alice is a genius and part of JAUNT.
She flies to Japan and transfers to Yukari's school, in order to recruit her into JAUNT, an organization built for genius children like Yukari and herself. She hits it off with Yukari rather well, but often antagonizes Hatou and Tenjou, especially the former.
Alice has a unique worldview like Yukari, leading to her perceiving mathematical equations as pictures and solving them by instinct.
- Age-Gap Romance: In timelines where they end up together, Alice is in her late preteen or early teenager years and Hatou is in her mid-teens. One of Hatou's incarnations actually calls 'herself' out on this, but clarifies that she only feels this way for Alice and no other younger girl.
- Alice Allusion: Intentionally styled her appearance after Alice from Alice in Wonderland because of wanting to distance herself from her past and hoping to be a fairytale-worthy girl. Thematically appropriate, as Alice's Adventures in Wonderland had multiple mathematical references hidden in the book.
- Armor-Piercing Question: The original timeline has Alice ask Hatou if she genuinely thinks she can protect Yukari and keep her powers a secret from everyone, already aware that Yukari, and Hatou, were in danger because the Tokyo Dismemberment Killer had learned about Yukari's eyes and targeted her for them. Hatou is left speechless, and this is one of the factors for why she ended up encouraging Yukari to join JAUNT.
- Dark and Troubled Past: Her mother was a drug addict that believed Alice was a spawn of the devil sent to punish her. She was physically and emotionally abusive, resulting in massive self-esteem issues for Alice.
- Did You Think I Can't Feel?: One timeline of Alice becoming Hatou's partner as the leader of JAUNT has her growing resentful towards her lover because Hatou continuously ignores her thoughts and wishes. Eventually, Alice points a gun at Hatou. The problem is that Hatou is aware of Alice's feelings and does genuinely love her, but that Hatou is always focused on the bigger picture of saving Yukari.
- Inferiority Superiority Complex: Her haughty attitude comes from a lack of self-esteem caused by her past.
- Insufferable Genius: Incredibly smug about her intelligence and thinks of non-superpowered people as 'peons'.
- Lipstick Lesbian: Becomes this to Hatou in timelines where they end up together.
- Logical Weakness: Her ability to see mathematical equations as pictures means she can instantly draw the correct answer, but this means that nobody but her actually understands what her picture means. This leads to her merely being able to give the answers verbally, as she can't write the equations or formulae down.
- New Transfer Student: Transfers into the cast's class during their second year in middleschool.
- Strong Family Resemblance: She appears to take a lot after her mother. This is why she dyes her hair blonde, to get as far away from that assosciation as possible. In the timelines where she grows resentful of Hatou, she let her hair become its natural color again, but kept it blonde in the non-resentful timeline.
- Unwitting Instigator of Doom: Wanted Yukari to join JAUNT because she genuinely thought that the organization would be strong enough to keep Yukari safe and let her nourish her powers fully. She didn't know that Yukari would die, nor wanted her to ever get hurt.
