Chapter XL: The Exponential Derivatives
Morning arrives not with sunlight, but with rain. The streets of London glisten like a sea of molten glass, and the rhythmic patter against the dorm windows sounds like a heartbeat — slow, deliberate, endless.
Nathaniel Cross sits by his desk, eyes fixed on the monitor as lines of mathematical equations scroll past the screen. The faint glow illuminates his pale face, reflecting off his crimson eyes like dying embers.
On the table lies a spread of open textbooks: Statics of Rigid Bodies, Structural Dynamics, and his notes from Professor Dempsey's lecture. Coffee stains mark the margins, a testament to sleepless nights and restless thoughts.
A knock comes from the hallway — familiar, steady, two short raps followed by one long.
Theo.
Nathaniel doesn't look up. "Door's open."
The door creaks, and Theo enters, shaking off his umbrella. He wears his usual navy coat and carries a brown paper bag under one arm. "Morning, vampire of the semester," he says with a grin. "I brought sustenance — for humans, at least."
Nathaniel cracks a half-smile. "I appreciate the gesture. Blood isn't on the menu today."
Theo laughs, setting the bag down. "Then we feast like normal people. Croissants and instant noodles — the breakfast of engineers."
Nathaniel closes his laptop and stretches. "A cursed combo, but fitting."
"Exactly."
Theo sits down beside him, unwrapping his croissant as Nathaniel flips open a notebook filled with force diagrams and handwritten equations.
"Rigid body equilibrium," Nathaniel mutters, tapping his pencil against the page. "You remember when this used to make sense?"
Theo groans. "Barely. I'm convinced Dempsey's questions are written in ancient Sumerian."
Nathaniel chuckles softly. "It's all vectors, mate. Free-body diagrams, internal forces, torque balances. Everything follows the laws of motion — even our mistakes."
Theo glances at him sideways. "You talk like Newton had a curse on him too."
Nathaniel smirks. "He did. Obsession."
Theo grins, then sighs. "Fair. Alright, walk me through this one again."
For the next hour, they dive into study. Equations fill the air like spellcraft — ΣFx = 0, ΣFy = 0, ΣM = 0 — the sacred trinity of engineers. Rain drums outside, steady as a metronome.
Nathaniel's voice is calm and analytical, but beneath it lies something haunting. His mind never strays far from resonance, from the faint hum he keeps hearing under the dorm floors.
He doesn't mention it yet.
After their study session, Theo collapses backward on the bed with a groan. "That's it. My brain's a damp circuit board."
Nathaniel closes his book, smirking. "You mean 'rigid'?"
"Rigid with pain, yeah," Theo replies dramatically, clutching his chest. "Nate, if I die, promise me something."
Nathaniel raises an eyebrow. "What?"
Theo points toward his laptop. "Clear my YouTube history. I don't want the world to know I watched twelve hours of Vedal Neural Vtuber highlights."
Nathaniel laughs — a real laugh this time. "Twelve?"
"Fine. Fourteen."
He opens his laptop anyway, typing VedalAI stream compilation into the search bar. The familiar cheerful synth voice of a green AI turtle VTuber echoes through the room. "Hello, chat! We're coding chaos today!"
Theo grins. "This guy's my spirit animal."
Nathaniel leans back in his chair, sipping from a can of soda. "You find peace in the strangest places."
Theo shrugs. "You find peace in math. I find it in green reptiles pretending to be programmers. Same energy."
For a few blissful minutes, it feels normal — two university students laughing at silly streams, the glow of the monitor soft against the rain-dark window. Nathaniel almost forgets what he is. Almost.
When the stream ends, Theo grabs a controller. "Alright, break time. You, me, Elden Ring. Loser cleans the mess."
Nathaniel smirks. "You sure you want that rematch?"
Ten minutes later, Theo's character is lying face-first in digital mud while Nathaniel's avatar delivers a perfect parry and final blow.
Theo throws his controller onto the bed. "You're cheating. Vampiric reflexes!"
"It's called precision engineering," Nathaniel teases. "You should try it."
Theo grins but looks at him more seriously now. "You seem... lighter today."
Nathaniel glances toward the window. The rain has stopped. The faint reflection of his crimson eyes stares back from the glass. "Maybe. Or maybe I'm just getting better at pretending."
Theo studies him quietly. "Pretending to be human?"
Nathaniel nods slowly. "Something like that."
It happens in the late afternoon. The air is still; the room filled with the gentle hum of Nathaniel's PC fans. Theo's watching another stream, this time of a virtual concert, while Nathaniel sketches mechanical diagrams in his notebook.
Then — a knock. Three times. Soft, deliberate, rhythmic.
Theo freezes. "Expecting someone?"
Nathaniel shakes his head. "No."
The knock comes again. Louder.
Nathaniel stands slowly, his senses sharpening. Beneath the ordinary hum of the building, he feels something else — a faint vibration, like an echo of resonance.
Theo rises too, slipping his hand into his pocket where a small folding knife rests.
Nathaniel grips the doorknob and opens it cautiously.
Two boys stand in the hallway. Both look barely older than twenty. One has messy blond hair and hollow eyes; the other, darker-skinned with a scar cutting through his left eyebrow. Rainwater drips from their coats.
The blond one speaks first. "Are you Nathaniel Cross?"
Nathaniel narrows his eyes. "Who's asking?"
The other one steps forward, voice low. "My name's Kingsley. This is Edison. We're here because... we know what you are."
Theo stiffens. "Careful with your tone, mate."
Edison raises his hands in peace. "We're not here to fight. We're here because we were like you — victims of the Gravenholts."
The name makes the air in the room turn colder.
Nathaniel opens the door wider. "Come in. And speak carefully."
They step inside.
The rain resumes as the four sit in the cramped dorm. Theo perches near the bed, ready to intervene if things turn ugly. Nathaniel leans against his desk, watching their guests.
Edison speaks first. "We were part of an experiment. Three years ago, in a research institute outside Dover — funded by the Gravenholt family. We were told it was a medical trial for regenerative therapy."
Nathaniel's voice is calm but cold. "Let me guess. Resonance-based cellular manipulation?"
Edison's eyes widen. "You know?"
Nathaniel nods slowly. "Continue."
Kingsley takes over. "They called it the 'Sanguine Frequency Project.' They said it would heal any wound, make the body stronger, faster. We didn't know it would... change us."
Theo frowns. "Change you how?"
Kingsley rolls up his sleeve. His veins shimmer faintly under the lamplight — glowing crimson for a brief second before fading. "It didn't turn us into vampires, not fully. But we're not normal either."
Edison adds, "We're what they called Resonants. Our blood reacts to certain sound frequencies. When the Gravenholts activated the resonance chamber, it burned into our cells. Some of us died. The rest..." His voice falters. "We ran."
Nathaniel's jaw tightens. "And you came to me because you think I can help you?"
Edison nods. "You're the only one who survived a direct bite from Eris Gravenholt and lived to tell about it. That means you're different. You understand both worlds — the science and the curse."
Theo looks between them. "Hold on — if what you're saying is true, there could be others still alive?"
Kingsley nods grimly. "Dozens. Maybe more. The experiments didn't stop. We've been tracking energy pulses from underground labs across England — the same frequency signature every time."
Nathaniel's voice turns sharp. "You're saying the Gravenholts are still conducting experiments?"
"Yes," Edison says. "And they're escalating. The frequencies have increased in strength. Someone's perfecting the formula."
A silence follows, heavy and suffocating. Rain beats harder against the window, and a flash of lightning illuminates the room.
Nathaniel speaks quietly. "You came to the right person."
Theo stares at him. "Nate—"
But Nathaniel cuts him off. "If the Gravenholts are still experimenting on humans, then they're not just engineers of resonance anymore. They're engineers of souls."
Edison opens his backpack, pulling out a small metallic device — a compact module no larger than a lunchbox. He sets it carefully on Nathaniel's desk.
"This," he says, "was recovered from one of the labs near Leeds. We think it's part of the resonance generator they used. It's dormant now, but it hums faintly when exposed to heat."
Nathaniel leans closer. The device is sleek — titanium casing, etched with faint sigils that look more like circuit traces than runes.
Theo whistles. "Looks like something straight out of cyberpunk hell."
Nathaniel presses his fingers against the surface. A faint vibration travels up his arm — harmonic, delicate, almost sentient.
"This isn't just a generator," he mutters. "It's a tuner."
Edison frowns. "A what?"
"A device that aligns biological frequency to a set harmonic baseline. Think of it like an audio equalizer — for blood."
Theo grimaces. "You make it sound like a disease with a rhythm."
Nathaniel's eyes flash red for a moment. "That's exactly what it is."
He picks up a screwdriver and begins prying open the casing. "If this tuner uses blood-based resonance, I can reverse-engineer the waveform. Maybe find the original frequency Eris used — the one that turned me."
Edison and Kingsley exchange a glance. "You think you can decode it?"
Nathaniel smirks faintly. "I'm an engineer. That's what we do — we solve what shouldn't be solvable."
Theo mutters, "And occasionally blow things up."
Nathaniel grins. "That too."
He connects the device to his laptop. The screen flickers, then displays a jagged waveform — oscillating in irregular bursts, almost like a heartbeat.
Nathaniel stares. "This pattern... it's incomplete. There's a missing resonance node — one that could stabilize the transformation process."
Edison whispers, "Which means?"
Nathaniel looks up slowly. "Someone's trying to create a perfect hybrid."
Outside, thunder rolls across the sky. The light in the dorm flickers once, twice, before stabilizing.
Theo finally breaks the silence. "So what now? You're not thinking of going after them again, are you?"
Nathaniel closes his laptop. His crimson eyes reflect the screen's glow. "I don't have a choice. If they're experimenting on humans — if they're perfecting it — then I need to stop them before they finish what they started."
Edison nods. "Then we're with you."
Theo throws his hands up. "Brilliant. Just what I wanted — a supernatural task force led by a half-vampire engineer. This'll end well."
Nathaniel smirks faintly. "You can back out anytime."
Theo crosses his arms. "Hell no. Someone's gotta make sure you don't fry yourself trying to save the world."
Edison chuckles. "Then it's settled."
Nathaniel stands, his long coat catching the dim glow of the room's lamp. "We start tomorrow. I'll analyze the tuner, trace the harmonic residue, and locate the nearest lab."
Theo glances toward the window, where lightning arcs across the horizon. "And after that?"
Nathaniel's expression hardens. "After that... we find out just how deep the Gravenholt legacy really goes."
The rain intensifies, drumming like war drums against the glass.
For a fleeting second, Nathaniel feels the pulse beneath the floorboards again — faint, rhythmic, alive.
The same vibration that's been haunting him since that night.
The same hum that whispers one truth he cannot escape.
The curse is evolving.
And he is its next equation.