"And what about the Delay Casting technique? You're the only one here who can perform it at that level. How do you explain that?"
"That's the second problem," Rein replied, turning toward the faint ring-shaped trace on the floor before the Forbidden Section.
"The Delay Casting used in this case was placed with precise control—both in position and in timing. Master, you know there are two types: direct-trigger and preset."
Rachel nodded.
"Exactly. Which means that even if you were outside the library, the spell could still activate here."
Rein let a corner of his mouth tilt upward.
"Correct. But with a critical limitation: the caster must remain within a fifty-foot radius."
Ingrid's breath hitched. Her mind flashed back to the battle—Rein had used Delay Casting multiple times, but never beyond that distance. And during the battle, he had been more than three hundred feet from the library.
Rachel stared at him silently, her crimson eyes radiating frost.
"A distance limit alone isn't enough to convince me."
Rein inclined his head, accepting the challenge.
"I can prove it. I don't like revealing this, but it's necessary for the explanation. Let me ask you something, Master Rachel: is there any spell known that can function without regard for distance?"
The elf shook her head slightly, red hair shifting with the motion.
"As far as I know, no. All spells have limits. The farther the target, the more mana required—and delaying a spell for long periods drains exponentially more."
At that moment, a pale white sigil flared into existence behind Rachel—circling once before releasing a brief burst of light across the shelves—then fading back into the dimness.
"What!?"
Belle snapped sharply.
"There's a strict no-spell rule in the library! Are you incapable of understanding that!?"
Rein lifted a hand politely, as if asking permission.
"Apologies. It was necessary. Master Rachel?"
The elf didn't wait. She raised a hand, flicking her fingers with casual authority. The fading glyph froze instantly—suspended in mid-air, locked in time like an insect trapped in amber. This ring was far clearer than the earlier one, still fresh with mana patterns intact.
Now Rachel's brows drew tight.
"What is this? Your Delay Casting's structure… why does it look like this?"
Rein gave an awkward smile and scratched his head.
He explained the fragments of Rein's earlier memories that had resurfaced moments ago—omitting anything related to Dr. Rhys, of course.
"It's embarrassing, but… I had to dismantle the original formula. The original range was about three hundred feet, but the mana and concentration required were absurd. I'm guessing the original formula demanded a Stratosphere-tier mage. But I—only a Troposphere-tier mage—couldn't make it work, no matter how I trained."
"So I engaged in a trade-off. I sacrificed range—capping it at fifty feet—to stabilize the mana consumption. The result is a delay limit of one hundred eighty seconds, but with a drastically reduced cost. It allows for rapid, consecutive deployment."
"You're insane!"
Both Rachel and Ingrid shouted at the same time.
Rachel's crimson eyes whipped toward him.
"Do you understand how dangerous it is to modify spell formulas of this tier? A single mistake in the structure and the mana backlash would kill even a Stratosphere-tier mage."
Rein shrugged lightly, unbothered.
"I tested it before fighting the warlock. Planned to use it as a trump card. You saw how that turned out—I lost anyway."
Rachel bit her lip and exhaled slowly before summarizing:
"Very well. The formula structures don't match—and in your current condition, you can't cast Lightning Bolt at all. Correct?"
Rein smiled and nodded.
"Correct."
"Wait…"
Belle's voice cut through the air.
She stepped forward, eyes trembling under the dim blue light.
"Editing spell formulas… that's not something possible for a first-year mage. Even professors need a decade of study to grasp fragments of high-tier formulae. Are you expecting us to believe you simply 'modified' one?"
Her voice carried something that wasn't quite anger anymore.
Her final words faded, but the echo lingered in the library's vaulted silence.
Rein looked back at her, his expression unreadable.
"Impossible… is correct," he said quietly.
For a split second, the library faded. His mind drifted back to another life—a bright studio, a camera lens, Dr. Rhys explaining quantum mechanics to an audience that just wanted a simple answer.
Simplifying the complex is harder than solving the equation.
"But everything we call magic was considered impossible—until someone understood its mechanism in a different way. Wouldn't you agree?"
Master Rachel narrowed her eyes. Her expression stayed composed, but something in her gaze shifted.
"…Go on."
Rein slowly lifted a hand. A thin line of light followed the motion of his finger, sketching a faint circular arc in the air before dissipating.
"You know well, Master Rachel, that every spell is governed by what we call the Mana Equilibrium Equation. If that equilibrium collapses, the magic circle destabilizes and breaks apart."
Rachel gave a slight nod.
"Yes," she said slowly. "It's hard, but it is indeed the foundation of all magic."
"Exactly," Rein replied. "That's where I started."
His voice remained level, but a faint gleam lit up in his eyes—the unmistakable glint of someone finally allowed to analyze something they loved.
"In that equation, the key variables are Time (T) and Distance (D). Normally, both are fixed within the magic circle to prevent mana dispersion. But I wondered… what if instead of fixing them, we make them dependent on each other?"
Ingrid's brow knit tightly.
"Dependent… how?"
"Instead of locking Time as a constant, I tied it to Distance using a decay coefficient." He traced a curve in the air, the blue light bending sharply. "This forces the spell to weaken logarithmically with distance, rather than shattering the circle entirely. It bends the rule, rather than breaking it."
Rein traced another glowing curve in the air. A soft blue mana graph appeared—dropping smoothly along a logarithmic arc—its reflection glinting in Ingrid's glasses.
The blonde girl stared blankly.
This story originates from Royal Road. Ensure the author gets the support they deserve by reading it there.
"What is he even talking about…"
Master Rachel's frown deepened. She absorbed every word, her gaze sharpening as Rein continued—the tone of a lecturer returning to a familiar podium.
In his mind, the fragmented memories of "the previous Rein" aligned like puzzle pieces.
No wonder the previous Rein muttered about 'killing time by solving calculus problems' in the Mana Realm…
Rein thought to himself, amused.
In human history—during the 16th and 17th centuries—astronomers and navigators faced similar problems. Calculations involving long decimals and trigonometric angles were so tedious that they sought ways to simplify multiplication into addition. And thus the concept of logarithms was born.
Spell circles, with their layered trigonometric structures and sensitive positional numeric values, were not so different. Most mages never questioned the formulas. They simply repeated what was taught—never understanding the underlying mathematics.
But the previous Rein had understood. Someone must have taught him. Or he had learned it before ever enrolling at Arcadia.
Rein exhaled once and gestured toward the glowing graph.
"You see? A standard Delay Casting decays linearly—the longer the delay, the more unstable it becomes until it collapses entirely. But I modified mine so the decay follows a curve, preserving stability within a radius of about fifty feet."
A faint hum resonated from the crystal lights overhead.
Librarian Belle stared at him, her eyes hard as polished stone.
"You speak nonsense. This sounds like someone twisting magical law into mathematics. You don't understand the architecture of spellcraft at all."
But Rein simply smiled softly, without irritation.
"I understand it sounds that way. But from the perspective of physics, it's simply adjusting the rate of energy dissipation in a closed mana system."
"Physics…? What is that? And just what are you talking about?"
Belle's voice trembled between anger and confusion—her skepticism palpable, her distrust layered beneath every word.
Rein met her gaze.
"So you're saying… a spell can be reshaped to operate according to variable energy dynamics, not the fixed-mana model."
"Yes," Rein replied, nodding. His eyes brightened immediately.
"Because mana is, fundamentally, just another form of energy. Until now, we've simply been describing it in the wrong language."
His tone was calm—almost serene—yet firm enough that even the air in the room seemed to still.
Ingrid's breath grew so faint it was barely audible.
Rein stepped forward, stopping in front of the bookcase where the residual magic circle still lingered.
"My Delay Casting technique channels mana along a time-curve constrained by distance. So even if someone tried to copy it, it wouldn't work. The parameters are tied to my own internal mana structure."
He lifted his gaze and met Master Rachel's eyes.
"That's also why the circle used in this case is completely different from mine. It isn't a curved equation—it's the traditional linear model."
"Impossible…"
Belle's voice trembled, the quiver unmistakable.
"You're telling me you've discovered a way to manipulate mana through time and distance without breaking a spell's structural integrity?"
Rein gave a simple answer.
"I only questioned something everyone assumed was impossible."
Rachel raised a hand to her lips, her expression tightening.
"But the evidence before me supports everything Rein just said."
At last, the elderly librarian fell silent.
The elf woman kept watching the boy—longer than necessary—her crimson eyes wavering between awe and suspicion.
Finally, she exhaled softly.
"A first-year student who can think like this… is more terrifying than the murderer."
Rein's mouth curved slightly. "Probably."
Ingrid stared at him and said nothing.
Belle, meanwhile, simply stood motionless—her expression unreadable.
"Even if I accept your explanation," Master Rachel said slowly, her voice low and resonant, "that still doesn't free you from suspicion."
"However… when morning comes, the Forensic Magic Department will conduct a formal investigation."
Rein nodded.
"That's fine. At the very least, I've probably irritated the real culprit by now."
"That entire explanation about the spell formulas... that was just a cover, wasn't it? You know more than you're letting on." Ingrid seized the opening immediately.
Rein rubbed the back of his neck, looking genuinely troubled.
"Well... 'knew' is a strong word. Let's just say I have a hunch." He glanced sideways, his voice dropping to a murmur. "But there's just one little thing that doesn't quite fit. Just one small detail... until I figure that out, I'd rather not embarrass myself by guessing wrong."
Rachel pressed on.
"And what would that hunch be?"
Rein arched a brow—then shifted the subject.
"Well, since I'll be here until morning anyway… may I request permission to sit in on the interrogation of the other seven students?"
Rachel paused, narrowing her eyes as if weighing something. Then she nodded.
"You may. But you are to remain silent. You are not allowed to interfere in any way. You are still under suspicion."
"Master Rachel, this is—" Belle started, scandalized.
But the elf raised a hand.
"I've already decided. Belle, return to your counter."
The elderly librarian let out a long exhale, suppressed her irritation, and turned away—vanishing into the dark aisles between the endless shelves.
Rein asked for permission to inspect the area once more before returning to the counter. Rachel considered for a moment, then nodded—but restricted him to no more than three minutes. Even so, she followed closely behind him. She did not allow the suspect to walk unguarded for even a single step.
The silence between them settled like dust in the library's eerie calm. Rein glanced around, his eyes catching the flicker of a dying magic lamp.
"Yeah… low-budget horror flick," he muttered, more to himself than anyone else.
The black-haired boy moved slowly, threading his way through the towering rows of shelves—walls of knowledge stretching endlessly in every direction. His footsteps echoed softly against the stone floor. His pale hand slid along the spines of books, pulling a few volumes out, flipping through a page or two, then returning them with meticulous care.
All the while, he questioned Ingrid about the contents of the section. The blonde girl answered each of his casual questions in a soft, uncertain voice. Her expression showed nothing but confusion.
Why was Rein strolling through the library like he was out for a leisurely walk… in a situation like this?
Yet the boy's eyes remained unnervingly calm. Ingrid, by contrast, felt herself growing more anxious by the second. Master Rachel, who walked silently beside them, was also strangely composed—as though she and the boy were conversing without words.
Rein gave a casual yawn, covering it with the back of his hand.
"You know, if this place had popcorn, I'd consider it a day well spent."
He paused.
“Something felt familiar.” he murmured under his breath. His fingers lingered on the spines a fraction longer than necessary—the way they did when a detail refused to stay where it belonged, when memory reached for something just out of reach.
Rachel continued shadowing him quietly.
When the three minutes elapsed, Rachel spoke, her voice soft yet firm.
"Your time is up, Rein."
He stopped, glanced once more at the forbidden shelves, and breathed out lightly.
"Understood," he replied, following her back without protest.
Ingrid walked beside him, her face still full of questions.
"Did you find anything?" she whispered, worry flickering in her eyes.
Rein only shook his head and gave her a small smile.
"Seems today just isn't my lucky day."
"You actually believe in luck?"
Ingrid lowered her voice as if afraid someone might overhear.
Rein chuckled under his breath.
"Luck is just a variable we can't calculate yet, Ingrid. Maybe today... it was simply a matter of timing."
She frowned at him.
"What are you talking about now…?"
But Rein didn't answer. He just lifted one corner of his mouth and kept walking, hands shoved in his pockets, already drifting elsewhere.
When the three returned to the central counter, they saw the remaining seven students already gathered. All of them wore the same expression: pale, strained, and unbearably tense.
Belle was standing with her back against the counter, arms folded tightly. She had clearly been addressing the students moments before, but the instant she saw Rachel approaching with Rein, she fell silent. The elderly librarian stepped back behind the counter—a wordless declaration that, from this moment on, the authority of the investigation belonged entirely to Master Rachel.
Rachel swept her gaze slowly across the group.
"Good… it seems everyone is present."
Her voice was even, but it rang across the hall with undeniable weight.
Rein forced his eyes half-open, taking in the group. Seven kids. Too many. His head throbbed.
Two boys and five girls cautiously stepped forward.
One girl stood with her right arm heavily bandaged, her posture sagging with exhaustion. Rein recognized the injury immediately—Tara. The girl he had saved earlier, along with her friend. The one who fell. He remembered the friend's scream—a high-pitched sound that had saved them both by sheer annoyance.
His gaze drifted to Tara's friend: the short-haired blonde girl, still ghost-white with shock. The two stood slightly apart from the others, as though avoiding someone's gaze.
Now they're avoiding everyone. Figures.
On the opposite side stood a tall, slender boy with ash-grey hair, fidgeting nervously beside a girl with long silver-grey hair. Her cold, sharp eyes and haughty posture made her instantly recognizable.
Ah. Those two.
The memory surfaced instantly: the staircase hall, the girl screaming orders, the boy chanting 'Sister Mirela' like a broken record. Their haughty posture remained, even in fear—unmistakably noble and undeniably idiotic.
Another group clustered together—a boy leaning heavily against a table, the very definition of dead weight, flanked by two girls. One sobbed openly; the other, wearing silver-rimmed glasses, patted her back in a futile attempt at comfort.
The Canteen disaster. Rein remembered the ten zombies he cleared just to get them out. Lucien was with them. Now he's the one missing.
Now, all seven stood in a line before him like a frozen tableau.
Rein leaned against the far edge of the table, completely silent—not looking at anyone, not speaking. His eyes were half-lidded, unfocused. A slow, utterly bored yawn stretched his jaw, the faint sound surprisingly loud in the heavy silence.
Ingrid glanced at him and said nothing. She knew better than to interrupt.
Rachel raised her hand. A faint blue arc of mana shimmered through the air. Her voice dropped into a cold, clear register:
"Let's start from the beginning. One at a time."
These entries expand the lore and mechanics introduced in this chapter.
Completely optional—read only if you enjoy diving deeper into the system.
Spell Techniques
Delay Casting – Modified Version (Rein)
A powerful and unorthodox technique developed by Rein. Unlike traditional delay casting—which decays linearly over time and distance—Rein’s version uses a logarithmic decay curve, tying time (T) to distance (D) via a decay coefficient, thereby stabilizing the spell within a radius of ~50 feet.
– Requires less mana than traditional long-range delay casting.
– Allows rapid, consecutive deployment within a limited radius (50–100 ft).
– Parameters are bound to Rein’s internal mana structure, making the spell nearly uncopyable.
– Rein created this version by dismantling a higher-tier formula and modifying it for Troposphere-tier usability.
“It bends the rule, rather than breaking it.”
Delay Casting – Original Version
Category: Arcane Technique
Tier Requirement: Stratosphere-tier or above
Type: Pre-cast Spell Deployment
Description:
Delay Casting is a high-level arcane technique that allows a mage to cast a spell in advance and delay its activation to a later time or specific trigger. It is often used for traps, battlefield control, or tactical ambushes.
Mechanism:
Comes in two primary forms:
– Direct-trigger: Activates manually or by remote signal.
– Preset: Activates based on fixed conditions (e.g. time, movement, presence of a target).
– Spell structure is preserved within a dormant magic circle, held in stasis until triggered.
– The spell's integrity decays linearly over both time and distance, reducing its efficiency if not triggered promptly or if cast too far from its origin point.
Performance Parameters:
– Maximum Range: Up to ~300 feet
– Mana Cost: High—increases exponentially with range or delay duration
– Decay: Linear over time and distance; longer delays = lower stability
– Complexity: Requires mastery of advanced spell structure preservation
Limitations:
– Inefficient for rapid-response combat due to preparation time
– High mana consumption discourages repeated use
– Vulnerable to environmental disruption (e.g. anti-magic fields)
Tier Restriction:
– Typically accessible only to Stratosphere-tier mages or equivalent theorists.
– Considered too unstable for lower-tier mages to execute without collapse or misfire.
Mana Equilibrium Equation
An advanced arcane formula taught in third-year mage theory at Arcadia Academy. Governs the stability of mana within spell circles. If the equilibrium is disturbed, the spell collapses.
Considered difficult and often failed by students.
– Used by Rein as a foundational concept to reconstruct Delay Casting.
Spell Decay Curve (Logarithmic Model)
A new model devised by Rein where the spell’s strength decays logarithmically rather than linearly. This allows:
– Longer retention of spell structure without full collapse.
– Adaptability within a certain radius.
Energy-Based Magical Modeling
Rein proposes that mana is simply another form of energy, and can be modeled using physics principles, including logarithmic decay, energy dissipation, and closed system dynamics.
– This idea shocks Rachel and Belle, who view magic and physics as separate realms.
– Rein implies magic formulas can be reverse-engineered like scientific equations.
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— Re:Naissance