Chapter 3: Helix of Memory 記憶の螺旋

I drifted through a vast sea of stars, where math and reality intertwined like constellations weaving silent patterns across the dark sky. Before me, Euler’s helix unfurled, a three-dimensional curve embodying one of the most profound truths I’d ever known. At its core was Euler’s formula:

e^(iφ)=cos⁡φ+isin⁡φ

I knew this meant the complex exponential traced a perfect circle in the complex plane as the angle φ swept through real numbers. But when time stretched into a third dimension, that circle spiraled upward, forming a helix, an infinite spiral weaving through space and time.

The cosine function traced steady oscillations along the real axis, while the sine function rose and fell along the imaginary axis. Together, they danced, two waves locked in perpetual motion, orthogonal yet inseparable. This helix wasn’t just a shape; it was a living signal, a cyclical pattern representing how phenomena vary continuously over time and space. It was made of two parts: the real, steady pulse of certainty, and the imaginary, shifting wave of possibility.

The spiral felt like the slow turning of a traditional Kyoto garden’s stone lantern, its shadows folding softly with the passing seasons — an elegant balance of permanence and change. The dream itself was a complex signal, layered with meaning from different sources, shifting and evolving across dimensions I was only beginning to understand. It whispered of hidden patterns beneath chaos, of truths encoded deep in the fabric of space time.

Then the helix stretched and flattened, rippling into waves, sine and cosine – fluid, dynamic and alive. Riding those waves was a lone old sailing ship, its sails billowing like the delicate silk of a kimono caught in a gentle breeze. On deck stood Akari, poised at the edge, with the moonlight, her gaze fixed on the vast ocean below. Without warning, she leapt into the waves, disappearing beneath the surface before I could reach her. “Akari – !”

My heart pounded as I watched the ship rock gently, lifted by invisible forces. I focused on the delicate balance beneath the surface — the ship’s weight pressing down, met by the buoyant force of the water pushing up. Archimedes’ principle in motion: the hull displaced enough water to create an upward force equal to the ship’s weight, keeping it afloat. The broad shape of the hull spread this force over a wide area, preventing it from sinking.

Above, the sails caught the wind, their broad surfaces angled just right to split the airflow. As the wind rushed over the curved front side of a sail, it moved faster than the air on the flatter backside, creating a difference in air pressure. This pressure difference generated lift — a force perpendicular to the wind’s direction that pushed the sails, and thus the ship, forward and slightly sideways.

Beneath the waterline, the ship’s hull resisted this sideways push. The broad, curved bottom of the hull pressed against the water, which pushed back with an equal and opposite force. This hydrodynamic force acted straight against the hull, preventing the ship from drifting sideways and helping to convert the sideways lift into forward motion.

Meanwhile, the ship’s weight pressed downward, balanced by the buoyant force from the displaced water pushing upward, keeping the ship afloat. Together, these forces—lift on the sails, hydrodynamic resistance from the hull, buoyancy, and weight—formed a delicate but steady equilibrium, allowing the ship to glide smoothly and powerfully across the waves.

As I traced the mechanics in my mind, just as the pieces began to align, the sharp ring of my alarm clock shattered the dream’s fragile clarity.

BEEP! BEEP! BEEP!

I jolted awake, heart racing, the last threads of the picture still swirling in my mind.

I washed my face, the cold water sharpening my senses and grounding me in the morning light filtering through the dormitory shoji screens.

Back in my room, I grabbed a marker and faced the whiteboard. The dream’s fragments crystallized into numbers and formulas. Slowly, deliberately, I began to write, calculating how the ship’s hull displaced water, how lift was generated by the sails, and how pressure varied across surfaces. These Euler’s formulas and the ships are indeed the pinnacle of science and engineering in the 17th century.

Engineers and innovators are seriously underappreciated — though I do enjoy throwing a bit of shade their way sometimes

Dressing quickly, I confirmed this week's work schedule and I grabbed my bag, leaving for the cafeteria.

—

The cafeteria hummed with morning chaos, unfamiliar faces, trays clattering, voices overlapping, the sharp tang of miso cutting through the air. I’ve never been fond of crowded spaces. The clamor and bustle wear on me. How I long for the quiet luxury of room service, breakfast delivered to my door, allowing me to savor the morning meal in peaceful solitude.

Crowds swarm like locusts,

Room service brings peace—and bills—

Lonely wallet cries

I wove through the crowd, tray in hand, my mind still snagged on the dream. Hoshino-sensei’s teasing voice, those looping curves on the chalkboard. But Kisaragi’s image grounded me — her deep, crimson gaze.

I took my cheapest combo of traditional Japanese breakfast to the open area of the cafeteria, soft bird calls along quiet paths, the subtle scent of earth and wood, a large delicate garden at the center of the cafeteria building, reflective ponds mirroring fiery leaves and the magnificent building walls enclosing the quiet area.

As I indulged myself walking along the garden bursting with vibrant spring blossoms in shades of pink, white, and fresh green, I sensed an overlapping chorus of gentle rustling leaves and soft bird songs.

Light, careful steps trailed me for a while. A higher frequency and light footfall. Short and measured strides suggested the person behind me wore a skirt or at least moved with a feminine grace, subtly altering the rhythm and sound of the walk, polished with an etiquette that embodied refinement. Most likely a female.

“I don’t think stalking someone before breakfast is the best idea,” I said confidently, then turned to face the person behind.

Porcelain skin, ethereal and almost translucent, contrasted sharply with her dark hair and deep red eyes — Kisaragi Akari. She looked like she had just stepped out of a winter dream, or maybe a ghost story.

“What are you doing…. You know, with those icy looks and silent footsteps, you’d make a perfect Yuki-onna. Just missing the snowfall.”

The chill in the air made me wonder, had I unknowingly attracted a stalker from the spirit world?

She looked flustered, eyes wide. “Ara… What a coincidence. Fancy meeting you here…,” she murmured, averting her gaze to conceal her embarrassment.

A soft sigh escaped me. “Impeccable timing. I’ve been looking for you. About what happened yesterday—I’d like to apologi…”

“Please, don’t apologize, Kanzaki-kun…” she said gently and sincerely. “I’ve been looking for you as well. And I must apologize for my rude behavior and overreaction in the club room yesterday.” She bowed with graceful sincerity.

Remarkable — a girl who takes accountability ? Wow, such integrity is a rare and precious sight

Unaccustomed to receiving apologies, my left hand instinctively rose to my neck. Gathering my courage, I asked shyly, “Would you like to join me for a morning meal ?”

With a quiet, almost imperceptible breath, Kisaragi tucked a loose strand behind her ear, her delicate low-twin tails swaying slightly. A faint, guarded smile flickered at the corners of her lips, an elegant mask shielding the surprise and secret joy that fluttered beneath her composed exterior. She gave a subtle nod, barely noticeable, yet filled with unspoken understanding.

—

We settled at a wooden table. She lowered her gaze, fingers nervously entwined, betraying a quiet shyness. Then, lifting her eyes, she wore a serene mask of composure. “Good morning, Kanzaki-kun,” she murmured, her voice gentle yet tinged with a subtle awkwardness. Her scent lingered softly around me, gradually enveloping my senses.

She was unnervingly close - too close, and the warmth of her presence mingled with that delicate fragrance, so distinctly different from Hoshino-sensei’s.

“Morning… You had breakfast already ?” I asked calmly and made an effort to follow up the conversation.

“Aa… I had them at home,” Kisaragi said with a small, almost bored smile. “The usual — matcha anpan and soft milk bread, yuzu chawanmushi, salmon with rice, and some pickled vegetables. There’s also a fruit salad with yuzu and berries, served alongside some yogurt. Same as every day, really. I don’t pay much attention anymore, it’s just... what I have for breakfast…”

I was speechless, my face a perfect mask of stunned silence, like a statue caught mid-thought, utterly defeated. That doesn’t sound boring at all… What’s with the five-star brunch menu? I mean, who wakes up every morning and thinks, “Let me start the day with yuzu-scented eggs and salmon with rice”? Meanwhile, I’m over here debating if instant noodles even count as a balanced breakfast.

I’m starting to suspect your “boring” breakfast is actually a covert flex. Next thing you’ll tell me is that you have a personal chef named Pierre who whispers random motivational quotes as you dine.

“That sounds like a fulfilling breakfast. Do you enjoy cooking, or does someone else prepare your meals?” I asked, stirring the natto into my rice with quiet curiosity.

"I do enjoy cooking, but my family chef prepares my meals every day. It's nothing special, though… the food is always beautifully presented and perfectly prepared, yet it somehow lacks warmth," she added with a resigned smile.

“At least breakfast doesn’t present too many problems, right? Or do you prefer something else? After all, eggs only ‘crack’ sometimes, but it’s the quiet moments that truly matter, not just the noise of a scramble,”

She glanced away briefly, her delicate fingers folding and unfolding the edge of her sleeve. Then she met my gaze.

“Perhaps the meal itself isn’t what matters most. It’s who sits beside you that flavors the experience. When the right people share the table, even the simplest dishes taste extraordinary.”

“Thats true, I would politely decline having a meal with some explaining spherical cows and using g = 10”

“Hahaha… But watch out, too much logic（論理）, and you might just end up lonely　（ロンリー）”

“Well, Mathematics students are in quarantine most of the time anyway”

We shared a moment of soft giggles

“What about you, Kanzaki-kun? Does the school cafeteria serve you enough? I imagine someone of your stature would need a rather generous portion,” she asked, curiosity flickering as she glanced at my tray.

“Well… you might be surprised, but I’m a bit tight on money” I admitted with a wry laugh.

“I earned a scholarship to enter the academy, thanks in part to Hoshino-sensei’s recommendation and a lead from a rather dubious alumnus I encountered during my part-time work.” I sipped my soup thoughtfully, searching for a way in.

A flicker of surprise and nostalgia crossed her face, then quickly faded. “Impressive, securing a scholarship at Yugen is no small feat,” she said softly. Her gaze dropped, and a strand of hair fell across her cheek.

“If you don’t mind, I would be happy to share breakfast with you sometime. There’s always enough to go around. And perhaps we could work on some math problems together… or do a bit of research…” Her fingers twitched gently, the faintest tremor betraying her quiet hopefulness beneath the composed surface.

This truly felt like an authentic five-star breakfast delivery. Most students I’ve met come from wealthy, entitled families. Kisaragi was clearly an outlier or perhaps something more, a Goddess in disguise

“Really? That would be awesome... But I hope it won’t be too much trouble for you ?”

“No, not at all,” she smiled

We exchanged an awkward glance, and silence settled between us, broken only by the gentle hum of the morning ambiance.

(Group of crows calling)

“Your work yesterday, that Gamma function, it was insightful. How do you make it look so effortless? I like your methods and way of solving problems a lot”, finishing my natto rice and tamagoyaki.

“It’s nothing extravagant, perhaps just experience. Kanzaki-kun, with your abilities, you’ll outpace me very soon. Besides, Mathematicians always have their own ways of seeing things, don’t you think?” Her pupils dilated slightly, fingers fidgeting subtly.

“Experience, huh? Well, your methods really left an impression on me. Speaking of which, how long have you been training in mathematics?” I asked as I cleared my tray.

“I began at three years old,” she replied with a wistful smile. “There’s simply no substitute for practice. By about five, I was working on university-level mathematics and reading advanced books. I started competition training around nine. What about you, Kanzaki-kun?”

“Yeah, you’re definitely the prodigy type. For me, it wasn’t until I was thirteen that I really changed my perspective. I met Hoshino-sensei, and she completely changed how I thought about math. Like you mentioned in the clubroom, I began to understand the reasoning and logic behind problems, rather than just working on them blindly.” I chuckled.

“We’ve met a few times at math training camps for competitions, but we never really talked until now. You really like math, huh?”

“Oh really? I have absolutely no recollection.” She smiled wryly. “Actually, I was too absorbed in the training to pay attention to my surroundings… my bad…”

“ Math and thoughts are the only places where I truly feel free.” She looked distant and empty for a short moment.

“That’s your talent. Not everyone has that ability to focus so intensely. I need to learn from you… I jump around very often”

“Not at all, It’s not really a good trait…I…”

“...”

“I…”

The morning school bell pierced the quiet and Kisaragi’s slutter

“Kisaragi, let's continue our conversation later. It was a nice chat. Again, sorry about touching the archive without permission.”

“Please…It is not your problem…feel free to use the archives and booklogs.” she said softly, rising with effortless grace, her fingers gently gathering the folds of her skirt.

“I’ll need to return my tray and freshen up a bit. See you in class later!” I said, hastily gathering my belongings and offering a quick wave.

I watched her retreat, her graceful silhouette and delicate form gradually fading into the corridor between the buildings. Some students glanced her way with quiet curiosity, while others subtly averted their eyes, giving her a wide berth as she slipped into the crowd.

Kisaragi Akari may look aloof, but she is definitely the most humble student I have ever met. Given from her status and background, she exhibits a genuine gentle and caring heart. Hoshino sensei was spot-on.

“Sigh… If only I’d had the courage to talk to Kisaragi sooner, maybe my math skills would’ve improved a lot more… Haha. Oh well, no time to waste now.”

As I returned my trays and freshened up, I stepped out slowly from the cafeteria and toward the first lecture hall. The campus buzzed with life-students weaving through pathways, animated conversations filling the air, upcoming events and contest posters are on the walls and bulletin boards.

Nearby, teachers scold students for untucked shirts and slouched postures, their voices sharp amidst the lively hum. Ahead, a cluster of students hurried past, their voices tinged with panic.

“Did you study for the quiz today? I barely had time to glance at the notes!” one fretted. Another replied, “I heard it’s going to be brutal, Tanaka-sensei never goes easy.”

Nearby, two others discussed “ Have you heard about the ghost story from the lab in the engineering building ? For the past-few days, people say that if you’re near the engineering lab after school, you feel sudden cold drafts that move against the air, like invisible hands brushing past.”

“Yikes…last night, I was walking past the ventilation shafts, and I swear I heard slow, rhythmic tapping.”

Based on my observations over the past few days, the students at this academy tend to fall into five distinct groups. There are the outliers, the problematic prodigies like Kisaragi Akari, whose brilliance is matched only by their unpredictability. Then, the grind gang, those who live in the library and labs, caffeinate themselves to oblivion, driven by relentless ambition. The silver-spoon squad, rich-kids who laid-back glide through with ease, their futures seemingly secured at top investment firms. The entrepreneurship swarm crowd, always buzzing with business ideas, seizing every opportunity to network and pitch. Lastly, the technology evangelists, convinced their idea will rewrite the rules of the world.

As I drew closer to the lecture hall, the noise gradually faded, replaced by a growing stillness that blanketed the quieter part of campus. This was the I-House or ‘introvert-House’, as the name suggested, a sanctuary for introverts and a home to the most obscure classes that guarantees you’ll not find a job – Abstract Math, Cosmology, Astroparticle Physics, Organic Synthesis, Neuroinformatics, Quantum Information Theory – all nestled here near the math clubroom building.

Seriously, I have applied to countless internships and co-op positions across various institutes, armed with nearly perfect scores. Yet, the recruiters told me the prerequisite was five years of experience for an entry-level role. How does one gain experience when even the starting positions demand it? Still, I hold onto hope that enrolling at Yūgen will make a difference, opening doors that have so far remained closed, the academy is highly connected to Universities afterall.

The atmosphere shifted palpably, the vibrant energy of the main campus gave way to a hushed calm, as if the building itself demanded focus and contemplation.

Today marked the first session of my elective courses – Advanced Real Analysis. Already, I could picture the faces in the room. Approaching the entrance, I checked the bulletin board: the hall number, the class list. 4 students in total. The instructor, Dr. Hoshino Akina, was a familiar name. Among the students, I recognized Kisaragi Akari and myself.

Was this not just another gathering of the Math Research Club?

Pushing open the heavy wooden door, a rich scent of aged timber and polished oak greeted me, grounding me in the room’s quiet dignity. I stepped inside to find those familiar faces waiting, the soft murmur of anticipation filling the tiered lecture hall. The seats, arranged in gentle tiers, curved gracefully around the podium where Hoshino-sensei stood. Soft light filtered through tall windows, casting a serene glow over the room and illuminating the vast blackboards behind her – an oasis of calm amid the campus bustle.

The front row was my favorite spot. I spotted Kisaragi already seated there, so I walked up and took the seat beside her.

“Look at us, choosing abstract math over a stable career and a functional social life,” I remarked, unpacking my stationeries and catching the subtle trace of her fragrance.

“It’s the only space and time where our minds can truly roam free, an excellent choice, Kanzaki-kun.”

As more students trickled in, one was noticeably absent. Hoshino-sensei had mentioned that some students attend remotely.

Hoshino-sensei gave me a knowing wink before beginning. “Welcome to Advanced Real Analysis, the course where we rigorously prove everything you thought you already knew... and then some. If you ever find yourself questioning reality, don’t worry, that’s just the math talking!”

The class giggled. She added, “By the end of this course, you’ll develop the ability to rigorously prove and apply fundamental theorems, solve complex problems involving integration and function spaces, and build a solid foundation for research in pure mathematics.”

As I sat engrossed in Hoshino sensei’s lecture, diligently jotting down notes, my attention was unexpectedly drawn to Kisaragi’s subtle presence. A delicate scent lingered around her, momentarily distracting me. Curious, I glanced at her notebook-each character neat, her handwriting immaculate.

My focus wavered repeatedly between the lecture and Kisaragi’s quiet gestures. I noticed her furrowed brow as she leaned forward, rubbing the bridge of her nose-a silent signal of discomfort.

Hoshino sensei’s lectures are truly exceptional, her ability to explain complex topics with clarity makes every hour feel like it passes in the blink of an eye. In one such lecture, as the session neared its end, she gave us a challenging problem to work on during the last 20 minutes, perfectly blending deep insight with practical engagement. Her teaching style not only makes difficult concepts accessible but also inspires active learning through well-crafted classwork.

Let A be a Banach algebra. Prove in detail that for any x ∈ A and φ ∈ A∗ , the function f(λ) = φ((λ − x) ^(−1) ) is an analytic function on the open region Ω = C − σ(x).

Kisaragi started sooner than I did. I have two ways of approaching this problem. One is to rely on elementary calculus and operator continuity, focusing on direct differentiation of the resolvent map and using the continuity of multiplication and inversion in the Banach algebra.

The other is a more constructive method, showing analyticity by explicitly expanding the resolvent (λ−x)^(-1) into a norm-convergent power series around a fixed point λ0, the classical Neumann series approach.

Alright, I got this

I began as soon as I could, but Kisaragi seems to have already finished. I can’t wait to compare our answers.

Having completed my Neumann series approach, I noticed Kisaragi resting her eyes, pale and sweating slightly.

“I just finished writing up my proof about the analyticity of f(λ)=φ((λ−x)^(−1)) using the Neumann series. I’d love to hear your thoughts,” I said, eager to bridge our work.

“Oh, that’s interesting. The Neumann series makes the resolvent so tangible and explicit,” she replied, her fatigue seeming to lift the moment we spoke about mathematics.

“I tried to keep it concrete, showing the power series expansion and how the radius of convergence naturally appears. It felt very hands-on. But I’m curious, what was your approach?” I grinned, feeling a bit self-conscious.

“Well,” she said with soft enthusiasm and modesty, “I explored the problem through the lens of holomorphic functional calculus. It’s a bit more abstract, but it reveals the resolvent as a fundamental analytic object in the Banach algebra, deeply connected to spectral theory.”

“That’s way beyond my understanding,” I admitted. “Honestly, it sounds impressive. I’ve read about functional calculus but never quite grasped how it works in practice. How does it show analyticity, anyway?”

“Essentially,” she explained, “the calculus lets us treat holomorphic functions of x in a rigorous way. The resolvent map λ↦(λ−x)^(−1)) is holomorphic as an A-valued function on the resolvent set. Then, since φ is continuous linear, composing it with the resolvent yields a scalar holomorphic function.”

“So it’s like you’re seeing the resolvent as part of a bigger analytic structure, not just a function to expand?”

“Exactly. It’s a more conceptual viewpoint. But your approach is beautifully clear. You get explicit series expansions that make the abstract theory feel concrete. I like that clarity.”

“No, not at all. My solution seems elementary here,” I said, feeling humbled. “Kisaragi, where did you learn this approach? It’s so elegant…I’d love to open up your brain.”

She smiled softly. “Oh, I picked it up from some classic texts-Dunford and Schwartz’s Linear Operators, Bonsall and Duncan’s Complete Normed Algebras, and Kato’s Perturbation Theory. Hoshino-sensei’s lectures helped tie it all together.”

“Hoshino-sensei’s lectures really are the best. She explains complex topics so effortlessly that an hour passes in the blink of an eye.”

“Yes, and the way she weaves deep theory with precision and speed - it’s magical. I feel lucky to have learned from her.”

“I guess I’ll hit the library later on, or perhaps Maruzen Kyoto bookstore”

There’s a full shelf of math books available

“Actually, we have them in the math club archives ”

We shared a smile, the unspoken excitement of discovery and mutual respect filling the room. Two different paths converging on the same elegant truth. A testament to the richness of mathematics and the joy of learning positively together, not hatred or jealousy.

At the front, I saw Hoshino sensei giving our moment a smile and a nod.

It's a bit embarrassing, focus on your work Hoshino sensei. Or perhaps you want to join us ? Hoshii No ？（ほしいの）

—

Its homeroom period next, we walked to our homeroom. Uchida’s usual spark was missing; she sat quietly, eyes cast downward, fingers tracing absent patterns on the desk. I greeted her softly, but she seemed miles away, lost in thought.

Not exactly a morning person ?

“Hey, Uchida, what’s wrong ? Elective class was too boring for you ?”

“Oh, Akari chan, Kanazaki kun. Nothing much… The lecture just now was something else…hahaha”

“What did you take anyway ?”

“Microeconomics…I am not too sure about it, I might switch classes. What about you and Akari chan ?”

“We actually took the same class, advanced real analysis, Hoshino sensei is our instructor”

“Envy…. Figured hahahaha. At least three of us have the same homeroom, that's great…Oh, by the way, did you guys hear about the rumors about the labs in the engineering building ?”

“Not at all” Kisaragi said “Yea, I caught someone talking about the irregularity in the buildings”

“My friend Rika is from the engineering club, apparently they have a science contest due in three weeks. She mentioned that the project is not going well and the buildings are haunted… Do you think supernatural exists ?”

“Yea, totally. I have a yuki-onna stalking me this morning”

“Huh, what on earth ?!”

I can feel Kisaragi's intense gaze and pressure looking towards me…

“Well, ghosts are broken whispers”

“Is that so ?” Uchida gestured her fingers and deep in thought

We continued to chat about random things until the homeroom teacher arrived.

—

Friday, the last class of the week ended early. As I walked towards the main library, the late afternoon sun bathed the building in warm, golden light. A gentle breeze carried the scent of blooming hydrangeas. The grand archive was a timeless place, traditional Kyoto craftsmanship amalgamated with floor to ceiling glass panels flooded the interior with warm natural sunlight. Outside, glimpses of manicured gardens with moss and stone lanterns peeked through the transparent walls, grounding the space in nature and tradition

There is still some time before the club meeting. Time to work on Hoshino sensei’s request and clue.

As I approached the service counter, a faint, satisfying click drew my gaze. A charming librarian half-hidden behind a neat row of returned books, was quietly tending to her lips. The lipstick moved with quiet assurance, a practiced gesture not meant for show but for comfort, the sheen tracing away any trace of dryness.

Noticing my presence, she paused mid-motion. In a heartbeat, she slipped the case from view, restoring her professional composure. Her eyes met mine across the polished counter, and with seamless grace, she welcomed me with a professional, knowing smile

“How may I service you today”

“I would like to enter the grand archive building for the academy chronicle booklog”

“Oh…that was unexpected. Normally, no one would enter that place. It's been quite busy recently”

“Oh really, are there any other things else to look at the archive ?”

“There are chronicle booklog, renovation building plans, academy architecture logs, publications, and financial logs. Please put your name on this sheet for record”

“Alright, thanks” Oh, it's true, someone has been visiting frequently… Aihara Haruto

“Phone and electronic devices are prohibited in the archive building, please leave it here. We will keep it secure”

“There you go”. As she’s handing the procedures, I checked the librarian shift and their names tag on the counter.

“Thank you for your patience, please follow me, I’ll guide you to the building”

We crossed some glass paneled corridor and as we arrived at the grand archive, the distinct smell of old books got stronger gradually.

“The archive closes at 1900 everyday, chronicle books would be on the first floor and second, ascending order from the left. You may also access some data through the computers in there”

“Thanks Uetake san”

“Oh…You know my name ? No problem, if you find yourself stuck or need anything, just ask. Library phones are available in the archive buildings.”

“Will do. Thanks”

She gave me a smile and as she turned away, a small faint of refreshing minty smell… A contrast to the fragrance of old archives.

Sitting there, surrounded by grand tomes and computer screens, the silence of the grand archive pressed gently around me. The records told a story of brilliance and success, one that made the math club a proud emblem of the academy.

Not surprised, Kisaragi’s name dominated the pages. She had overwhelmingly won countless international math competitions, earning gold medals and representing Japan abroad with utmost distinction.

Her victories were marked in detailed reports, accompanied by photographs and commendations. The club’s successes weren’t just individual, team competition logs from about a year and a half to two years ago were plentiful, showcasing consistent triumphs in national and international contests.

Unfamiliar names of math club members, Yukimura Yukiko, Sakurai Hiroki, and Sahara Aoi appeared often as key members of these teams. The camaraderie and quiet intensity of those seasons seemed to linger on the pages.

There’s actually more members than I thought it would… Sakurai Hiroki.. Sounds familiar…

Beyond the competitions, Hoshino sensei’s and Kisaragi’s contributions were well documented. She was deeply involved in cutting-edge mathematical research, collaborating with prominent universities both in Japan and overseas. Published papers, joint seminars, and funded projects painted a picture of a respected academic making steady progress in her field.

Yet, as I turned the pages, something shifted, slowly, almost imperceptibly, like a small thread coming loose in an otherwise carefully woven tapestry.

Records showed that after a single major competition roughly nine months ago, Kisaragi was the only member still taking part in contests. Team entries and reports involving other members stopped abruptly. Official minutes noted declining participation, but offered no further explanation.

More quietly unsettling was Hoshino’s record. The chronicle noted that she had been sharply demoted from her position as director of the math department, coordinator of math gifted programs and suspended for an unspecified period. The details were minimal, just straightforward facts, untouched by comment or context.

The math club itself teetered on the verge of disbanding. Logs mentioned appeals filed twice to save the club, the reasons behind this were vague, lacking clarity. These appeals suggested that someone was making a last effort to keep the club alive, even as it slowly fell apart.

Amid this unsettled backdrop, a notable change appeared: Kisaragi had replaced Sakurai Hiroki as president of the math research club. Whether this was a hopeful move to bring stability or a sign of deeper change was unclear, but it marked a quiet turning point.

Financial reports confirmed the growing troubles. Funding for the club had been reduced steadily, and internal memos referred to “membership losses” and “concerns about club management.” Yet these too were vague, leaving much unsaid.

The math club’s story was one of bright peaks followed by a lingering silence.

I closed the book gently, feeling the quiet around me grow heavier. The polished achievements seemed to fade beneath a veil of unspoken questions.

The stillness of the grand archive had felt at first like a place where time had stopped, where everything lingered in the thick dust and faint scent of old books. But after reading the records, the silence sharpened. Suddenly, time seemed to tick faster than my heartbeat, more urgent than the steady passing of reality outside these walls.

As I got overwhelmed by the weight of the information, I tried to access the data archive, to check the students record, but access was denied.

Damn it, only if I could check the detailed records of Hoshino sensei and the math club members…

I checked the time, it's almost time for the club meetup.

I better not be late

Feeling slightly defeated, I returned the books. As I packed up, a new resolve flickered, one that edged on mischief, or perhaps necessity. A plan was forming…nasty plan

—

I walked back to the counter. Uetake and the other librarians were sorting the books. I cleared my throat.

“Hello, are you done with the archive materials? Would you like your personal belongings now?” Uetake asked, professional as always.

“Hey, Uetake-san. Actually… I have a question about a column of books in the quantum physics area. Could you help me for a moment?”

She blinked. “Quantum physics? Science is not my expertise… But, sure?” She looked at the others, who stifled grins. “I’ll be right back.”

We strolled into the quantum section. Unsurprisingly, empty but for dust. The silence pressed in.

Uetake looked around. “Well, the quantum physics area. Feels like I’m in a parallel universe where I understand any of this.” She grinned gently “What’s your question?”

I lowered my voice. “Sorry for dragging you here. The physics column’s a decoy, actually. I, uh, needed to talk to you privately.”

She stiffened a little. “That sounds… ominous. Is this where you confess your undying love ?”

“Not quite. I need access to the student archive for the math club. And, well, to their club's past data.”

She gave me a wide-eyed look, part scandalized, part impressed.

“Wow, straight to the black market requests. Should I be worried you’re also running an underground smuggling business?”

“Only on weekends,” I deadpanned. “Seriously, can you help?”

Uetake crossed her arms. “You know students can’t access school-sensitive data. Even if, hypothetically, I was the student librarian head—”

“That’s exactly why I asked you,” I interrupted, voice dropping further, “since you do know all the… let’s say ‘less public’ pathways.”

She frowned. “Sorry Kanzaki-kun, I can’t help you break rules.” Then, her tone grew teasing, “ Nice try trying to charm your way out of this though.”

I leaned in, lowering my voice conspiratorially. “You really want to talk about breaking rules?”

Her eyes narrowed, playful suspicion replaced by genuine caution.

“Huh, What do you mean?”

“Isn’t vaping e-cigarettes in the library and school, especially that refreshing menthol ice flavor… against the rules?”

Silence. Uetake’s ears went a little pink. “Wha—What are you talking about?”

“Come on. It’s spring, the air’s crisp, but there’s a faint minty breeze when you’re walking pass. Plus, your lips… classic dryness from regular vaping.”

I flashed a knowing smile. “I’m not judging and it's none of my business. You’ve got a great taste for choosing mint flavour, but rules are rules, right?”

She gawked at me like I’d turned into Schrödinger’s cat. “That’s… Are you some kind of flavor-detective? Should I be worried you’ll analyze my snack wrappers next?” She huffed, glancing nervously at the empty aisle.

“Relax. I haven’t cracked your snack alibi… yet.” I winked. “But if you help me, just this once… I haven’t seen or smelled anything. Quantum principle: unobserved, unpunished. Deal ?”

She stared at me a moment, then let out a dramatic sigh. “You are impossible… Fine. I’ll get what you need. Honestly, this is a one time thing. You breathe a word of this, you and the math club are doing synchronized radio calisthenics behind the gym every morning.”

“Thank you, Uetake sama ! I love you ! I owe you my future in Blackmail Sciences.”

She blushed red and couldn’t suppress her voice “ WHAT!”

Everyone in the library turned in our direction. One librarian drops a book in surprise. I give her the quiet sign gesture , “Shuuu, please be quiet — head librarian”

Uetake returned the favour and gave me a middle finger. Well, I kinda deserve that

She whispered, “Honestly, go die… You owe me more than that… I have 2 more conditions.”

“Anything for you, Uetake-sama.”

She shook her head, mock-scandalized. “I want your help… with my calculus homework. It’s eating me alive… Also, with the data, don’t get us both expelled. Oh, and you better have the world’s best lesson plan ready.”

“All in a day’s work for the notorious math research club, we have Kisaragi Akari as the president too. You’re more than welcome to join, we welcome new members !” I flashed her a cheesy thumbs up.

“Sigh… I should’ve realized, you guys are smart… Another parallel world for me…When do you need it ?”

“Preferbably by next Monday”

“Sigh…Alright alright”

We made our way back to the counter. Uetake slipped a note across with a practiced librarian poker face. “Next time, try asking the library AI robot for help. It’s faster.”

I gave her a salute. “Will do, chief.”

As I grabbed my bag, I could swear I heard her mutter, “Dork,” but I caught the hint of a gentle smile.

On my way out, I checked the note she slipped to me and couldn’t help but laugh as I raced out to the math club.