The Arithmancer

""You know the power the Dark Lord knew not?" Hermione said. "It's me!""

- Lady Archimedes, chapter 79

An epic work of Harry Potter fanfiction by "White Squirrel", comprised of the titular fic, The Arithmancer (covering years one through four) and Lady Archimedes (covering years five through seven). They were originally intended to be a single story, but when it reached half a million words before the completion of fourth year, the author divided it into two installments. Its sequel, Annals of Arithmancy, covers the years after the defeat of Voldemort, and is considerably shorter at 24 chapters and just shy of 155,000 words.

The Arithmancer is set in an Alternate Universe in which Hermione Granger isn't just frightfully intelligent, she is also a mathematical prodigy, and tests into Arithmancy starting in her first year. She becomes the protégé of Septima Vector, Hogwarts' Arithmancy professor, and before she's even out of her second year she's clearly going to be a force to be reckoned with. By the end of her fourth year she's already published a half-dozen papers on groundbreaking work in almost all fields of magic, has two magical patents, markets a line of potions kits, has invented spells that surprise and sometimes terrify the people who learn of them, and is the silent partner in one upcoming business -- but one of her biggest priorities is keeping her friend Harry Potter alive in the face of Voldemort's return.

Doing so makes her just as big a target as Harry, because if there's one thing Voldemort and the Death Eaters can't stand, it's a Muggle-born who knows more (and more about) magic than they do, and worse, is a creative outside-of-the-box innovator. The combination of Muggle knowledge and magical methods makes her more than just a dangerous student -- it makes her a direct threat to their ideology. She's also a deadly threat to a Ministry which wants nothing more than for Harry Potter to disappear.

But neither group knows just what it's facing -- and the trouble they will bring down upon themselves for making an enemy of Hermione Granger, who will become known to the Wizarding World as Lady Archimedes, the Arithmancer.

A well-written and well-thought-out tale, The Arithmancer is outstanding for the careful research and planning its author has put into the increasingly significant deviations from canon caused by the differences in Hermione and her accomplishments. But she is no Mary Sue or even a Canon Sue -- unlike her counterpart in the original stories, this Hermione is prone to overwork and insomnia which makes her careless, reckless and off-kilter and suffers breakdowns and near-breakdowns on what is far too close to a regular basis. Like Harry, she shoulders a huge amount of responsibility as the Death Eaters take over England, and she worries that she's not up to the tasks she and others ask of her. But regardless of the obstacles in her way, Hermione continues forward, bolstered by a faith in the power of mathematics and magic combined, and knowing that if she doesn't do it, no one else will -- or can.

"Bellatrix cackled. "And you think you can stop me this time, little girl?" "You know the power the Dark Lord knew not?" Hermione said. "It's me!""
 * Abusive Parents: Dobby's responses to Hermione's questioning when the Grangers offer him a job hint that the Malfoys do not beat just their elves, but that their family discipline is also strict to the point of extremity (and has been for generations).  It's enough to briefly make Hermione almost feel sympathy for Draco.  Almost.
 * Adaptational Badass: Hermione.  By the end of Lady Archimedes she's a sword-wielding, Magitek-armored Magic Knight able to go toe-to-toe with Bellatrix Lestrange and win.  And this is mostly with the side benefits of the things she's really interested in pursuing and studying.
 * Adult Fear: The Grangers have every right to be terrified for their daughter, as every year she's at Hogwarts gets more and more dangerous until she's actively withholding information from them in Third Year for fear of being yanked out and transferred elsewhere.  Which they in fact do for her fourth year, sending her to Beauxbatons.  Only an educational decree forcing her to go to Hogwarts keeps them from doing so in fifth year; and it's only Hermione pointing out that she will be a legal adult shortly after school starts and will be able to simply ignore their wishes that keep them from doing so again in sixth year.
 * Alien Geometries/Eldritch Location: Hogwarts, full stop.  Hermione decides after her first few days of classes to map the castle so that she can find her way about faster, and discovers that it is non-Euclidean -- and worse, the lengths of hallways and walls gradually change even over the course of a single day.
 * The upper reaches of the Grand Staircase of Hogwarts are positively perverse, growing more alien the higher you get. This, however, turns out not to be a function of Hogwarts' construction/nature, but rather a bizarre side effect of its wards.
 * And then there's the setting of the third task of the Tri-Wizard Tournament, which is an Escher-inspired building-sized tesseract.
 * Altar the Speed: Immediately after the Battle for Hogwarts, Ginny informs her mother that she will be marrying Harry as soon as legally possible -- on her 17th birthday.
 * Anger Born of Worry: George lashes out at Hermione in the wake of the debacle in chapter 47 of Lady Archimedes entirely because of this -- worry for both his brother Fred and for Hermione, who is suffering from sleep deprivation and overwork again, and who blindly apparated into the middle of a firefight at the Twins' shop without thinking about what she was doing, and nearly got blindsided by a Killing Curse in the process.
 * Anticlimax Boss:
 * Antimatter: Concerns that her researches into applying higher maths to Transfiguration might make it possible for a wizard to create antimatter lead Hermione to
 * An Arm and a Leg:
 * The Apprentice: After she graduates from Hogwarts in 2001, Georgina Vector apprentices under Hermione.
 * Artificial Limbs: In addition to Mad-Eye Moody, of course, there is.
 * As the Good Book Says...: Hermione's ritual to keep someone from saying Voldemort's name includes a line from Psalm 141.
 * Her researches into soul magic lead her to delve into the holy texts of multiple religions, relevant snippets of which we see "over her shoulder".
 * The ritual to remove the horcrux from Harry uses a verse from the Song of Solomon (2:10-11).
 * Ultimately, Hermione builds a ritual around a passage from the book of Job (Job 3:3-10).
 * Her ritual to kill dementors uses the original Greek text of 1 Corinthians 15:55.
 * As You Know: Played with.  Around Halloween of fourth year, Hermione begins expounding on the varieties of color-changing spells in trying to explain the potential uses of a field of higher math to Septima Vector.  Vector shuts her down almost immediately.
 * Ascended Extra: Septima Vector, who is practically a non-entity in the original books, is a major figure in these stories, as befits Hermione's Arithmancy teacher and mentor.
 * Asexuality: Charlie confirms he's asexual in chapter 17 of Annals of Arithmancy.
 * Attention Deficit Ooh Shiny: Hermione constantly suffers from a low level of this where intellectual pursuits and challenges are concerned.  It's almost never Played for Laughs, and frequently is Played for Drama.  She sometimes has to rein in her racing thoughts when it's counterproductive -- for instance, during a rescue mission late in Lady Archimedes, she's in the middle of battle and has to stop herself from thinking about how to turn wands into sniper weapons.
 * This tendency gets particularly bad when Hermione's stressed and overworked, such as during the first few months Hermione is working out of the Resistance base in Nottingham in year six. She is so overwhelmed by the need to do so many things that she utterly fails to focus entirely on any one of them, and at the same time begins driving herself into another sleep-deprivation-fueled breakdown.
 * Aura Vision: As part of her long-term project to get the horcrux out of Harry, Hermione works on several spells designed to make the soul of its subject visible.
 * Award Snub: Because of political pressure exerted by Dolores Umbridge and the Fudge administration, Hermione is denied the Wenlock and Gamp prizes for her work proving the sixth exception to Gamp's Law.  The prizes instead go to her collaborators, Professor Vector and Rebecca Gamp -- but Rebecca refuses to go along with the attempt to make Hermione an Unperson and uses her acceptance speech to announce to the attendees and the press that Hermione is the one who should actually receive the awards.
 * Awesomeness By Analysis plus Good with Numbers: This is Hermione's stock-in-trade in this story -- a mathematical prodigy capable of performing complex calculations in her head, she tests into Arithmancy in her first year, and goes on to publish ground-breaking work in professional journals and apply principles of chemistry, physics and physiology to magic with astounding (and sometimes terrifying) results.
 * Badass Boast: Hermione gets one in the final lines of chapter 79 of Lady Archimedes:

""I am Lady Archimedes, Slayer of Dementors!""
 * She gets an accidental one in during her third Sorting, when she demands that the Hat put her back in Gryffindor:

""I'm highly logical at doing things quick and dirty with a minimum of effort.""
 * Badass Bookworm: This is the canon Hermione cubed.  She passes her Arithmancy NEWT before fifth year and starts working on a Mastery in her fifth.  She invents spells that terrify people on both sides of the war.  She's a published researcher into arcane magics before she's past her fourth year.  She essentially invents Magitek. She comes up with the way to kill Voldemort at the end -- and she battles Bellatrix Lestrange one-on-one while at a severe disadvantage but still triumphs.  After the Battle for Hogwarts is over, she's told that she's probably the most accomplished and deadly fighter in all of Magical Britain.
 * Badass Longcoat: In the summer between third and fourth years, Hermione receives one made of basilisk hide from a pair of cursebreakers who used her basilisk-proof glasses to kill it.  It gets pretty much shredded in the Battle of Hogwarts, but in recognition of her relief efforts in the wake of the 2004 Indian Ocean earthquake and tsunami, the Indian Cursebreakers' Association gives  her another one.
 * Banana Republic: On multiple occasions during and after fifth year, Hermione and her parents frequently compare Wizarding Britain under Fudge and Umbridge to both one of these and to the former Soviet Union.
 * Be Careful What You Wish For: "Me and my big mouth," Georgina Vector mutters when her first weeks as Hermione's apprentice in Annals of Arithmancy take her into the heart of (very dangerous) giant territory.
 * Beige Prose: When asked in Annals of Arithmancy chapter 13 to consult on the cause of problems with the Firebolt Millennium broom, Hermione's initial analysis is, "It's too fast."  (She does answer in more detail shortly afterward.)
 * Big Bad: Voldemort, of course, in The Arithmancer and Lady Archimedes.
 * In Annals of Arithmancy the escaped Barty Crouch Jr. becomes this, starting with the mass breakout of dementors from Azkaban that he engineers.
 * Big Brother Is Watching: In 2012, an article Hermione reads as a followup to finishing a David Brin novel alerts her to the danger the proliferation of both CCTV cameras and smartphones pose to Wizarding World and the Statute of Secrecy.
 * Bizarrchitecture: The constantly-moving, Escher-inspired tesseract in which the third task of the Tri-Wizard Tournament takes place, complete with multiple Gravity Screws.
 * Black Dude Dies First: Lee Jordan's death during the Ministry Battle at the end of fifth year is the first death seen among the anti-Voldemort forces.
 * The Blacksmith: In chapter 5 of Annals of Arithmancy, Hermione takes on a challenge to create a sword for the King of the Goblins in exchange for Hogwarts getting to keep possession of the Sword of Gryffindor.
 * Blob Monster: The Shoggoth-like thing made from wood chips, dust, fluff and other random stuff which was the last "defender" summoned from the Great Tower by Professor McGonagall's spell
 * Body Horror:.
 * What Hermione does to defeat is even worse by some lights.  It's certainly Nightmare Fuel.
 * Bookie: Starting fairly early on, Hermione uses her math skills and Arithmantic prognostication she learned in class to calculate the chances of various Quidditch teams -- both in the school and on the professional level -- winning. She's a borderline case, in that she doesn't actually take any bets, but she is accurate enough in her assessments that the Weasley Twins, among others, enjoy a fair amount of success with the bets they make using her advice.
 * Break the Cutie: The events of Hermione's first few weeks at Hogwarts, through no fault of anyone except maybe Draco Malfoy, all combine to leave her vulnerable to a breakdown that's triggered by Ron being nasty to her on Halloween (and culminates in the infamous troll incident).  Afterwards, though, Hermione discovers she has more friends and support than she realized, and enlists their help in preventing future stresses.
 * It almost happens again in the first part of her second year, when she believes that Draco Malfoy is actively planning to kill her via the Heir of Slytherin and his monster. Going home for Christmas (plus Ron, Harry and the Twins interrogating Malfoy with veritaserum and reporting back to her) lets her get her balance back to carry her through the rest of the school year.
 * It finally happens in her third year, when the convergence of many factors -- most of all understanding the nature of Dementors, a fight with Harry and Ron, and the stationing of guard trolls at the entrance to the Gryffindor dorms, which triggers a phobic reaction she didn't know she had -- sends her into a downward spiral. She had all but given up when the Weasley twins drag her back from rock bottom, and she comes back stronger and more determined.
 * Brief Accent Imitation: When one of the Hogwarts House Elves suggests Dobby might know "old elf lore", Hermione is so startled by the concept that she momentarily slips into House Elf vernacular herself.
 * Brilliant but Lazy: Ron.  He speaks four languages (two fluently), can impersonate voices flawlessly, is a chess prodigy, is better at Ancient Runes than Hermione, quotes Rudyard Kipling, and shows occasional flashes of insight and inspiration that surprise and impress her.  But he'd rather loaf around and have fun than do his schoolwork.  When he surprises her at the end of third year with some remarkable improvisation with runes, he says (paraphrasing her own earlier description of herself):

""Whoa, freaky food," Ron said, seeing the international selection. "What's this one?" "Bouillabaisse," Hermione said. "Bless you.""
 * Buccaneer Broadcaster: "Radio Free Britain", set up and run by the Twins.
 * But for Her It Was Tuesday: In what is implied by the narration to be Harry's thoughts, this is how Hermione's seemingly-casual alchemical creation of carbon nanotubes, which was still out of reach of Muggle scientists, is described.
 * Calling Your Attacks: Snape chides Hermione for doing this at the Department of Mysteries (using the trope name), allowing Rookwood to reverse-engineer her spells.
 * Card Sharp: Sonya the House-Elf.  She'll clean you out of gobstones if you're not careful.
 * Cessation of Existence: The comprehension that Dementors appear to cause this to immortal souls (as well as the Wizarding World's casual acceptance thereof) is the direct trigger for Hermione's third-year breakdown.  Years later she puts a great deal of effort into finding a way to destroy Dementors because in part she has faith that the souls they've consumed are merely contained, not destroyed.
 * Chekhov's Gun: Several.
 * The most prominent is the Foundation Stones of Hogwarts, which Hermione learns about in literally her first moments inside the castle in her first year, and which turn out to be critical to Voldemort's defeat, seven years later, along with the magical network of which they are a key part that is spread across all of Great Britain.
 * Nearly as important is Hermione's (and Ron's!) initial exposure to runes during a special open lecture in first year.
 * To a lesser degree, knowing about the Knight Bus by having taken it in the summer after First Year, Harry is able to suggest it as an alternative to stealing Mr. Weasley's car when Dobby blocks the way to Platform 9-3/4.
 * The Chessmaster: Hermione explicitly describes Ron as this several times, partly as a literal description -- Ron is a prodigy at chess, after all -- and partly because some of his chess skills translate into strategic thinking and other useful talents.
 * Child Prodigy: Hermione, from the first sentence of the story; that is, at least until September 19 of her second year, after which she is a Teen Genius.
 * Ron isn't far behind her, as far as she's concerned.
 * Clockworks Area: In one scene from chapter 14 of Annals of Arithmancy, Hermione is one of a team of cursebreakers working on a Hindu tomb sealed with an extraordinary set of clockworks.
 * Clothes Make the Superman: In what amounts to The Stinger to the entire canon-inspired storyline, Hermione discovers that Voldemort's unique and mysterious power of flight came from essentially turning a Magic Carpet into a set of robes. As of the start Annals of Arithmancy, she's trying to make her own set from scratch, while learning how to actually use them for anything more than just hovering.  By chapter 9 of Annals, she's succeeded.
 * Consolation Award: Rebecca Gamp gives Hermione her Wenlock Prize after the awards ceremony where Hermione was snubbed, and tells her to have it re-engraved with her name.
 * Convection, Schmonvection: Averted in chapter 31 of Lady Archimedes, when Hermione opens a door in the Department of Mysteries and almost gets her face burnt off by the blast of heat coming off the lava within.
 * Corporal Punishment: The by-laws of Hogwarts still permit it as long as the punishment does not cause "serious injury"; however, "serious injury" is not defined. Because of the leeway this gave Filch and other disciplinarian staff, Dumbledore formally forbade it when he became headmaster.  When she issued the educational decree which gave her complete control over all discipline, Umbridge reinstated its use.
 * Cowgirl: Luna dresses as one for New Years Eve 1999 at Hoover Dam.
 * Crazy Prepared: Hermione slowly becomes this over the years, adding backup wands, creating personal weapons, and starting in sixth year wearing multiple layers of enchanted carbon nanotube armor under and as part of her school uniform.  It takes her a bit longer, but she eventually figures out how to blend nanotubes and Lycra to make blade-proof stockings.
 * Voldemort attacks Hogwarts with an anti-bullet ward on himself.
 * The Cuckoolander Was Right: One of the reasons Hermione is friends with Luna Lovegood is that she respects the occasional piercing insight Luna's unusual viewpoint can provide.
 * Cue the Sun: The moment of sunrise, unseen but signaled by Hermione's watch alarm, is the moment the disadvantages imposed on her as part of the price of the  ends, allowing her to finally let loose with her most destructive magic against.
 * Day of the Jackboot: In one of the more prominent examples of how things get worse faster than canon, Voldemort takes over the Ministry midway through Hermione's sixth year -- and does it in a more sophisticated and subtle way than the canon version.
 * De-Power: Due to a combination of the Cruciatus and severe brain trauma (both thanks to the Carrow siblings),.
 * Death by Adaptation: Many characters who survived in the original books  do not survive this story.
 * Death Ray: In Annals of Arithmancy Hermione modifies an alchemical "Bottled Sunshine" recipe to store much more energy, and mounts the canisters of stored light in a rifle-like affair to make it easier to hit Dementors with it.
 * Demonic Possession: In one segment of Chapter 14 of Annals of Arithmancy, Hermione is called upon to help a young Mexican boy who's been taken over by a dark spirit in an Aztec mask.
 * Determinator: Hermione when it comes to numbers.  She never loses count of anything, she can use mathematical sequences as Occlumency mantras, and even the Imperius can't force her to get a math problem wrong.
 * Did You Just Punch Out Cthulhu?: The general reaction to Hermione's ritual to kill dementors.
 * Difficulty Spike: Following the classic fanfic advice "if you give Frodo a lightsaber, you have to give Sauron the Death Star", pretty much everything is harder or worse for the heroes, starting right from the gauntlet defending the Philosopher's Stone, through the Tri-Wizard Tournament, to the protections on Voldemort's horcruxes and the Death Eaters taking over the Ministry in sixth year.  Among other things.
 * Dirty Coward: Zacharias Smith, in Tonks' opinion, for sheltering in the kitchens with the younger kids during the Battle for Hogwarts.
 * Disney Death:
 * Don't Call Me "Sir"!: After Georgina becomes her apprentice, Hermione insists that she not call her "Mistress".
 * Doorstopper: The Arithmancer and Lady Archimedes clock in at 529,133 and 597,295 words respectively.  At about 155,000 words, Annals of Arithmancy is substantially smaller.
 * Empathic Environment: The  causes a heavy cloud cover to swirl into existence over all of Great Britain, in defiance of meteorological expectations.
 * Engaging Conversation: When Hermione reveals to the Weasley twins in third year that she's brewing veritaserum in Moaning Myrtle's bathroom and she wants them to finish the project over Christmas break because she'll be home, they simultaneously hug her and declare, "Marry us!"
 * Equivalent Exchange: Dumbledore brings up this topic by name in his private lessons with Hermione in sixth year.  Hermione keeps coming back to it when researching horcruxes and how to get the one in Harry out.  And in chapter 5 of Annals of Arithmancy, she explicitly cites this principle as the operational basis of Ritual Magic.
 * Every Car Is a Pinto: Explicitly averted when Voldemort starts flinging cars at Harry and Hermione during the attack on the hospital in Nottingham.  The aversion is lampshaded when Hermione absently notes that the cars didn't blow up like in the movies.
 * Face Fault: It's not called that, but Hermione literally falls over in surprise and shock upon hearing Molly Weasley swear for the first time.
 * Faking the Dead: Hermione convinces her parents to leave the country at the end of her fifth year, and with Snape's cooperation fakes a Death Eater attack that destroys her family's home and appears to kill them.  (This is not spoilered because it's a secret from the reader for all of maybe six pages before Hermione reveals the truth to the Weasleys and Harry.)
 * In sixth year, she uses a genuine Death Eater attack on the Lovegood home to make it appear that Xenophilius Lovegood has been killed, thus allowing him to run a new anti-Death Eater newsletter from a safe location.
 * Family Business: Arithmancy and spellcrafting for the Gamp family, the latest of whom, Rebecca, is one of Hermione's classmates.
 * Fandom-Specific Plot:
 * The bog-standard "soulbond" plot gets averted and briefly discussed in the wake of.
 * The classic "Harry earns the respect and backing of the goblins for something trivial" plot is averted, discussed and mocked in chapter 7 of Annals of Arithmancy, when Hermione worries that the sword she made for the Goblin king may have accidentally made the Goblin Nation her "best friend", and notes that she doesn't think she could stand the absurdity of it. She is reassured that no, the Goblins just consider her work equal to the lower grades of Goblin manufacture, and that's all.
 * Fate Worse Than Death: Being a ghost.  You're permanently stuck in the emotions and mindset you were in when you died, you can't change in any appreciable way, and your memories of anything other than a few years on either side of your death and the last few years of your existence eventually fade away.
 * Hermione considers.
 * Finishing Each Other's Sentences: While the Twins do this as a matter of course,.
 * For Want of a Nail: Little differences start adding up almost from the first.  The Halloween troll incident goes somewhat differently from canon; the end-of-year confrontation with Quirrell goes wildly different.  And it keeps going from there.
 * Foreign Language Tirade: Despite being French, Fleur swears extensively in Serbian at one point -- a reference to the origins of vila in Eastern European folklore.
 * Foreshadowing: Hermione's concerns about Voldemort possibly dropping a horcrux in the ocean is not only a reference to another fanfic, but is also.
 * Forging Scene: Utterly averted with Hermione's swordsmithing and other blade-crafting -- she does it all via runes, arithmancy and visualization.  Given that the sharp parts of the blades are carbon, not metal, this makes sense -- but even the metallic parts, like the tungsten ballast, are built up atom-by-atom with her magic, rather than heated as a mass and shaped on an anvil.
 * Four-Fingered Hands: The House Elves.  Hermione is a frequent visitor to their quarters for the best part of a year before she notices this about them.
 * Freak-Out: Hermione on Halloween of her first year.  Although just as in canon Ron's rude comment in Charms sends her off crying in the girls' room, it's the really just the trigger event that lets loose the result of some two months' worth of cumulative stresses, including her own tendencies toward undersleep and overwork.  When her breakdown ends in the aftermath of the infamous troll incident she comes out of it with a different perspective, and finds that she has many friends who are willing to, and do, give her the help and support she needs to cope with Hogwarts until she can manage it on her own.
 * Two years later, Hermione has what she describes as "an existential crisis" when Professor Vector (reluctantly) explains the Dementor's Kiss, and what it means. Combined with a dramatic fight with Harry and Ron, the stationing of troll guards at the entrance to the Gryffindor dorms, and the threat of Sirius Black, Hermione finally hits rock bottom.  It takes the Weasley twins dragging her out of the Room of Requirement to get her back on an upward path, but she comes out of it stronger and more determined.
 * Especially toward the end of the story, the more stressed and short of sleep Hermione gets (and the more she uses Ravenclaw's Diadem), the more likely she is to have a minor melt-down at some key point.
 * Frickin' Laser Beams: With the help of an experienced alchemist, Hermione adapts a "bottled sunlight" recipe to create metal casks holding enough sunlight to equal a 10KW laser -- which she can fire in a beam.
 * From Bad to Worse: In Annals of Arithmancy, we find out that.
 * On a more personal level, Hermione goes directly from 9/11 to a mass breakout of dementors from Azkaban.
 * Fully-Clothed Nudity: Invoked by Mad-Eye Moody when discussing how much his eye can actually see under someone's clothing -- apparently it needs an actual air gap to see into, so anything skintight (like most underwear) is still opaque to him.
 * Gambler's Fallacy: Hermione's first reaction upon hearing about Sirius Black's escape from Azkaban is to assume that it has something to do with Harry; then she upbraids herself and invokes this fallacy by name.
 * Gesundheit: From chapter 66 of The Arithmancer:


 * She calls him on this, knowing that he speaks French fluently and should be perfectly aware what bouillabaisse is.

"It's not like an evil psychopath sneaks in and tries to kill somebody every year or something."
 * Ghost Amnesia: Part of what makes being a ghost a Fate Worse Than Death is that you eventually forget anything other than a few years on either side of your death and the last few years of your current existence.
 * There is one profound exception to this in the story -- the Grey Lady, Helena Ravenclaw, was so angered by how Tom Riddle seduced the location of Ravenclaw's diadem from her and then turned it into a horcrux, that her fury over the transgression still burns brilliantly a half-century later.
 * Glad He's on Our Side: Septima expresses this sentiment about Hermione to her face in chapter 35 of Lady Archimedes, when she learns the details of the curses Hermione's designed.
 * Later Snape says this to/about Hermione after Dumbledore's death when he gives her all his spells except for Sectumsempra and she tells him it's okay because she's already reverse-engineered it.
 * Go Mad from the Revelation: At the start of fifth year, Septima uses these exact words when she jokes about the effect of yet more Muggle higher maths -- especially fractals -- on her sanity.
 * Gone Horribly Right: The second, successful ritual to remove the horcrux from Harry.
 * Good with Numbers: Hermione is a math prodigy and instant calculator who's already taking college-level math courses when she enters Hogwarts at age 11. She tests into Arithmancy in her first year, and things start diverging from canon rather dramatically from there.
 * Gosh Dang It to Heck: Hermione uses "Holy cricket!" as an exclamation all the way through her late teens.  By the end of the story she's swearing more like an adult, though.
 * Grappling Hook Pistol: The homoaraneus spell acts as one.
 * Green-Eyed Monster:
 * As in canon, Ron, of course, and his jealousy-driven pre-Tournament break with Harry is arguably worse than in canon because it's exacerbated by the dual impact of hero!Harry and arithmancer!Hermione making him feel doubly useless.
 * Rebecca Gamp, for whose ancestor Gamp's Law was named and whose whole family has been arithmancers and spellcrafters for generations, is profoundly jealous of Hermione's mathematical gifts and the string of papers she's published before she's finished fourth year.
 * Grey Goo: In the spring of seventh year, Hermione realizes the potential for a magical Grey Goo disaster with the right (or wrong) combination of runes and copying charms.
 * Groin Attack: When under veritaserum Peter Pettigrew admits to having used his rat form to spy on her while she was dressing, Hermione's response is to knee him in the balls.
 * Hand Cannon: It never gets a proper name, but in seventh year Hermione builds a Magitek gun that holds 30 very large bullets and can fire them full-automatic.  She kills Augustus Rookwood with it -- ten bullets to take down his shield, and another ten to thoroughly perforate his torso and head.  (The last ten go wild as she's suddenly yanked/thrown by magic while she's shooting.)
 * Handguns: Hermione builds several Magitek guns over the course of the story, including a magical machine gun she uses to take out Augustus Rookwood, and.
 * Hangover Sensitivity: Winky demonstrates this after Hermione, Dobby and Sonya rescue her from rock-bottom.
 * Happily Adopted: Septima Vector adopts  after the Battle for Hogwarts.
 * Heel Face Turn:
 * Rebecca Gamp. Played with, in that despite Draco Malfoy's best efforts she is never actively an enemy to Hermione, just The Rival in some ways, and they work together well on Hermione's paper about the sixth exception to Gamp's Law.  But she's still hostile to Hermione because arithmancy and spellcrafing come so easily to the younger girl.  However, Rebecca gives up on that hostility entirely when she declares in her acceptance speech that the Wenlock and Gamp prizes she's just been awarded should have gone to Hermione, who's been denied them for political reasons.
 * Rita Skeeter, in a way. Discovering what "human rights violations" were gave her a new perspective on her role as a journalist, and in Hermione's employ she documents the atrocities committed by the Ministry under Voldemort.
 * Hellfire: Hermione begins using thermite to smelt metals while at Beauxbatons.  Her first try causes an explosion, destroys the crucibles she was using, burns through multiple fire protection charms, melts a sink, prompts a MythBusters Shout-Out -- and terrifies a boy who had been interested in her.  The staff responding to the explosion alert think she was using fiendfyre -- until she explains she was using a Muggle substance that burns hotter and more destructively than fiendfyre.
 * Hideous Hangover Cure: Averted.  When Hermione asks if there's a potion for hangovers, Dobby tells her "only headache potion and orange juice".
 * Hold Your Hippogriffs: For the most part these stories limit instances of this trope to the usual oaths sworn on various parts of Merlin's anatomy or wardrobe, but Hermione comes out with "wild niffler chase" completely out of the blue at one point in the middle of Lady Archimedes.
 * Homeschooled Kids: To get out from under Umbridge and her threats in fifth year, Hermione (with Dumbledore's help) arranges to withdraw from Hogwarts and get tutoring from Horace Slughorn after Christmas break.  She still continues working on her mastery with Vector, though.
 * I Am Not Left-Handed: There are numerous instances where Hermione has a hold-out surprise ready, starting from the most literal case (teaching herself to cast left-handed in the weeks when her right hand was recovering from frostbite) to her climactic battle with Bellatrix Lestrange.
 * She actually quotes the Trope Namer when dueling Seamus Finnegan during his first D.A. session, having started out casting with her off hand and then, after fighting him to a draw, switching to her right hand and demolishing him.
 * I Have Many Names: Hermione starts collecting names as early as fourth year, when some of the students at Hogwarts start calling her "The Arithmancer".  She chooses "Lady Archimedes" for herself, of course, and later takes some perverse pride in being "Undesirable #2".  By her early twenties, she's known internationally as "The Demonslayer", and the Dementors call her "The Angel of Death".  And after she gets her doctorate, she tries to get people to call her "The Doctor", mostly unsuccessfully.
 * I Need to Go Iron My Dog: Harry's lame excuse for leaving a D.A. session early (at Hermione's request) in chapter 20 of Lady Archimedes.
 * If My Calculations Are Correct: When explaining her analysis of the clue for the second Task to the Tri-Wizard champions, Hermione actually uses the phrase "according to my calculations".  Other than this one case, Hermione never again utters this Stock Phrase in any of its various forms, but other characters express its sentiments for her to show their faith in her mathematical abilities.
 * In the Blood: In chapter 18 of Annals of Arithmancy, Marcus Vector admits to worrying about this just before he leaves for his first year at Hogwarts.  Hermione and Septima disabuse him of the fear that he might be anything like, and further, Hermione encourages him to befriend  because she might suffer from those who believe the same of her.
 * Incendiary Exponent: While at Beauxbatons, Hermione begins studying metallurgy, and for lack of any other means available to her starts using thermite to smelt metals.  The first time she tries it, though, it causes an explosion that damages a potions lab station and scares away a boy who was interested in her.
 * The Insomniac: Hermione is prone to bouts of sleeplessness as her stress level and/or workload increase.
 * "Just Joking" Justification: Possibly in play at the very end of the main story when Hermione offhandedly tells her parents she never built a magical nuke because she never found any uranium deposits rich enough.  When she sees her parents' horrified expressions she claims it was a joke -- but given everything else she had in her Bag of Holding that wasn't mentioned "on-screen" before she unpacked it in front of them, it's hard to believe it actually was a joke.
 * Kick Them While They Are Down: Hermione expresses her displeasure with Lockhart's attempt to obliviate her before they enter the Chamber of Secrets by kicking the crap out of him after Professor Vector wraps him in an Incarcerous and knocks him down.  She kicks him again, after they all get out, to punctuate her description of his actions.
 * Both she and Ginny both kick Peter Pettigrew when he admits under veritaserum to having watched them getting dressed and undressed while he was in rat form.
 * La Résistance: Hermione is already styling their side as the Resistance even before Voldemort takes over the Ministry -- and actually says "Vive la Résistance!" at the end of chapter 47 of Lady Archimedes.
 * Lampshade Hanging: In-Universe.  The Muggle professor who oversees Hermione's correspondence math courses bemusedly asks in a letter if "Vector" is really her teacher's name.
 * During the second task of the Tri-Wizard Tournament Hermione and other watchers present on the lake shore comment on how there actually isn't anything to watch. (Hermione being Hermione, she comes up with a way to send a set of Omnioculars after the champions.)
 * Laser-Guided Cat: At the end of her third year, Hermione invents a spell to generate a (weak) laser.  Although she tries to explain the value of lasers to her roommates, the first thing she does with it is entertain Crookshanks and her roommate's cat Wendelin.
 * Lensman Arms Race: In 2012, Hermione discovers one between the Wizarding World's efforts to hide itself and muggle surveillance/computer technology that the wizards are doomed to lose.  The best case she can work out is the utter collapse of the International Statute of Secrecy by 2030.  Worst case... it should have already happened.  Publishing her findings gets her in a world of trouble.
 * Lethal Harmless Powers: Among the other truly frightening things Hermione does with arithmancy, she combines a simple "punch" spell with a simple "timer" spell to create an equally simple spell that stops a person's heart.  (And the fact that it is no more "dark" than a bludgeoning curse is even more unnerving to those who look at its design.)
 * Light Is Good: An explicit equivalence made in the story, born from canon usage, but taken Up to Eleven with the entire field of light magic Hermione creates from first principles to oppose various dark magics.
 * Life Energy: The ritual Hermione develops to kill Dementors and free the souls they've consumed drains all the life energy out of the area in which it's cast, leaving it a permanently dead zone that will never support life again.
 * Literal Metaphor: When recounting to her parents the events at the end of the Tri-Wizard Tournament, Hermione tells them
 * Loophole Abuse: Hermione gets quite good at this.
 * She gets past Vector's encryption-based trap guarding the Philosopher's Stone by way of two loopholes -- one, figuring out how to reset the trap to a "start" condition, and two, realizing that while the trap never started with a seed value under 10000 for its calculations, it didn't reject one, either, so she restarted it with a seed value that she could factor in her head, then acted as a man-in-the-middle attack.
 * They later discover that Quirrell simply brute-forced his way through by hitting the guards' "sensors" with a color-blindness spell -- exploiting a different loophole.
 * She later follows up on a hunch and gets McGonnagall to confirm that the Underage Magic detectors only register wand magic (so as not to inconvenience Pureblood families who have lots of device magic and magical toys around the house), and then creates rune clusters (which are pre-charged to cast spells) for both Harry and herself to take home for the summer break.
 * When she discovers the existence of toy wands that do not register on the Trace, she learns enough wandlore to start making her own to use to keep in practice over the summer and holidays -- and to later use as holdouts. (And she keeps on learning wandlore, impressing even Ollivander.)
 * She gets around several of Umbridge's "Educational Decrees" by changing the terms or context in which she does something that would otherwise be forbidden. Umbridge is constantly playing "catch-up" to her.
 * In general, every time Hermione learns of a loophole that the Purebloods have had written into the restrictions on underage magic, it leads her to something she can study and exploit even better than they can.
 * George actually comments (approvingly) on her ability to exploit loopholes in chapter 34 of Lady Archimedes.
 * Mad Mathematician: Averted, although after seeing some of the things that Hermione comes up with before she even takes her OWLs, some people aren't so sure.  And Septima jokes about going mad from exposure to Muggle higher maths.
 * Magic Knight: Hermione, by the end of Lady Archimedes.  Magitek armor, buckler and sword, magical rifle, innovator of terrifying spells, able to go toe-to-toe with Bellatrix LeStrange and win...  yeah.
 * Magical Defibrillator: Literally.  Hermione develops a spell specifically to act as a defibrillator, after she develops a spell that stops the target's heart.
 * Magical Incantation: The number of syllables in an incantation and their stresses/rhythm are dictated by the mathematics of the spell, and the words can be in almost any language as long as they describe the spell's function in some way.  Hermione creates spells in Dog Latin, real Latin, Spanish, Swedish, Greek and several other languages (even plain English!), and in one case improvises a color change spell in a pinch by solving the math in her head and then coming up with an appropriate Dog Latin phrase that matches the number and pattern of syllables it calls for.  She also turns the Latin terms for several medical conditions into incantations that inflict those conditions on a target.
 * Given the appropriateness of certain pre-existing phrases (such as those medical terms) to the spells she casts with them, one suspects she designs the spells from the start to use them.
 * Magitek: Born from her efforts to help Harry survive the Tri-Wizard Tournament, Hermione figures out how to magically extract raw elements from soil and rock, and begins teaching herself metallurgy and a very idiosyncratic form of smithing and metalcraft.  She then comes up with a way to grow carbon nanotubes with magic.  By sixth year she's wielding an enchanted tungsten-and-nanotube sword, carrying a nanotube shield and wearing nanotube armor.  And that's just the beginning... by seventh year she's creating hybrid magical-technological guns capable of fully-automatic fire, and hand grenades containing both magical and mundane attacks.
 * At one point in Lady Archimedes, Hermione admits to fantasizing about turning part of Antarctica into a magitech-powered Utopia for Muggle-borns.
 * Magnetic Weapons: By January of her fifth year, Hermione designs and builds a fully-magical (no magnetism involved) rail gun.  This is initially just to test the bullet resistance of her basilisk-skin coat, but she eventually improved it for the sake of seeing what she could do.
 * The Maiden Name Debate: When she and George get engaged before the Battle for Hogwarts, Hermione informs him that she will be keeping her maiden name, because it's almost impossible to transfer all her papers and credits to a new last name.
 * Mathematics: Hermione's stock in trade.  At age 11, she is already literally years ahead of the 13-year-olds starting Arithmancy with her.
 * Professor Vector openly admits that Muggle mathematics and the teaching thereof are superior to Wizarding.
 * Metaphorically True: In Annals of Arithmancy chapter 15, George and Hermione can't tell their muggle surveyor that they want their house built in a particular spot because it'll be sitting on top of a ley line intersection, so they tell him it's because the location has good feng shui.
 * Mindlink Mates:
 * Misfit Mobilization Moment: Dumbledore's Army and the Order of the Phoenix both stop hiding and turn out to be very effective when Hermione calls them to the defense of Hogwarts.
 * Mistaken for Terrorists: When Voldemort and the Death Eaters take over the Ministry, they not only pursue Harry and Hermione in the Wizarding world, they arrange to have them branded as IRA terrorists in the Muggle world as well.
 * The Mole: Percy Weasley eventually became this in the Ministry under Voldemort.  But when he returns to his family with evidence for Muggle relocation camps, he outs himself and doesn't risk returning.
 * Monumental Damage: The Battle for Hogwarts results in a lot of damage and destruction to the castle, starting with bridges and causeways blown up by the defenders to deny their use to Voldemort's forces, and ending with the fall of the Astronomy Tower caused by the .  In the immediate aftermath of the Battle, Professor McGonagall declares the castle uninhabitable; it takes several months' effort to get back into a shape barely acceptable for the fall semester.
 * More Deadly Than the Male: Ron quotes the Trope Namer at one point to describe Hermione.
 * Mouse World: The House Elf quarters above the Great Hall.
 * Muggles Do It Better: After a couple years' worth of work, Hermione makes her own version of the Marauder's Map -- and applies GUI principles to its design in order make it more powerful and easier to use than the original.
 * The mission to shield the world anchor stones at the South Pole to keep them from disrupting the Muggle science station's experiments would not have succeeded without some key ideas that the scientists stationed there (and read into the existence of magic) came up with.
 * Mundane Solution: This could be seen as one of the themes of the story, as both heroes and villains come up with simple solutions to problems that can't be solved with magic.
 * Quirrell steals the Mirror of Erised and drags it all the way to the Hogwarts boathouse instead of standing around trying to figure out how to get the Philosopher's Stone out of it.
 * Hermione reasons that if you can't see the basilisk's eyes, you can't be affected by them, and creates sunglasses of the precise hue needed to block them from sight. Her first try reduces the killing gaze to a knockout that lasts a couple hours; her second reduces it to a headache.
 * Magical shields defend against most magical attacks, but are either vulnerable or transparent to physical attacks. So Hermione builds a Magitek gun for herself to take down those shields and then punch big holes in the Death Eater behind them.
 * Household spider-extermination spells work on Acromantulas.
 * Mushroom Samba: The practical result of staying awake for three days in a row, aided by Pepper-Up potions, to make sure Harry can survive the first task of the Tri-Wizard Tournament.  Hermione's not exactly hallucinating by the end, but she's not entirely in control of herself, either...
 * Hermione is prone to overwork and sleep deprivation, and it always results in a state of altered consciousness where her judgment is severely impaired and her impulsiveness and temper are both enhanced.
 * My God, What Am I Doing?: Hermione's frequent reaction when she finds herself developing very dark and/or disturbing curses during the first few months in the Nottingham base.
 * Mythology Gag: Multiple.  A few examples:
 * Her first impression of Quirrell is that he "couldn't fight off a band of pixies".
 * Percy Weasley boasts of taking 12 OWLS but gets evasive when she asks how he can do this when it's only possible to take 10, suggesting he's using a time-turner. (And likewise his brother Bill before him.)  Since Hermione never needs a time-turner herself in this story, she remains forever puzzled how Percy managed it.
 * In a letter she sends to her parents after the troll incident in first year, Hermione uses statistics and what little actuarial knowledge she has to to reassure them that it was not only a fluke but that Hogwarts is demonstrably safer than a Muggle school. Then she adds

""Well, I heard that she broke into Gringotts, stole a dragon, and rode it into battle!""
 * Dobby throws a dagger at Bellatrix during the escape from Malfoy Manor.
 * "NOT MY BROTHER, YOU BITCH!"
 * In chapter 24 Annals of Arithmancy, a compartment full of Hogwarts students on the Express trade stories about Hermione in the presence of her daughter Emmy. The only story that didn't happen (and that Emmy objects to) is one that echoes an event from Deathly Hallows:

"The next morning, they walked out onto the stage, and the world changed."
 * Nature Documentary: One of the first things Hermione films with a "Mementoscope" (in AA14) is Neville finding and harvesting a magical plant in British Columbia.
 * The Nineties: The setting for The Arithmancer and Lady Archimedes, and Pixelwriter1 pays attention to what was going on in the "real world"; it sometimes intersects with the Wizarding World action.  The first nine  chapters of Annals of Arithmancy also take place in this period.
 * No Export for You: Averted with a Slovak translation by "Moon-sora", to be found at www.sanguis.cz under the username "Stellar".
 * Non Sequitur Thud: Penelope Clearwater says "did anyone get the number of that truck?" after waking up from being knocked out by the basilisk's gaze through sunglasses designed to filter it out.
 * Hermione's "I have to go to sleep" immediately before passing out at the party after the first task of the Tri-Wizard Tournament probably counts.
 * Noodle Incident: "Uncle Jack's second wedding", which Hermione seems to use as a benchmark for disastrous weddings.
 * And Aberforth Dumbledore references the canon "goat incident" as a reason why no one would accept him as the new Minister for Magic.
 * Norse Mythology: The goblins are very strongly implied to be the dwarves of Norse myth.
 * The Nose Knows: House-Elves have profoundly sensitive noses, and are able to identify and track individuals by their scents.  The Hogwarts elves also use this to match laundry up with its owners -- after it's been washed.
 * Not His Sled: Because of perturbations caused by the change in Hermione's path through her years at Hogwarts, the course and climax of each year is different from canon, growing from small(ish) to majorly so.
 * "Not Making This Up" Disclaimer: When she mentions to Vector at one point that she is worried about accidentally creating Antimatter by applying her advanced math theories to transfiguration and consequently blowing up the castle, Hermione has to explain to her that no, she wasn't joking, and yes, antimatter is a real thing.  Later she has to make the same assurances to her parents in a letter.
 * Nothing Is the Same Anymore: Annals of Arithmancy ends on the revocation of the Statute of Secrecy and the revelation of the magical world to the non-magical one:

""So on a scale of one to whatever it was you did to Umbridge, how horrifying is this going to be?" George said. Hermione looked over the rune setup one last time. "I'd say somewhere between Inferius and what Filch and Mrs. Norris get up to in their spare time," she replied."
 * Now What?: After the Battle for Hogwarts, there's a good chapter's worth of Hermione, Harry, and other survivors wondering what the next step is now that Voldemort is defeated, and who should lead the Ministry.
 * Off with His Head: Late in Lady Archimedes Hermione decapitates Fenrir Greyback with her enchanted tungsten and carbon nanotube sword.
 * Oh Crap: Vector's reaction to the combined revelation that a) Antimatter is a real and dangerous thing and b) Hermione is concerned about her researches making it possible to transfigure some into existence.
 * Oh God, with the Verbing!: During the excursion into the Chamber of Secrets, Hermione expresses her displeasure with Gilderoy Lockhart by kicking the crap out of him.  When she does it some more after they reach the infirmary, he complains, "Again with the kicking?"
 * Older Than They Look: Hermione thinks Dobby looks middle-aged, and that only because of his mistreatment by the Malfoys; it turns out he's almost seventy years old and has worked for three generations of Malfoys.
 * On a Scale From One To Ten/Broke the Rating Scale: A type B of the former and a mixed type 2/3 for the latter can be found in this passage from chapter 73 of Lady Archimedes:


 * One-Dimensional Thinking: Averted by both Hermione and Bellatrix Lestrange when the Astronomy Tower comes down on top of them.
 * One of the Seven Signs of the Apocalypse: When Argus Filch goes about smiling and happy the morning after Hermione shows him how to brew potions with her rune clusters, the Weasley twins pronounce it a "sign of the apocalypse".
 * Fred and George again go on about signs of the apocalypse early in third year, after a Quidditch practice generates no criticism from Oliver Wood.
 * One of Us: Hermione, who is an avid fan of fantasy and science-fiction and frequently compares concepts, creatures and objects she encounters in the Wizarding world to things she's seen in books and movies. She's also constantly quoting F&SF works even though the magicals around her have no idea what she's referring to, and she names the artifacts she creates after ideas, things and even just words from such works. (See the simply massive Shout-Out list over on Trivia page.)
 * Her father is clearly responsible for her tastes, as he catches her references and makes his own back at her.
 * In-Universe implementation: When Hermione enlists Lavender and Parvati to help her give Hagrid a makeover for the Yule Ball in fourth year, and demonstrates that she has hair-styling charms to contribute to the effort, Lav and Parv hug her and shriek, "One of us!  One of us!"
 * The One Thing I Don't Hate About You: When Hermione has a paper published in a potions journal in her second year, Snape grudgingly gives 10 points to Gryffindor and allows that he would be willing to mentor her in advanced potions studies should she wish to pursue them.  He admits to "professional admiration" as the reason.  It doesn't stop him from still being a Jerkass to her, even from his painting after he's dead.
 * Open-Heart Dentistry/Meatgrinder Surgery: When Bill Weasley is seriously injured while rescuing Luna Lovegood from Malfoy Manor, and they can't risk taking him to St. Mungo's, Hermione is forced to try a blend of Muggle surgery and magical healing to save his life.  It doesn't quite fix him up, but it lets him last long enough for them to get him to a Muggle hospital.
 * Open-Minded Parents: The Grangers are surprisingly reasonable about Hermione's being part of Wizarding Britain, and even when they insist on transferring her to Beauxbatons only do so after great provocation and for entirely good reasons.  This is helped by the fact that Hermione is far more dedicated and sincere about keeping her parents informed about her life in the magical world than her canon counterpart ever appeared to be.
 * Opposite Gender Clone: Along with other manipulations, this is part of Hermione's plan to preserve and expand the giant population in Annals of Arithmancy, once she gets enough genetic samples.
 * Our Ghosts Are Different: See Fate Worse Than Death, above.
 * Our Souls Are Different: Or at least different perspectives on them show different properties and behaviors, not unlike the quantum mechanical "observer effect". Hermione initially has problems with her "soul detection" spell because she uses a Hindu framework and terminology in an attempt to see what amounts to the Christian ideal of the soul as defined/confused by translations into English from the original Greek (which used two different words for two different concepts, that are both translated into the same word in English).  She ultimately has to investigate not only the Greek but the original ancient Jewish writings as well as talk to Padma and Parvati about their religion in order to figure out why she's not getting the results she expects.
 * Over 9000: In what may be a Shout-Out, this is Hermione's estimate of the number of floating candles in the Great Hall during her Sorting.
 * Percussive Maintenance: Hermione stops Fleur's post-partum bleeding with a dark spell she reverse-engineered after seeing a Death Eater cast it, and explicitly compares its use to "fixing your telly by kicking it".
 * Percussive Therapy: Hermione resorts to this as stress relief in the Room of Requirement, starting in fifth year when Umbridge targets her.
 * Pet the Dog: Hermione chooses Filch as one of her test subjects for her potions research in second year in part because she thinks it will help him.
 * Plagiarism: Dolores Umbridge accuses Hermione of stealing her work from pureblood wizards like her collaborators Professor Vector and Rebecca Gamp.
 * The Power of Blood: Symbolically invoked with Hermione's efforts to get blood samples from all living giants in chapter 10 of Annals of Arithmancy, with which she hopes cloning technology can be used to rescue the species.
 * Powder Keg Crowd: Pretty much all of the (non-Slytherin) Hogwarts student body by the end of fifth year, but the D.A. most of all.  Umbridge sets them off when she tries to stop Septima (and others) from going to Harry and Hermione's aid at the Ministry of Magic, resulting in a (brief) battle that ends Neville Longbottom blasting Umbridge across the great hall with a Bombarda spell after she Crucios Luna.
 * Precision F-Strike: The first time Hermione swears in the story, when she realizes what to do about Riddle's diary, she shouts, "Not today, you son of a bitch!"
 * Primal Scene: Hermione compares  to something so private and intimate that it shouldn't be seen by others, and explicitly uses walking in on one's parents playing bondage games in bed as a comparison.
 * Pull the Thread: Hermione does this several times for "common knowledge" in the Wizarding World, starting with the accepted story of Sirius Black's betrayal of the Potters (at which time the trope is referenced by name).  She usually finds things unraveling into something completely different, although not always very quickly.
 * Putting on My Thinking Cap: Once they remove the horcrux from it, Hermione makes frequent (sometimes constant) use of Ravenclaw's Diadem to clarify and speed up her thinking.
 * Race Against the Clock: When the operation to retrieve Hufflepuff's cup results in the very visible death of Nagini, Voldemort decides to move on Hogwarts to check on the state of Ravenclaw's diadem (which was retrieved and de-horcruxed without his knowledge long before).  This forces Hermione to start  at Hogwarts' Anchor Stones immediately, while the Order of the Phoenix and Dumbledore's Army defend the castle from the attacking forces long enough to let her complete the ritual.
 * As in canon, Voldemort gives the defenders an hour to hand over Harry Potter, but it's just an excuse for his forces to rest and regain their strength after their initial failed attempt to bring down Hogwarts' defenses tires them out.
 * Rape Is a Special Kind of Evil: Barty Crouch Jr. is shown to be a Complete Monster when it's revealed that he's kept Bertha Jorkins as an Imperiused Sex Slave for four years, repeatedly raping her and eventually fathering a child on her.
 * Razor Floss: Hermione adapts her carbon nanotube synthesis spell into something that can create spools of carbon nanowire, and teaches it to Harry.  It saves their lives when they go after the locket horcrux in Voldemort's cave-o'-inferi.
 * Reading the Enemy's Mail: Umbridge does this to all mail leaving and coming into Hogwarts while she's the High Inquisitor.  Worse, she has the mail altered in both directions to conceal what she's doing from recipients outside Hogwarts, and to coax students into incriminating themselves when writing to family.
 * Reality Ensues: Might be seen as a theme of the story; many of the differences from canon happen simply because one or more characters ask or do something reasonable that never seems to occur to anyone in canon, and they keep on being common-sense about it.
 * An example -- one change is that (due to her childhood) Hermione doesn't want to lose her connection with her parents even as she enters a new world they can't really be part of, so she writes them more often than we ever see in canon and keeps them far better informed about her life in the Wizarding world -- even of the bad things that happen, which leads them to grow increasingly disillusioned with the reassurances that Hogwarts' staff give them about student safety. Consequently, when things get too bad in third year, they transfer her to Beauxbatons for her fourth year, and would rather she not go back to Hogwarts in subsequent years.
 * Even the aftermath of victory is touched by this trope -- things like restarting the Ministry and clearing Harry and Hermione of the accusation of being IRA terrorists take time and effort. And dozens if not hundreds of Voldemort's army manage to get away.
 * Reasonable Authority Figure: Professor Vector.  And the respect Hermione subsequently has for her helps keep Harry and Ron from writing off Slytherins entirely, resulting in (among other things) several Slytherin members in the D.A.
 * Red Eyes, Take Warning: According to Bill, Hermione's eyes were blinking back and forth between brown and red while fighting off the locket horcrux's attempt to possess her.
 * The same flickering happens to Harry when the first attempt to get rid of the horcrux in him doesn't quite succeed, and wakes it up.
 * Ripped from the Headlines: Numerous "real-world" events and cultural trends from the period during which the story takes place have small and large affects on the plot.  One of the most prominent is Comet Hale-Bopp and the Heaven's Gate cult.
 * In chapter 15 of Annals of Arithmancy, Hermione and George (and many other Weasleys) help with the aftermath of the 2004 Indian Ocean earthquake and tsunami. And they also respond to the July 2005 bombings.
 * And a few years later they are part of the rescue teams after the Haitian earthquake of 2010.
 * Ritual Magic: Where Hermione's researches and advanced Arithmantic work inevitably leads her.  She eventually develops rituals to  and to kill.
 * Rooftop Confrontation: Between Hermione and Bellatrix Lestrange, during their fight at the Battle of Hogwarts.  It's nowhere as easy as the movies make it out to be, something that Hermione muses on ruefully as she gathers scrapes and tears sliding down the roof.
 * Room Full of Crazy: Hermione's loft in the Nottingham factory/base starts looking like a mathematical version of this, being lined with blackboards covered with arithmantic calculations from multiple parallel projects she has in motion.
 * Rules Lawyer/Exact Words: Hermione notes that House Elves seem quite skilled at finding interpretations of their instructions that still let them do what they want. She gets very good at it herself in order to get around some of the more restrictive orders her parents give Dobby regarding her safety.
 * This later serves her well against Umbridge, as Hermione finds loopholes in and interpretations of her decrees that she then exploits to thwart and infuriate her.
 * Running Gag: Hermione hexing Voldemort in the face in a crisis, and then freaking over it much later.
 * An In-Universe running gag develops when the Weasley Twins start demanding Hermione say something only she would say just to make her spout off a few sentences of higher math.
 * Sadist Teacher: Snape and Umbridge as in canon, of course, but this fic takes Umbridge Up to Eleven:  when Hermione has her own detentions with Umbridge and her quill, Umbridge's reactions suggest to Hermione that she's a sexual sadist and is aroused by Hermione being forced to harm herself.
 * Schoolgirl Lesbians: It's never explicitly described so (beyond an off-handed indication that Sally-Anne sleeps in Lily's bed), but Hermione's roommates Lily Moon and Sally-Anne Perks effectively come out when they go to the Yule Ball together in fourth year.  They have a particularly bad falling-out over Harry and Dumbledore's claims that Voldemort is back a year later, then reconcile at the end of fifth year.
 * Send in the Clones: Hermione proposes getting tissue samples from as many giants as possible, in the hopes of cloning them to keep them from dying out.
 * Servant Race: The house elves, who were created to be servants from Uplifted Animals rather than enslaved, as is generally assumed in Potter fic (and canon).
 * Shame If Something Happened: While trying to break Hermione in Lady Archimedes, Umbridge explicitly threatens to expel her if she doesn't cooperate with her own torture, then immediately have her parents dragged in front of the Wizengamot for her subsequent truancy, and strongly implies they will be thrown into Azkaban.
 * Hermione's therapist mentions early in Annals of Arithmancy that she was threatened by "men in black" if she didn't stop being vocal about how it was impossible (in her professional opinion) for Hermione to be an IRA terrorist.
 * She Cleans Up Nicely/She's All Grown Up: The combination of her hair-management spells plus getting her teeth magically fixed during the summer between third and fourth year has even more of an impact on Hermione's looks than her canon changes did, and she stuns virtually everyone when they meet up again for the World Cup.  They also improve her self-confidence noticeably.
 * Shell-Shocked Veteran: Hermione starts showing symptoms of PTSD starting in the summer after her first year.  She tends to have nightmares for a while after any particularly traumatic event, such as her torture at the hands of Bellatrix Lestrange in Lady Archimedes.
 * In chapter 7 of Annals of Arithmancy she unexpectedly discovers she suffers from flashbacks to the Battle for Hogwarts during her Defense NEWT exam.
 * Hermione is once again on a hair-trigger for some months after Barty Crouch is captured in chapter 12 of AA.
 * Shown Their Work: The author has done their research -- all the advanced mathematics Hermione employs during this fic is the real thing.  And Hermione herself is based on genuine mathematical child prodigies.
 * Shrouded in Myth: To her annoyance, Hermione starts being affected by this trope by the end of her second year.  And after she engineers the defeat of Voldemort and kills Bellatrix Lestrange in an incredibly terrifying manner, she's regarded as possibly the most powerful person in Wizarding Britain; certainly one of the scariest.  It seems that one of the reasons she works at the Twins' joke shop in Annals of Arithmancy is to show people she's not this impersonal, implacable force of magic, but a regular person.
 * By the time her daughter Emmy is a first-year student in 2019, Hermione is literally a figure of myth, with the students in Emmy's compartment on the Hogwarts Express sharing "Hermione Granger stories", almost all of which are true.
 * Sinister Surveillance: During year five, Umbridge (or her agents) are actively reading and altering every piece of mail going in or out of Hogwarts, looking for "sedition" and censoring anything they don't want getting out to the public at large about what's going on in the school.  They are either very sloppy or there's just too much mail for them to keep track of all the conversational threads, because an oddly-phrased and somewhat inappropriate comment in a letter back from her parents clues Hermione in that something's going on.
 * Smart People Play Chess: Both Ron and Hermione are chess prodigies.  Ron is just a bit better than she is.
 * Sniper Rifle: At the Battle for Hogwarts, Hermione quickly creates a Magitek sniper rifle with seven shots based on her earlier magical gun designs and gives it to Justin Finch-Fletchly to take long-distance shots at Voldemort.
 * Soapbox Sadie: Hermione is slightly more given to furious lectures about right and wrong in this story than she is in canon, at least during the first few years.  At the same time she finds out more about her subjects, so her lectures are usually fact-based, and in some cases, her canon rants don't happen because she's better informed about their subjects.
 * Socialist Realism: In chapter 61 of Lady Archimedes Hermione notices that the new statue in the Ministry that replaced the "Statue of Magical Brethren" partakes strongly of Soviet-style art; in fact, she notes with some confusion that despite espousing a right-wing ideology and policies strongly backed by the upper classes, the Death Eaters seem to prefer Soviet-style methods and symbolism.
 * Something Only They Would Say: When Hermione storms into Hogwarts right before the second Task and tells Harry to cut a class to work with her, the Twins (tongue-in-cheek) suggest she's an impostor and demand that she say something only the real Hermione would say.  (She rolls her eyes and spouts off a few sentences of higher math, to which they respond "False alarm!"  Later, challenging her just to get a brief recitation of math becomes a Running Gag for the Twins.)
 * She later does the same thing any time anyone challenges her to prove her identity.
 * Sorcerer's Apprentice Plot: Hermione has a minor meltdown in seventh year when she realizes that the potential for a magical Grey Goo disaster exists after she has a nightmare which employs this trope.
 * Spared by the Adaptation:
 * Speculative Fiction: Hermione is explicitly a fan of SF and Fantasy, one of the things that sets her apart from the other children before she gets her Hogwarts letter.
 * Spell My Name with a "The": By fourth year, people are referring to Hermione as "The Arithmancer", with Audible Capital Letters.
 * Spirited Young Lady: Sonya/Sonnitt is the House Elf version of a rebellious teenager, at least at the start of the story.  As she matures she still remains quite unconventional, for example musing longingly on the loss of chances for adventure when Hermione withdraws from Hogwarts at Christmas break in her fifth year.
 * The Stations of the Canon: While some of the Stations don't get visited simply because the story is almost entirely from Hermione's point of view and she wasn't there for them, and others are perturbed entirely out of existence, a few do show up.  However, as befits a good Alternate Universe where For Want of a Nail is in play, the only Stations visited are the ones that the changes in Hermione cannot possibly affect (such Dobby's entry into the story, the Tri-Wizard Tournament, or the Prophecy and its results) or those which are too close to the point of divergence and haven't been perturbed enough to not happen (most of First Year).  The further into the story you go, though, the larger the differences get and the fewer Stations appear "on schedule" or in any recognizable form.
 * Steampunk: Hermione explicitly uses this term to describe the styling of her "bottled sunlight" Death Ray.
 * The Stinger: In what is basically an epilogue to the primary story, Hermione discovers the secret of Voldemort's mysterious power of flight: a Flying Carpet neatly tailored into a set of robes.
 * Stockholm Syndrome: Hermione compares aspects of the house-elf mindset to this.
 * Stranger in a Familiar Land: What happens to most Muggle-borns after spending too much time in the magical world.  Hermione works hard to avert this trope for herself personally.
 * Strawman Fallacy: Early in fifth year, Hermione points out that the arguments presented by Slinkhard in the defense text Umbridge uses are built entirely on this fallacy.  This does not endear her to Umbridge.
 * Stuff Blowing Up: Arithmancy + soil chemistry + dragon = instant unconscious dragon. Good thing there were shields protecting the audience...
 * By seventh year, Hermione's using rituals and alchemy to create C4, nitrocellulose, chlorine trifluoride... Learning this, the Weasley Twins celebrate finally having corrupted her completely.
 * Super Window Jump: Hermione performs one through a Hogwarts window as part of her running fight with Bellatrix Lestrange during the Battle of Hogwarts.
 * Swiss Army Superpower: Arithmancy becomes this in Hermione's hands, when combined with advanced Muggle mathematics and basic Muggle science.  She uses it to create explosives, nanofabricate weapons and armor, create gems and jewelry, and.
 * Swiss Bank Account: Hermione opens a "numbers only" account at Gringotts for her jewelry business.  She is assigned vault number 1337.
 * Tainted Veins: As one of the prices paid during the ritual, a Necrotising curse taken by Professor Babbling becomes blood-borne and turns her veins black before it kills her.
 * Take Our Word for It: Used almost word-for-word by Hermione while trying to convince Bill Weasley of the existence of continental drift.
 * A Taste of the Lash: Umbridge sets up a whipping post in the Great Hall and has George tied to it at the end of fifth year; Argus Filch is in the process of whipping him when Hermione storms in.
 * Teen Genius: Even more so than canon!Hermione, once she grows out of being a Child Prodigy.
 * Tempting Fate: When writing her parents to reassure them that the troll incident in first year was a one-time aberration, Hermione said, "It's not like an evil psychopath sneaks in and tries to kill somebody every year or something."  Lampshaded after the events at the end of first year when Hermione mentions that very passage while discussing what to tell her parents about that.
 * She doesn't learn from this and other experiences. As late as year six, she's still saying "It'll be easy" about dangerous missions, to the point where Harry retorts, "Don't jinx us!"
 * In Annals of Arithmancy chapter 13, Hermione idly notes that if no one's tried to make a nuclear bomb with magical methods in the last 60 years, there's no urgent need to worry about someone doing so now.
 * There Are No Therapists: Averted -- for humans.  Hermione sees one almost every summer ("a couple of times each July") to cope with the events of the previous school year.  The only exceptions are the summer after third year, and the period where she's on the run as an alleged IRA terrorist.
 * The first few chapters of Annals of Arithmancy use an 18-year-old Hermione meeting with the very same therapist as a framing device.
 * Dean Thomas mentions that he saw a therapist in the summer after the end of Lady Archimedes.
 * However, the trope is very much in play within the Wizarding World, as Hermione privately notes during chapter 3 of Annals of Arithmancy.
 * Facing Winky's slow breakdown, Hermione is annoyed to discover that house elves have no counselors or advisors among themselves to help elves in a bad state -- at least in part because elves in a bad state are usually very quickly dead.
 * Thinking Out Loud: Hermione tends to talk through her arithmancy while wearing the Diadem of Ravenclaw.  Her companions on the run don't mind, they find it entertaining if incomprehensible.
 * Third-Person Person: House elves, as in canon, tend to refer to themselves in the third person as a matter of course.  When Hermione realizes that Dobby has mostly stopped doing so, and is getting strange looks from other elves because of it, she deduces that the elves may have been deliberately conditioned into using that speech pattern by the wizards who uplifted them, as part of creating a Servant Race.
 * Throw-Away Guns:
 * This Is for Emphasis, Bitch: In Lady Archimedes chapter 29, Hermione storms into Hogwarts and finds George tied to a whipping post.  She whirls on Umbridge, saying "Get away from him, you bitch!"  Then again, this is less emphasis than simple categorization and identification.
 * And then there's "NOT MY BROTHER, YOU BITCH!" during the Battle for Hogwarts.
 * Time Skip: Annals of Arithmancy frequently skips several weeks to several months (if not longer) between scenes, unlike the day-to-day and sometimes hour-to-hour pacing of The Arithmancer and Lady Archimedes.
 * Time Travel: Putting aside the canonical time turner stuff (which actually never happens in this fic), the Hogwarts Express always arrives exactly on time, no matter how much time its passengers perceive passing.  For example, at the end of her first trip home, Hermione was concerned about the train arriving a half-hour late, only to discover that her parents saw the train arrive exactly on schedule; upon checking, they found that her watch was more than 30 minutes off compared to her parents'.
 * A far more mundane (and amusing) example appears in chapter 9 of Annals of Arithmancy. Luna arranges for herself and friends,  including Hermione, to be on Hoover Dam for local midnight on New Year's Eve 1999 -- and then steps back and forth across the dividing line between time zones there saying, "It's 1999.  It's 2000.  It's 1999.  It's 2000."
 * To the Pain:
 * Torches and Pitchforks: Harry gets run out of Hogwarts in the middle of sixth year by an angry mob of Slytherins that the faculty cannot keep under control.
 * Transgender: Hermione is surprised to learn that metamorphmagi can switch genders, although it isn't as immediate as their other changes; Remus mentions that Tonks tried being a boy for one summer when she was younger but didn't particularly like it.  (It's also why she dislikes her very feminine first name.)
 * In Annals of Arithmancy chapter 18, we learn that Tonks' 11-year-old son Sasha has been trying out being a girl on and off. Before he leaves on the Express he gets warned that he may be able to get into the girls' dorm that way, but will get expelled from it if he turns back -- as he might in his sleep.
 * Treasure Map: A pirate-style "treasure map" is inside the "egg" retrieved in the first task of the Tri-Wizard Tournament.
 * True Love's Kiss: Turns out to be the last, missing, piece of the ritual to expel the horcrux from Harry.
 * Turn of the Millennium: Starting with chapter 10, Annals of Arithmancy moves into this era.
 * Twin Telepathy: Discussed -- or at least thought about -- by Hermione in her first year after witnessing several instances between Fred and George.
 * Understatement: After being hit with the Cruciatus curse, Luna Lovegood comments, "That was most unpleasant."
 * Unfortunate Names:
 * The Unmasqued World: At the end, they abolish the statute of secrecy because it will eventually become impossible to maintain.
 * (Now they can explain where the term "eigenvector" comes from.)
 * Unreliable Narrator: Hermione in Lady Archimedes chapter 57, by Word of God (in an author's note at the beginning of chapter 58).  While the narration is not first-person, we do see most of the action through her eyes, and in this chapter she is once again sleep-deprived and yea-short of a breakdown.
 * Unspoken Plan: Many instances, leading directly to many instances of the next trope.
 * Unspoken Plan Guarantee: So prevalent that the first time we see an extended planning session -- for the raid on the Ministry in Lady Archimedes -- it rings major warning bells.
 * The ritual is subject to this.  While we see bits and pieces as it's developed and assembled, we don't find out exactly what it's supposed to do until practically the moment it's performed.
 * Uplifted Animal: Hermione uses these exact words to describe the nature of House Elves to her parents, based on what the elves at Hogwarts told her; the now-extinct "wild elves", from whom House Elves were bred, are implied to have been a species of non-sapient fae like garden gnomes, pixies and fairies.
 * Utility Belt: Alone of the House-Elves of Hogwarts, Sonya wears a toolbelt at all times.
 * Utility Magic/Mundane Utility: Hermione's first magical innovation lies somewhere in a grey area between these two tropes.  During her second year she adapts a method of storing a single spell casting in a runic design into a way for Muggles, Squibs and those who haven't mastered the spells used in advanced potions-making to brew potions requiring spells.  She submits a paper to a potions journal on the discovery, getting a publishing credit that actually earns her points -- and professional respect -- from Professor Snape.
 * Very Loosely Based on a True Story: According to Professor Rakepick in chapter 5 of Annals of Arithmancy, Indiana Jones and the Temple of Doom is actually based on a job she did as a freelance curse-breaker.  This is also a bit of a Brick Joke, since very early on in The Arithmancer, Hermione likened curse-breaking to being Indiana Jones.
 * Virtual Reality: After trying the Twins' new Daydream Charms, Hermione tells them that they've invented magical Virtual Reality.
 * Voice Changeling: Ron can impersonate voices flawlessly.
 * Voice of the Resistance: "Radio Free Britain", which is far more of a general resistance program than "Potterwatch" from canon Harry Potter.  Xenophilius Lovegood's mimeographed newsletter Liberation just as much so even though it's not a radio broadcast.
 * Vomit Indiscretion Shot: Bill, Harry and Hermione all throw up after cutting the inferi in Voldemort's cave to bits with nanowire.
 * The War on Terror: Chapter 10 of Annals of Arithmancy includes a scene with Hermione, George, Georgina, Harry and Ginny all in New York City two days after 9/11, helping with the cleanup on the magical side.
 * We All Do It Together: Harry and Ron join Hermione in driving the basilisk fang through Riddle's diary at the end of their second year.
 * Weekly World News: One of the three publications Umbridge bans in the wake of the Quibbler interview.  (The third is Playwizard.)
 * Weld the Lock: Hermione's Door-Sealing spell Lokutharmeth literally does this, welding the lock and hinges together and fusing the entire door to its frame, turning it essentially into a wall and making it immune to door-opening spells.
 * What the Hell, Hero?: Hermione delivers a blistering speech to Dumbledore after she learns that Order of the Phoenix member Sturgis Podmore was given the Kiss by a Dementor during the escape of Death Eaters from Azkaban in year five, essentially accusing him of playing fast and loose with the lives (and souls) of Order members.  Subverted, though, in that Dumbledore carefully explains why things played out the way they did, and Hermione is forced to agree with at least some of his reasons -- although she never entirely trusts him (or rather, his decisions) again.
 * White Magic: As a result of needing to find ways to destroy horcruxes, remove the horcrux in Harry, and kill dementors, Hermione essentially creates an entire school of Light magic to oppose dark magic, starting with little more than the Patronus charm.  Ironically, much of it is born from Hermione's study of the darkest magics.
 * Witch Packing Heat: Hermione creates a Magitek machine gun, and uses it to kill Augustus Rookwood when Voldemort and the Death Eaters attack the group retrieving Hufflepuff's cup.  And she's got a similarly Magitek revolver as a hold-out weapon during the Battle for Hogwarts.
 * Workaholic: Hermione is prone to starting work on a project, and simply not stopping, even for sleep, meals or boyfriend.
 * Xenafication: Somehow being a math prodigy inevitably leads to Hermione being the most dangerous person in Wizarding Britain.
 * You Are Better Than You Think You Are: The central thesis of Hermione's side of a very loud argument she has with Ron near the end of their second year, where she points out that everyone in his family is exceptional at something, him included, and she can't figure out why he wants to believe he isn't.  She eventually gets her point across to him.  This argument results in both Harry and Ron taking harder courses in their third year than they do in canon, because she convinced them that they were more than capable of it, and might even enjoy them.  Which they do.