#induced geometry

[aviancataclysm]

said i'd be working on X but secretly practicing VeritY instead (it's the most doable medium demon for me rn from vibes since it feels easier to get consistent than HeLL, will just take more atts than easy demons............. aside from B we do NOT talk about B) although what the HELL IS THAT SHIP/UFO DUAL???? AT THE VERY END TOO????????? my worst skill is dual if we don't count swing so this is going to be FUN

[apolaskiart]

Frost and Gricko's tattoos for the iasuw au! Moving on to the kinda complex designs that made me have a bit of a crisis (legit), these ones are just as fun to make but relatively challenging to the previous one in terms of "what do I even put?".

I'll be yapping on my thoughts/headcannons regarding these below, so feel free to dive in! A warning that it is quite lengthy because of said crises-induced reflecting session (a proud citizen of yap city indeed)

First off, we have to talk about the technicalities of Frost's tattoos. It actually put me in a crisis when making this because the first question that came to mind when finding inspo was was "how the hell do you put tattoos on a tiger?"

Aside from the issue of tattooing onto fur, there is the presence of stripes that make it difficult to create a design in the first place. So for this a.u's sake (and my well being) we can treat fur like skin where tattoos can easily be applied and expressed, but would have a shorter lifespan, aka fade quicker, as a con so retouching would be more often. It can also overlap the patterns of the natural fur if designed as such (as I did with Frost).

With this, characters who have fur (e.g. Jornir) could possibly be given tattoos designs in the future while side stepping the technical issues to avoid putting to much focus on it. This could apply to other characters who may have leathery or feathery skin types.

Now of to the designing part. Unlike Gideon and Torbek, the aesthetic/style of the tattoo was not apparent at first and took a bit of a backseat to the actual design elements for Frost. Originally, using a purely geometrical style did not feel satisfying. After revisiting his canon for some ideas, an illustrative style was added to contrast the geometry which then seemingly worked out.

"Frost's design is built mostly of geometry (circles, squares and triangles) to reflect the motion of balance between familiarity and change, logic and unpredictability, comfort and discovery. Strict in pattern and position, most are simple as to take into account the stripes of his fur.

"The only complicated design, a dragon circling a tower and followed by a koi fish, was inspired by the legend of a koi travelling an upstream waterfall to turn into a dragon, signifying strength and perseverance. It is also a sign, that behind a rigid demeanor is a fiery passion waiting to be unleashed." -> The connected yarn was to give the idea that Frost can weave this path of his, but a connection as well to my other hc that it is his main reminder of his home in Yulong.

Things also mostly come in eight (resembles infinity as well as signs for wealth and success)! It was quite fun determining how to add this in as well :D

For the actual main inspo, IVE's "HEYA" has been on the forefront. Combined with another inspired by the phrase "When tigers used to smoke…" (which is the literary equivalent of "once upon a time…" and what has "once upon a…" in their name?), I must say that culture took the reigns in directing Frost's design and imho I would say that, compared to others, his was more appropriate to have strong semblances of his home as a remembrance (e.g. yarn, temple) during his travels.

Also I used a green coloring scheme because literally all other colors did not look as good as i intended. Fate really wanted him to have a green-orange scheme.

Now we got Frost out of the way, its Gricko's turn! Despite being challenging as well, Gricko's design had assistance from punk/heavy metal aesthetics. Though the only idea that I really had mostly was the logo of different band names

I will gladly argue on why Gricko's college band name should be "Goblin Deez..." Imagine, you can say nuts if you are being funny or hands if you want a fight. Anything really, which is liberating at its finest.

From here though, the main idea really that bloomed after this was that most of his tattoos were going to be personal too him!

"Aside from the egregious tattoo of his band name, the tattoos all over him speak of his journey. A pinup of a lady troll and a crown from the hit tv series game of chairs, for his childhood dreams of being a king and bagging a hot troll. A scale and guitar for his college pol. sci days. Others speaking of his collected hobbies and knick- knacks throughout a particularly challenging adulthood. Yet on his chest is his most cherished, his center and everything, which is none other than Hootsie."

The covered half sleeve tattoos on his arm ? That's to cover up the name of his exes (Headcanon that Gricko was just as much a womanizer as Gideon, but mostly in his college to early adult life. He slowed down once Hootsie entered the picture). Also its just more badass looking with designs of the monsters his canon self uses lol.

ALSO ALSO PAINTED NAILS, I'LL ARGUE WITH THE WHOLE COURT ROOM THAT HE AND HOOTSIE PAINT EACH OTHERS NAILS AS A HC!!!!

End of yapping session. Meeting adjourned!

[bogleech]

All my life I’ve been unable to understanding finding an animal “gross” just for its natural appearance and I still can’t accept that anybody really means it. “Gross” is something an animal might DO or a condition it might be in, like when a dog rolls around in roadkill, right? I can get finding some animals “scary” for how they look or how they move, but....gross? Like an insect, all by itself, is some sort of unclean filthy gag-inducing “gross” to some people? How? What??? You’re saying there are basically unsanitary SHAPES? Specifically for animals? A creature can have a geometry that makes some people nauseated?

Or is it like some people have difficulty contextualizing insects or worms as individual animals and instead hold them in the same mental category as almost like a “substance” or a “texture,” like living “dirt?” Is THAT what it is?

[your-yandere-bestfriend]

　　　　　ₓ˚. ୭ ˚○◦˚.Wet dreams.˚◦○˚ ୧ .˚ₓ

Todoroki Shoto

Based off the song Wet Dreamz by J. Cole.

(Guys do I drop this after a 2 year hiatus or no )

。。。 Though it was the second day of school already, there had already been talk of a new student—most likely gossip overheard from the U.A. staff. Typically a new student wasn’t of much appeal, this was a huge school after all, even though it was prestigious, but what made the U.A. students so chatty about this new student was the fact that she was a foreigner. There had only even been three American students in the long history of U.A. high school, so getting a transfer was not only impressive, due to the fact that she wasn’t required to participate in the entrance exams, and also exciting.

The bell chimed for second blocks end, and next for the students of class 3.A., was the drowse inducing subject. Math. The teachers filtered out in order to teach their proper subject, after all just because this was a hero school didn’t mean that they were excused from engaging in normal, more uneventful subjects. Todoroki sat with perfect posture in the back of the room, awaiting the teachers entrance. His ears perked up when he heard Midoriya speak of the new girl who might’ve been making her first entrance today, though he didn’t quite care for a new student, it honestly had nothing to do with him, he hadn’t found a need for more friends, Midoriya, Uraraka, Iida, and Floppy felt plentiful.

The door slid open, the chattering of the class going still. In walked Cemento, but it wasn’t just him, it was also the new girl, and now that he has seen her with his own eyes, he could understand what the excitement was for. She had mesmerizing, smooth skin, she was delicate looking, with the such pretty eyes, they put his heterochromia ones to shame. Along with her pretty eyes and gorgeous figure her hair was long, around 30 inches, and red just like his left side, Todoroki couldn’t care less if it was real or not. He was sure his mouth was keenly open, but he knew he wasn’t alone, even the girls in the class were shocked at her appearance.

Cemento guided her to the front of the large classroom, in front of the expensive smart board that wasn’t yet displaying geometry problems, thankfully.

Cemento was preparing to give her the go ahead to start speaking but she already took that initiative for herself.

“Hi everyone it’s an absolute pleasure to meet you all! I’m … and I look forward to getting to know each and every one of you,” she beamed.

Sure she was already beautiful but todoroki could feel fire coming out his right side when she smiled revealing a straight line of pretty, white teeth. His multicolored eyes glanced around his classroom, and even the notorious Bakugou was in awe, a sight he has never yet seen.

“It is an absolute honor to have you here … ! Your Japanese is impressive!” Iida stood up moving his arm in the odd robotic like motions, but todoroki doubted anyone missed the telltale pink blush flushed across his pale face.

… bowed in response, traditional Japanese etiquette that she had obviously studied along with the language.

His eyes followed her long legs as she walked to the only empty seat in the room. Right next to him.

[duckprintspress]

Celebrate Native American Heritage Month with 7 Queer Books We Love

November is National Native American Heritage Month! We’re celebrating with books (as always, lol). We asked our rec list contibutors for their favorite queer books either by Native American authors or starring Native American characters. Most of these books (maybe all, I couldn’t confirm for all the authors) are both! Contributors to the list are Nina Waters, hullosweetpea, D.V. Morse, Shea Sullivan and an anonymous contributor.

-

Indiginerds edited by Alina Pete

First Nations culture is living, vibrant, and evolving…

…and generations of Indigenous kids have grown up with pop culture creeping inexorably into our lives. From gaming to social media, pirate radio to garage bands, Star Trek to D&D, and missed connections at the pow wow, Indigenous culture is so much more than how it’s usually portrayed. These comics are here to celebrate those stories!

Featuring an all-Indigenous creative team, INDIGINERDS is an exhilarating anthology collecting 11 stories about Indigenous people balancing traditional ways of knowing with modern pop culture.

-

Postcolonial Love Poem by Natalie Díaz

Postcolonial Love Poem is a thunderous river of a book, an anthem of desire against erasure. It demands that every body carried in its pages – bodies of language, land, suffering brothers, enemies and lovers – be touched and held. Here, the bodies of indigenous, Latinx, black and brown women are simultaneously the body politic and the body ecstatic, and portrayed with a glowing intimacy: the alphabet of a hand in the dark, the hips’ silvered percussion, a thigh’s red-gold geometry, the emerald tigers that leap in a throat. In claiming this autonomy of desire, language is pushed to its dark edges, the astonishing dune fields and forests where pleasure and love are both grief and joy, violence and sensuality.

Natalie Diaz defies the conditions from which she writes, a nation whose creation predicated the diminishment and ultimate erasure of bodies like hers and the people she loves. Her poetry questions what kind of future we might create, built from the choices we make now – how we might learn our own cures and ‘go where there is love’.

-

A Snake Falls to Earth by Darcie Little Badger

Nina is a Lipan girl in our world. She’s always felt there was something more out there. She still believes in the old stories.

Oli is a cottonmouth kid, from the land of spirits and monsters. Like all cottonmouths, he’s been cast from home. He’s found a new one on the banks of the bottomless lake.

Nina and Oli have no idea the other exists. But a catastrophic event on Earth, and a strange sickness that befalls Oli’s best friend, will drive their worlds together in ways they haven’t been in centuries.

And there are some who will kill to keep them apart.

-

Never Whistle at Night: An Indigenous Dark Fiction Anthology edited by Shane Hawk and Theodore C. Van Alst Jr.

Many Indigenous people believe that one should never whistle at night. This belief takes many forms: for instance, Native Hawaiians believe it summons the Hukai’po, the spirits of ancient warriors, and Native Mexicans say it calls Lechuza, a witch that can transform into an owl. But what all these legends hold in common is the certainty that whistling at night can cause evil spirits to appear–and even follow you home.These wholly original and shiver-inducing tales introduce readers to ghosts, curses, hauntings, monstrous creatures, complex family legacies, desperate deeds, and chilling acts of revenge. Introduced and contextualized by bestselling author Stephen Graham Jones, these stories are a celebration of Indigenous peoples’ survival and imagination, and a glorious reveling in all the things an ill-advised whistle might summon.

-

The Witch King (Witch King series) by H.E. Edgmon

Wyatt would give anything to forget where he came from–but a kingdom demands its king.

In Asalin, fae rule and witches like Wyatt Croft…don’t. Wyatt’s betrothal to his best friend, fae prince Emyr North, was supposed to change that. But when Wyatt lost control of his magic one devastating night, he fled to the human world.

Now a coldly distant Emyr has hunted him down. Despite transgender Wyatt’s newfound identity and troubling past, Emyr has no intention of dissolving their engagement. In fact, he claims they must marry now or risk losing the throne. Jaded, Wyatt strikes a deal with the enemy, hoping to escape Asalin forever. But as he gets to know Emyr, Wyatt realizes the boy he once loved may still exist. And as the witches face worsening conditions, he must decide once and for all what’s more important–his people or his freedom.

-

Elatsoe (Elatsoe series) by Darcie Little Badger

Imagine an America very similar to our own. It’s got homework, best friends, and pistachio ice cream.

There are some differences. This America been shaped dramatically by the magic, monsters, knowledge, and legends of its peoples, those Indigenous and those not. Some of these forces are charmingly everyday, like the ability to make an orb of light appear or travel across the world through rings of fungi. But other forces are less charming and should never see the light of day.

Elatsoe lives in this slightly stranger America. She can raise the ghosts of dead animals, a skill passed down through generations of her Lipan Apache family. Her beloved cousin has just been murdered, in a town that wants no prying eyes. But she is going to do more than pry. The picture-perfect facade of Willowbee masks gruesome secrets, and she will rely on her wits, skills, and friends to tear off the mask and protect her family.

-

Black Sun (Between Earth and Sky series) by Rebecca Roanhorse

A god will return When the earth and sky converge Under the black sun

In the holy city of Tova, the winter solstice is usually a time for celebration and renewal, but this year it coincides with a solar eclipse, a rare celestial event proscribed by the Sun Priest as an unbalancing of the world.

Meanwhile, a ship launches from a distant city bound for Tova and set to arrive on the solstice. The captain of the ship, Xiala, is a disgraced Teek whose song can calm the waters around her as easily as it can warp a man’s mind. Her ship carries one passenger. Described as harmless, the passenger, Serapio, is a young man, blind, scarred, and cloaked in destiny. As Xiala well knows, when a man is described as harmless, he usually ends up being a villain.

What are your favorite queer books with Native American representation?

Want to chat your favorite reads with us? Join our Book Lover’s Discord server!

Update your Goodreads TBR with any of these books by visiting our queer Native American books shelf  on Goodreads!Shop books with Native American rep using our rec list on our Bookshop.org affiliate page!

[materialsscienceandengineering]

Excited state dynamics are essential for understanding fluorescence properties in molecules, impacting their application in technologies. Recent research at Shinshu University explores how molecular structure and geometry influence light emission in aggregation-induced emission molecules. The study reveals that changes in molecular shape affect emission behavior in both solution and solid states. These insights are crucial for advancing applications like organic light-emitting diodes and bioimaging, enabling innovations in material design and energy interactions. Light emission from molecules, particularly fluorescence, has fascinated scientists for over a century, revolutionizing areas like imaging, sensing, and display technologies. Recent advancements have brought attention to aggregation-induced emission (AIE) -- a unique phenomenon where molecules emit light more efficiently when in a solid or aggregated state. Studying the reaction dynamics underlying this phenomenon, is thus, important for understanding the molecular structural changes.

Read more.

[hexheathen]

SCP - Unknown

Item #: SCP-█████ Object Class: Keter

Special Containment Procedures: SCP-█████ is to be contained in a reinforced subterranean containment zone measuring [REDACTED] meters in diameter. The chamber walls must be coated in a proprietary alloy developed under Project ████████ to mitigate SCP-█████’s anomalous effects. Access is restricted to personnel with Level 4 clearance or higher, and all interactions must occur remotely via drone-operated systems.

Any personnel entering SCP-█████’s containment chamber must wear full-spectrum visors and Level III hazmat suits to counteract its [REDACTED] visual distortions and biological hazards. In the event of a containment breach, Site ██ is to initiate Protocol “Oblivion Net”: total lockdown with on-site warheads primed for immediate detonation. Under no circumstances are any reflective surfaces or biological samples to be introduced into SCP-█████’s vicinity.

Description:

SCP-█████, referred to colloquially as "The Unknown," is a humanoid entity measuring approximately 7 feet in height when fully upright, though it often adopts a hunched or semi-quadrupedal posture. Its physiology is highly mutable, oscillating between tangible flesh and [DATA EXPUNGED], rendering traditional analysis nearly impossible.

Key features include unnaturally elongated limbs, sharp, angular protrusions along its vertebrae, and a head encased in a [REDACTED] that refracts light in anomalous ways. Notably, SCP-█████ lacks visible eyes, yet it demonstrates acute environmental awareness, responding to stimuli with unnerving precision. Its face appears to shift subtly, giving the impression of watching without any defined gaze.

SCP-█████ currently resides within what has been described as a “skin shell,” a body once belonging to a deceased D-Class personnel, designated [REDACTED]. This shell, while outwardly human, is notably altered:

The skin appears pallid and waxy, with deep scar tissue radiating across the chest and abdomen.

Movements are disjointed and irregular, often accompanied by audible cracking sounds.

SCP-█████ utilizes this host as a façade, manipulating it with inhuman precision while maintaining a semblance of humanity.

Within the skin shell, thermal imaging reveals SCP-█████ itself as a dense, shifting mass of [DATA EXPUNGED], suggesting its true form is compacted or compressed to inhabit its host. Attempts to extract SCP-█████ from the skin shell have resulted in failure and increased aggression from the entity.

Its most anomalous property, “UVX Distortion,” involves manipulating light and sound to create persistent illusions of serpentine forms and fractal geometries. Victims of UVX Distortion often become disoriented and herded to the SCP’s location. After that, they report hearing phrases such as “cry, cry,” and “your fear makes you whole” before succumbing to [REDACTED].

UVX Distortion and Biological Toxins

SCP-█████’s most anomalous property is classified as “UVX Distortion,” a multifaceted phenomenon involving biological, psychological, and visual effects:

UVX Toxin Production: SCP-█████ produces an airborne neurotoxin designated UVX-13, which binds to synaptic pathways in the brain. Victims exposed to UVX-13 experience disorientation, paranoia, and sensory distortion. Prolonged exposure results in:

Blurred Vision: Perception of shifting shapes and serpentine forms.

Auditory Hallucinations: Persistent whispering, sobbing, and rhythmic ticking.

Cognitive Impairment: Difficulty forming coherent thoughts or distinguishing reality from illusion.

UVX Biological Impact:

Studies of UVX-13 samples reveal it mimics specific neurotransmitters, inducing a temporary state of hyper-awareness followed by severe cognitive shutdown.

The toxin causes cellular degradation in nervous tissue, leaving survivors with long-term psychological trauma and reduced motor function.

Victims report an intense sensation of "being watched" and recurring dreams of [REDACTED].

Visual Anomalies: SCP-█████ manipulates light to create persistent optical illusions resembling fractal geometries, shadow-like tendrils, and serpentine entities. This effect, combined with the toxin, overwhelms the victim's senses, making escape nearly impossible.

Behavioral Control: Individuals exposed to UVX-13 demonstrate unusual patterns of compliance with SCP-█████. These subjects have been observed walking directly toward SCP-█████ despite signs of fear or pain.

Acquisition:

Following multiple disappearances, SCP█████ was first encountered near [REDACTED] Greenville Theater. Mobile Task Force Theta-9 (“Trailblazers”) was deployed. SCP-█████ displayed hostility, resulting in █ fatalities and ██ injuries, before being subdued with experimental [REDACTED] weaponry.

Incident Report ████-A:

On ██/██/20██, SCP-█████ breached containment during routine maintenance. Security footage shows SCP-█████ phasing through [REDACTED]. Surviving personnel reported hearing voices resembling deceased loved ones and experiencing severe emotional distress. The breach was resolved after [DATA EXPUNGED], though ██ staff were declared MIA.

Post-incident analysis strongly suggests that SCP-█████ possesses highly dangerous cognitohazardous properties capable of [REDACTED]. This revelation underscores the critical importance of our ongoing research and the need for immediate containment measures.

Experiment Log █████-C: Test ███-07 Objective: Determine limits of UVX Distortion and toxin spread. Method: Remote drones equipped with Class-IV visual inhibitors and toxin detectors.

Results: Drone operators experienced hallucinations after [REDACTED] minutes, reporting visions of [REDACTED]. Biological analysis of air samples revealed UVX-13 concentration exceeded safe levels within 1.2 seconds of SCP-█████'s presence. a small .3 mm hole was found. Test aborted due to equipment failure and psychological strain on operators. Hole has been fixed.

Addendum █████-B:

Field Research Notes:

SCP-█████ shows fixation on individuals with high emotional distress. Patterns suggest it selects victims based on [DATA REDACTED].

SCP-frequently exhibits a deeply unsettling personal interest in those it encounters, often recounting specific, deeply personal details about their lives. This behavior is theorized to increase victim vulnerability, causing significant discomfort and unease among those affected.Unverified accounts suggest SCP-█████ has engaged in cryptic dialogues about “the Fog” and “the End.”

Interview Log █████-01

Interviewer: Dr. Amelia Crowe

Subject: SCP-█████

Date: ██/██/20██

[BEGIN LOG]

Dr. Crowe: SCP-█████, can you hear me?

SCP-█████: (A deep, layered voice, fragmented and uneven, responds after a long pause) Yes. Yes. I hear the... tick... tick… ticking. Your time runs thin.

Dr. Crowe: My time? What do you mean by that?

SCP-█████: Do you not feel it? The weight. The crushing tide of the Fog. It watches. It... [REDACTED]... waits.

Dr. Crowe: The Fog? Is this an external entity you serve?

SCP-█████: Serve? No. It is me. I am it. You are all drowning in its shadows.

Dr. Crowe: What do you want from us?

SCP-█████: I want to see. To know. To... unravel. Your chains tighten as you beg for them.

Dr. Crowe: Chains? Elaborate.

SCP-█████: You carry them. Wound tight. Around your soul.

*[SCP-█████ leans toward the microphone. Static overtakes the audio.]

Post-Incident Report:

Personnel present during the interview with SCP-reported experiencing recurring nightmares and severe emotional distress for several weeks. This psychological strain underscores the need for caution and the suspension of further direct communication until containment protocols are revised.

[kc5rings]

gear ask: boots vs mitts, which is more fun to you and why?

(also "blackout poetry but with a person" is rewiring my brain a bit so thank you for that)

For boots I’m gonna assume you mean ballet/pony boots since as opposed to just regular boots since mitts is the other option

It’s pretty situational but I’d probably go with mitts being generally more fun

With both options (assuming they are the only gear being used) you severely limit the actions a person can take without actually restraining their body all that much

With ballet boots they pretty much prevent walking entirely unless you’ve had lots of practice or are actually a ballerina. This also makes them a fun choice for a character who is actually a dancer to either show off their mastery or make them struggle where they would normally excel. They are an intense piece of gear and agony for someone who isn’t accustomed to them, fun but very situational

Pony boots are often lumped in with ballet boots as being super intense/painful, but are actually much easier to learn and downright comfortable once you do. Good quality ones are made with running and pulling heavy weight in mind, since that’s what they are often worn for. Great for the workout kink minded petplay fan but again, very situational. Not a great idea to wear real horseshoes inside for example

Mitts though, you can use in most any situation you want. Once a pair of properly fitted mitts are on the wearer is completely dependent on others for even the most basic tasks. A person who’s a workaholic is suddenly completely unable to type but otherwise free to wander and relax, a simple door is suddenly a sweat inducing geometry problem to try and tackle solo and a locked door is impossible even with the key in the room

Our hands are the primary means we have for interacting with the world, removing their use removes a massive amount of agency from a person, which can intensify a scene with other gear or force a person who has trouble letting go of control to accept that they can’t do anything but give in for a little while

[positively-knotted]

Dissertationposting 2: Curvature & Hypersurfaces

(Note: I'm not gonna say anything about what I mean by "curvature", as if you haven't already seen it in some context I don't think you're gonna get much out of these posts :/. But for clarity, I'll only ever talk about scalar curvature and call it R. If you're used to Gaussian curvature written K, this is the same except R = 2K. Oh also all my manifolds are oriented.)

It may not be immediately obvious why we would want to consider hypersurfaces when trying to understand curvature - after all, R³ is flat, but contains surfaces with all kinds of curvature. So a motivating example may be in order. This is in fact the example that spurred all of the developments we'll talk about, and is of particular importance in theoretical cosmology! Maybe I'll say more about that later.

Consider a manifold homeomorphic to the n-torus Tⁿ - or more properly, Tⁿ with a choice of geometry (Riemannian metric). Intuitively, this shouldn't be able to have R > 0 everywhere, in the same way that T² can't. Proving this is surprisingly hard, but one sensible approach would be to try induction. After all, T³ is just T² × S¹, and S¹ is easy to understand. Thought of the other way around, we want to find nice hypersurfaces and do inductive descent until we reach dimension 2, then apply Gauss-Bonnet.

But if any old hypersurface doesn't say much, what about particularly nice ones? The obvious candidates are so-called stable minimal hypersurfaces. These are minimal points for area, in the sense that if you perturb them very slightly, their area must increase (e.g. the meridian of a standard torus in the motivating example). The big result about these is as follows:

Lemma 1.

If Σ is a stable minimal hypersurface in a manifold (M, g) and f is any function on Σ, then [1]

Here the left side is the gradient of f (in the normal calculus sense), and \II is the second fundamental form, a number that tells us something about how Σ sits inside M. You can think of it as a kind of error term, but the important bit is that it's squared, so non-negative. R is the scalar curvature of the ambient manifold M, and R_\Sigma is the induced scalar curvature of Σ.

You've probably never seen this before, even if you've done differential geometry. I don't know why this formula isn't better known, it's super useful, as with clever choices of f it gives big results. Just taking f=1 shows that for a stable minimal hypersurface, the intrinsic curvature has to be greater on average than the external curvature. This is a pretty big step forward!

Ok, so we have our choice of useful hypersurfaces. Now we just need to show that they always exist. And they do! In fact, they exist for each homology class:

Lemma 2.

Let (M, g) be a closed n-manifold, 3 ≤ n ≤ 7. Then for any class α ∈ H_{n−1}(M), we can find a closed stable minimal hypersurface Σ such that [Σ] = α in homology.

Let's unpack this a bit. We can think of hypersurfaces as living in a particular homology class in the usual geometric way. It's a standard result from differential topology [2] that we can in find a hypersurface living in any homology class, and that slightly perturbing it won't change that class. The interesting bit here is that we can always take a stable minimal representative, in sufficiently small dimensions. [3] Annoyingly, this means everything from here on out only applies in dimensions less than 8, even though there's no good topological reason why it isn't true more generally. (It definitely is true more generally, we just need a stronger version of this lemma and that makes it an analysis question.)

Next time, we'll use this to show that Tⁿ doesn't admit positive scalar curvature! Notes below the cut.

[1] Proof of Lemma 1. Start with the usual Gauss equation. Take the trace to pass to Ricci curvature, then again to pass to scalar curvature. It turns out that the irritating terms from varying dimensions cancel out! More detail in the screenshots below:

[2] Remember that there is a bijection between H¹(M) and homotopy classes of maps M -> S¹, pairing [f] with f^*(ω), where ω generates H¹(S¹). We can assume f is smooth, choose a regular value t, and set Σ = f^{-1}(t). Then [Σ] is Poincaré dual to f^*(ω).

[3] The actual argument here is pretty standard for the analysis I'll be omitting. In general, if we want to show that an object in space X with property P exists, we'll pass to a bigger space Y where standard results give us an object with that property; then somehow argue that P implies that it's actually of type X. Here, we pass from submanifolds to currents, and minimise area for currents in a given homology class. By measure theoretic magic, this minimisation forces the singular set of the current to have codimension at most 7, so in dimensions less than 8 it is in fact a submanifold.

[rock-swag-tournament]

pyrite propaganda: pyrite is so amazing i’m not even kidding. in my mothertongue, instead of being called fool’s gold, it’s called cat’s gold and we all love cats right?

also, fossils can become pyritised, meaning that we have literal DINOSAUR FOSSILS that are made of pyrite!!! beautiful shiny golden pyrite!!!

plus pyrite has a lot of chemically similar minerals that are awesome that it can occur with as well. i love chalcopyrite because i love copper (CuFeS2 if im not mistaken) and arsenopyrite is haha funny because its chemical composition is literally FeAsS and it has arse in the name as well (sorry).

it also forms in cubes and im p sure the other shape is a dodecahedron (sorry im not good at remembering geometry and im writing this in a pyrite-induced feverish haze so im not gonna google that rn) and we love 1. minecraft (cubes) and 2. dnd (dodecahedron)

i literally love this rock so so so much i will cry forever if it doesnt win (real)

YES TO ALL OF THIS! And thank you especially for shouting out chalcopyrite i love chalcopyrite.

[queenofcandynsoda]

Carmine the Bloodshed

(Thank you @jknerd~)

TW; Self-harm

Carmine the Bloodshed

Other Names: Carmine the Bloodshed (カーマイン・の・さっしょう Chimamire no Carumin), The Psycho’s Son, The Red Devil, Carmine Spini, R-O-001

Age: 7

Affiliation: Deepground; Shinra Electric Power Company (Formerly), Weiss’ Army

Occupation: Child Soldier, Sniper, Assassin (trainee)

Residence: Deepground Offspring Nursery (formerly), None/Nomadic (currently)

Family: Rosso the Crimson (mother), Cerise (younger sister), Eerie (younger sister), Cordovan and Maroon (younger twin brothers), Jasper (younger brother), Peach (youngest sister), Madder (younger brother), Cardinal (younger brother), Chili (youngest brother), The Restrictor (biological father)

Abilities: Firearm Proficiency (Rifle, Sniper Rifle, Shotgun, Handgun, Assault Rifle), Supernatural Gunmanship (Supernatural Accuracy, Supernatural Reflexes, Supernatural Dexterity, Quick Draw), Glowing Eyes, Knife Proficiency (Switchblade, Razor, Scalpel, Clever, Kitchen Knife), Superior Human Physiology (Flash Step, Supernatural Stealth, Afterimage Creation, Bulletproof Durability, Self-Sustenance, Disease Resistance, Enhanced Intelligence, Supernatural Strength, Healing Coma [after blood loss], Mental Regeneration), Blood Manipulation (Bleeding Inducement, Flammable Blood, Corrosive Blood, Haemokinetic Combat, Blood Bullets), Adaptive Regeneration [after MANY attempts to euthanize him] (Acid Immunity, Poison/Venom Immunity, Water Immunity, Fire Immunity, Explosion Immunity, Blunt Force Immunity, Cutting Immunity), Feign Death, Supernatural Cells, Killing Mastery, Killing Instinct (reluctant), Anatomical Mastery, Weakness Detection, Humanity Retainment, Indomitable Loyalty (to his mother and Weiss), Mathematics Mastery (Geometry, Shatterpoint, Numerical Precision, Calculation, Ricochet), Temporal Sense, Combat Adaptation

Likes: His family, Freedom, Daylight, Collecting souvenirs, Girl-in-the-Picture (Vermillion), Guns, Hot Chocolate, Burgers, Pizzas, Loyalty to Weiss, Target Practice

Dislikes: THE RESTRICTOR, Shinra Company, Professor Hojo, Doctor Fiorenzo Rosales, His Murderous Thoughts, Being controlled, Intense Training, Greedy People, Spoiled Brats

Origins: Carmine is a member of the Off-Color Tsviets and the first son and child of Rosso the Crimson. His biological father is the Restrictor, the cruel overseer of Deepground. From birth, Carmine was forced to train to be the most effective killer that could surpass his mother’s abilities. His body has been pushed beyond its limits to the point it is a wonder how Carmine lived past the age of five. After his birth, his mother attempted to hide him but he was quickly taken away and placed in the Offspring Nursery. Since then, he was subjected to torturous experiments as Rosso gave birth to his siblings due to her body being modified to be pregnant for three months. The mother and son would communicate at every opportunity, even having the chance to see his younger siblings. 

Due to the brutal experience he suffered, Carmine has become mentally unstable. He has become hostile to “Shinrites,” meaning people who work for Shinra”, and would aim his rifle at them, believing they intend harm regardless. He tends to be vulgar whenever he feels defensive, especially when it comes to his siblings and mother. This would also lead to profanity and threats of violence. 

Despite these frightening traits, he does his best to create and maintain his humanity. He would make himself bleed daily to remind himself that he is still a living person, not a weapon. Carmine had developed a reputation for trying to escape since he was about four years old. His common method is to use the air vent. This led him to enter various places in the Shinra Tower, such as the Materia Research Facility, SOLDIER Floor, Visual Entertainment Hall, the President’s Office, executives' offices, Hojo's laboratory, and the Skyview Hall, his favorite place. He would collect items, such as office supplies, Shinra/SOLDIER merch, souvenirs, and human teeth from Hojo’s lab. He also managed to collect Lazard’s pens, the Turks’ weapons, Palmer’s luxury eating utensils, Heidegger’s medals, Hojo’s lab equipment, Scarlet’s picture of her daughter, Vermillion, Rochelle’s makeup, Rufus’ coins and shotgun bullets, Junio’s handbags, and President Shinra’s car keys to one of his sports cars. He would then give most of them to the other children in Deepground, such as his siblings and his peers like Fuchsia. There are even times that he took jewelry and fur coats to Rosso in secret. 

When Sonon and Yuffie got captured, Carmine was one of the first to interact with the former. Though their first interaction was brief, the ninja intrigued the young boy. Once they get to meet more formally, Sonon is assigned to fight him, later, he tells him about the “Outside”. Sonon said how Wutai was a great nation before Shinra ruined it and that there was so much freedom. Carmine was amazed by this and would repeat it to the other children. 

Once Yuffie becomes pregnant, Carmine overhears conversations about a potential dissection of the baby, which would lead to its death as they are deemed “disposable”. The boy immediately told Sonon, who then told Nero, Weiss, and Yuffie. The Pure White Emperor then created an escape plan that would lead them into Wutai. Days later, Carmine hit his head hard enough that he got a concussion during training. In the infirmary, when Shelke is assisting in examining him with the doctors, she discovers that Carmine's “obedience” chip has been destroyed. This allows him to go against the Restrictor and gain free will. From there, Weiss sees him as essential to the escape. Soon after, Weiss secretly told the young boy how he could help. 

There are three tasks he needs to do once he escapes;

Seek out Viceroy Sarruf for Weiss to remove him from power for the Kisaragi Family to reclaim control over Wutai

Search for Wutai’s materia, especially the Leviathan materia

Return to help with the breakout once he gets Shelke’s message 

As a way to escape, Carmine forced his body into “Bleeding Sleep” to give the appearance of being dead as blood came out of his mouth and his heart stopped. Several Deepground children, including some of his siblings, pretend to mourn for him. The Restrictor, disgusted by Carmine’s “corpse”, threw him away in the trash truck. Carmine uses “Bleeding Sleep” long enough to wake himself and crawl out of the trash. He looks out of the trash truck to see the sun for the first time, amazed by the sight of freedom. Using this as an opportunity, he jumped out and headed to the nearest town outside of Midgar, Kalm. From there, he learns more about 

Along with getting a red hoodie, black pants, and slightly ragged white sneakers, he also gets a small rifle and stolen materia for any self-defense. 

Now, with all of his equipment, Carmine hopes to complete his tasks to ensure the escape from Deepground and the rescue of his family. As he travels, he learns to become more human and gain experience. 

[vampirevirus]

☠ intro post ☠

✶⋆.˚ hello, i'm diskey! i'm a 15 year old artist. i go by they/he/she/it + neos. (you can also find the other names i go by there!)

this is my more personal/casual sideblog. i also still post art here! this is mainly just a blog to more mindlessly ramble and be both cringy and more blunt about shit that Bugs me .. also vent from time 2 time .. warning that i can get quite rude-sounding/critical here! ..

you can refer to my main blog for more info abt me:

♥ .. (has my byi, dni, kinlist, and more!) .. ♥

╰┈➤ https://www.tumblr.com/dallydillying ࣪ ✶⋆.˚

𖦹・゜!! fandoms/special interests !!・゜𖦹

most active/hyperfixated on are in red !!

✶⋆.˚ sorted by mediums ✶⋆.˚

╰┈➤ books/movies: warrior cats, electric dreams, wonder (both the book and movie)

╰┈➤ web series/online media: osc [bfdi, ii, tdos, hfjone, ppt2, etc] eddsworld, happy tree friends, dick figures

╰┈➤ shows: spongebob, ginga, oobi, chalkzone, moral orel, loiter squad, home movies, rick and morty, aqua teen hunger force, 12 oz mouse, superjail, lazor wulf, henry danger (hear me out okay), blues clues/blues room, team umizoomi, max & ruby, wonder pets, tickety toc, fanboy and chum chum (i am So sorry), pocoyo, mlp:fim, wow wow wubbzy, unikitty, yo gabba gabba, peep and the big wide world, wild kratts, nature cat, storybots, ruby gloom, doug [nickelodeon since i haven't seen the disney iteration], making fiends, rocko's modern life, robot jones, mao mao: heroes of pure heart, sheep in the big city, foster's home for imaginary friends, robotboy

╰┈➤ games: cookie run kingdom, sally face, touhou, corpse party, detroit become human, undertale/deltarune, wobbledogs, portal, night in the woods, the walking dead games [telltale], danganronpa, omori, geometry dash, bully [video game], the i became a dog games, mouthwashing, henry stickmin, fnf, ddlc, animal crossing

╰┈➤ multi-section media/misc: pokemon, spy vs spy/mad, lalaloopsy, hoops and yoyo, the kagerou project, vocaloid, blaseball, razia's shadow [musical], batman

╰┈➤ bands/artists: the beatles, system of a down, tyler the creator, car seat headrest, kmfdm, korn, malice mizer, sade, esthero, erykah badu, billie holiday, imogen heap, death grips, underscores, ween, pearl jam, say anything, sublime, cocteau twins, red hot chili peppers, aphex twin, tally hall, weezer, streetlight manifesto, ludo, the cure, the smiths, kendrick lamar, lemon demon/neil cicierega, radiohead, glass beach, panchiko, tennis, linkin park, 2pac, static x, they might be giants [WILL FOR SURE BE UPDATED. i definitely forgot some.]

𖦹・゜!! TAGS !!・゜𖦹

CHANGELOG (1/2/25): #vanityvague and #vanityvents are now #vaguevampire and #vampirevents!

______________________________________________________________

╰┈➤ #diskey discussions: talking, hyperfixation-induced rambling and theorizing, basically just normal posts really

╰┈➤ #diskey drawings: art i decide 2 post here

╰┈➤ #diskaroke: me quoting song lyrics

╰┈➤ #diskuote: me quoting media i like

╰┈➤ #diskourse: involves blunt gripes/complaints i have with fandoms, also talking about controversial subject matters

╰┈➤ #vaguevampire: vagueposting

╰┈➤ #vampirevents: vent posts

☣ stamp dump below [no visuals in this post made by me] ☣

....... [don't feel like tagging] .......

[cbirt]

Researchers at the MIT-IBM Watson AI Lab have achieved a significant breakthrough in the field of molecular property prediction. By introducing the Grammar-Induced Geometry Framework, the researchers address the challenge of curating labeled data for developing accurate deep-learning models. This framework leverages a learnable hierarchical molecular grammar to capture structure-level similarity, paving the way for data-efficient property prediction crucial for drug discovery and material sciences. The framework demonstrated its excellency for large datasets and extremely limited data, outperforming supervised and pre-trained Graph Neural Networks. This article delves into the Grammar-Induced Geometry Framework, its advantages, and its potential implications.

Fundamentally the framework is based on Grammar-induced Geometry that graphically represents the space of molecules, and every path spanning the root to leaf delineates a grammar production sequence that prompts a particular molecule. Just like following grammar rules, we can formulate diverse sentences, in formal language theory, grammar depicts a set of production rules formulating the procedure of building validated strings from a language’s alphabet. For instance, two molecular structures having a similar substructure would use the same sequence of grammar production rules.

Continue Reading

[madamlaydebug]

Haha! Makes sense. 🤓

📷: Art by Ahmed Elblas

MER: THE GREAT PYRMID OF GIZA

The Great Pyramid Of Giza Known as Mer to the ancient Kemites is the most enigmatic structure on the face of the planet. Mer which translates to the “Place of Ascension” is the only surviving wonder of the ancient world and has inspired much speculation as to why it was built and what was its function.

According the the ancient Kemites themselves the Pyramids served as a ritual center for the Per Ankh schools of initiation. The Kings and Queens chambers were designed to harness resonance frequencies to induce higher states of conciousness. The structure of the pyramid was designed using sacred geometry which allowed the structures to tap into the subtle energies of the earth and the cosmos. The ancients harnessed this enegery for a number of purposes. It is said that the Pharaohs would use the Mer structures which were incased in highly reflective white limestone, capped with gold to "Turn night into day". A feat of such greatness would surely ensure their names and legacies would live on for thousands of years. They were right.

The mathematical accuracy and astronomical information encoded into the structure has baffled scientists for decades. The great pyramid is aligned within three sixtieths of a degree of true north, a more accurate alignment than any other structure on earth. It is not only aligned almost perfectly to the cardinal points, but its placement on the earth is intentional as well placing it directly in the center of the world's landmass.

The level of technological sophistication used to build this great monument far exceeds the capabilities of today’s greatest minds and we could not build anything close to the great pyramid today even with our perceived advanced technology and building machinery. The ancient Kemites did not use the inch as they do in our modern system.

They used the royal cubit which is one 25 millionth of the polar diameter of the earth which is the exact distance from the north to the south pole. If you chop that distance into 25 million pieces you get the royal cubit.

The length of a base side at the base socket level is 9,131 inches which translates to 365.242 royal cubits. This just happens to be the earthly year right down to a quarter day. The measurements of the length and width of the perimeter of the great pyramid corresponds to an exact fraction of both the longitude and latitude measurements at the equator. Scaled up this means the great pyramid directly corresponds to the circumference of the equator as well as the measurements from the equator to the pole, making it a scale model of the northern hemisphere.

If you take the location of the Great pyramid as a coordinate this number sequence matches the speed of light traveling through space measurement in meters per second. None of this is a coincidence and the vast information encoded about the earth and its relation to the cosmos points to the fact that these ancient Africans were far more advanced than we could ever imagine and the methods in which they collected and incorporated these high sciences into their structures and cities still escape scientists today.

Today I give thanks to the ancient Kemites and those that came before for their contributions of Mathematics, Sacred Geometry, Architecture & Astronomy. I am grateful for these gifts you gave to the world.

Black Genesis by Robert Bouval and Thomas Brophy

https://www.amazon.com/Black-Genesis.../dp/159143114X

𓊵𓏏𓊪 𓋹 Hotep Be at peace

Follow our YouTube Channel:

https://www.youtube.com/@knowthyselfinstitute

Visit our Virtual Museum:

https://www.knowthyselfinstitute.com/museum

"I have not spoken angrily or arrogantly. I have not cursed anyone in thought, word or deeds." ~ 35th & 36th Principals of Ma'at

[theblackbookofarkera]

Mushroom Forest of Dratal

What was once a pristine broadleaf forest now stands as testament to corruption from beyond the stars, where cosmic spores fell like rain to transform Dratal into a realm of psychedelic horror. The ancient trees still reach toward the sky, though their bark now serves merely as host to countless varieties of fungi that pulse with unnatural colors and whisper maddening secrets to those who venture too close.

The corruption runs deep, having transformed the very soil into a living matrix of fungal threads that pulse with alien purpose. These mycological networks stretch for leagues underground, connecting the entire forest in what some scholars believe to be a single vast organism. When one digs into the earth, the soil bleeds phosphorescent ichor and the fungal threads writhe like dying worms.

The air itself is thick with spores that dance and swirl in patterns suggesting conscious design rather than natural air currents. These spores affect all who breathe them, inducing visions that range from transcendent to horrific. Many explorers report seeing the same hallucinations - vast cities of living fungus, beings of pure geometry drifting between the trees, and most commonly, visions of the forest's final transformation into something utterly alien to our reality.

Life persists in Dratal, though twisted into forms that mock natural order. Massive spiders, their bodies swollen with fungal growths, weave webs of impossible complexity between the trees. These webs shimmer with psychic resonance, and those who touch them report feeling the collective consciousness of the forest for brief, sanity-shattering moments. The spiders themselves seem to serve as guardians or caretakers, tending to the mushrooms in ways that suggest disturbing intelligence.

The wyrigs of Dratal represent nature's failed attempt to adapt to the forest's corruption. These creatures, hybrids of boar and pig bloated by fungal infection, hunt in packs through the psychedelic undergrowth. Their flesh is marbled with fungal threads, and their eyes glow with bioluminescent light. When slain, their bodies rapidly decompose into new clusters of mushrooms, continuing the forest's endless cycle of corruption.

The mushrooms themselves defy cataloging, as new varieties seem to spontaneously evolve with each passing season. The Praath have documented over three hundred distinct species, though their taxonomists often go mad before completing their studies. Some specimens sing in voices that sound disturbingly human, while others move about on root-like appendages when they think no one is watching. Most common are the Dreamer's Caps, whose spores induce prophetic visions, though the futures seen are invariably dark and terrible.

Despite (or perhaps because of) their toxicity, the fungi of Dratal have drawn alchemists and magick-workers from across Arkera. Some varieties can cure ailments thought incurable, while others induce states of consciousness that allow communion with entities beyond our reality. The most sought-after specimens are the Ghost Bells, pale translucent mushrooms whose consumption allows one to perceive all possible futures simultaneously - though few minds can survive such revelation intact.

Poisons derived from Dratal's fungi are highly prized by assassins, as they not only kill but often transform their victims in disturbing ways. The infamous Golden Tears mushroom, for instance, causes its victims to sprout fungi from their eyes and mouth while still living, eventually transforming them into a new fungal colony. The Praath Holdfast has strictly banned the export of such specimens, though a thriving black market persists.

Several groups have attempted to establish research stations in Dratal, but prolonged exposure to the forest inevitably leads to contamination. The researchers begin to exhibit fungal growths of their own, their minds becoming linked to the forest's collective consciousness. Most concerning are reports that these transformed researchers may retain their faculties while serving some larger purpose beyond human understanding.

The corruption continues to spread, albeit slowly, with each passing year seeing the forest's borders expand by small but measurable amounts. The Praath maintain a quarantine zone around Dratal, though their efforts seem futile against a force that operates on a timescale far longer than human civilization. Some of their seers predict that given enough time, all of Slukea will become an extension of whatever alien entity the forest represents.

I have sampled many of Dratal's fungi in my studies, though I dare not speak of all I have learned through such experiments. Some knowledge is too heavy for one mind to bear, some truths too terrible to comprehend. The forest holds secrets from beyond the stars, but it also serves as warning - there are some gifts from the cosmos that humanity should never have received.

[coming-up-with-usernames-is-hard]

PhD Blog Week 8

Courses

CFT: More messing around with correlators, radial quantisation, lots of things that are almost vertex operator algebras without ever saying that

Diff Top: Main complaint this week is that he keeps mentioning bundles without defining them, but I finished the assignment so that's good

Lie Algebras: Root systems, mostly just linear algebra, should finish the classification this week

Talks

Integrable Systems Seminar: Spherical double affine Hecke algebra, still don't really know what it is but despite that the talk was actually one of the most understandable seminars I've been to

Algebra Seminar: More Yangians, still don't know what a Yangian is, followed for about ten minutes before getting lost. The preseminar was good, but didn't help follow the main seminar

Example Showcases: Mostly pretty good this week. The first was on geometric applications to number theory, simple start showing that some equation has no solutions over the integers, then the schemes appeared and I was lost. This seems to be a common occurrence. I should learn what a scheme is. Second talk was on Feynman diagrams and how they arise in QFT, it was a good explanation of a lot of physics in just half an hour, and it was nice to be back on familiar ground after the étale fundamental group. Third one was on the Witt and Weyl algebras, a good explanation but I felt that the talk lacked a conclusion. The final talk was on topological data analysis, very interesting application of things that I don't know that well, and a little bit of rep theory.

Reading Groups

Complex Geometry: The Weyl group part 2, I missed part 1 but it still mostly made sense

Infinity Categories: Really interesting this week. We looked at how to define monoidal categories, the approach taken was to move away from the notion of a biniary product and phrase symmetric monoidal categories as co-cartesian fibrations, then the monoidal structure is naturally induced from maps in FinSet_*, and replacing finite sets with ordered sets gives a non-symmetric structure. Then this (much more complicated) definition generalises to infinity categories.

Categories: The 2-category of categories, after infinity-categories 2 feels like a very small number! I've also agreed to give a talk in a couple of weeks so I need to brush up on universal properties

Supervisor Meeting

Finally heard from my second supervisor as we discussed Wronskian solutions to differential equations, not my favourite area of maths but hopefully once it's related to the algebra I won't have to deal with the differential equations much

Teaching

Two tutorials this week, the work sheet was harder this week as they've just started graph theory, the final question was to prove that the utilities problem has no solution which was a pretty big ask