The three of them arrived at the Magic–Combat Combined classroom.
Of course, since Vasileo didn’t know what was going on, he was nervously watching the two of them.
Inside the academy, they had been sniping at each other with every single step, but as soon as they stepped outside the building, they went quiet as if by magic. The atmosphere between them even felt mild.
To Vasileo, who had been worried about when they might explode, it was a rather baffling sight.
“Now, stand right there.”
Frondier had Vasileo move to the center of the classroom. Then, together with Elodie, he stepped a little ways back and watched him.
“Let’s begin.”
“...Begin what?”
Vasileo had no idea what was happening.
Frondier smiled faintly.
“The final question on your exam. The bonus problem.”
“...!”
At that instant, Vasileo thought:
Here it comes!
So he really got angry because my answer was that ridiculous!
Even so... why is Elodie-sensei here too?!
Was my answer that disrespectful?
What is this? A new form of teacher bullying?
“U-um, I didn’t write that answer as a joke—”
“Show me.”
“Huh?”
Still smiling, Frondier extended his hand.
“Show me your ‘answer’ right here. During the exam, you couldn’t construct the formula, so I couldn’t verify it.”
“...Ah, what?”
Vasileo still couldn’t keep up with what was happening.
At that point, Elodie spoke.
“That last problem required full mastery of theory and knowledge—and, more importantly, the absolute intelligence of a mage: intuition. Without that, you couldn’t solve it.”
“...Ah, r-right?”
“So try it here. The answer you came up with for that problem. Show us your solution process.”
Vasileo blinked.
Show the solution process? Did that mean his answer was at least somewhat close to the real thing?
But why are they suddenly so kind and gentle? Weren’t they just fighting earlier?
It was oddly frightening.
Vasileo scratched his head, then took something out of his pocket—a crumpled piece of paper. He unfolded it and frowned as he stared at it.
At the sight, Frondier and Elodie let out small, quiet laughs.
Vasileo glanced at them and asked cautiously:
“Um... is it okay if I talk while I do it?”
“Of course. That’ll be even better.”
With Frondier’s cheerful permission, Vasileo nodded.
“Um, well, first of all... this formula doesn’t manifest as magic.”
“Why not?”
“Because, um... well.”
Vasileo looked around, spotted a suitably long stick, and began drawing the magic formula on the ground. Naturally, he kept glancing back and forth between it and the paper to check that he was drawing it correctly.
“To explain why, you first need to understand the theory behind the structure of formulas.”
“Because the formula in the question was constructed incorrectly?”
At Frondier’s question, Vasileo shook his head.
“Even though it was constructed properly, it still doesn’t manifest. That’s why theory is needed—to see whether the theory itself is wrong, or whether the interpretation of the theory is wrong. You have to know where the mistake lies.”
Gradually, Vasileo became calmer. As he spoke, a trace of conviction appeared in his eyes.
“A magic formula is a magical language. If fire had a will, and if it spoke of what it was burning; or if waves spoke of what shape they would take next; or if rain spoke of when and how it would fall—then those would be the languages they speak. We interpret those languages and mimic them.”
“But we aren’t fire, or waves, or rain.”
Elodie said, and Vasileo nodded.
“Right. That’s why our words are borrowed. Since we aren’t truly those beings, we can’t become them. That’s why magic is temporary—it doesn’t persist. It’s not matter, but a phenomenon.”
Both Frondier and Elodie nodded at that explanation.
“Then what’s wrong with the formula from the last question?”
“The problem isn’t in the formula itself. The issue is how it was transcribed.”
Vasileo pointed at two spots in the formula he had drawn on the ground where the lines overlapped.
“These two parts are where three separate formulas intersect. This in itself isn’t a problem—many formulas overlap. This one looks like it was assembled that way.”
“When you say ‘looks like,’ you mean it actually isn’t?”
“...”
Vasileo’s words stopped there.
He pursed his lips and spoke in a smaller voice than before.
“...Maybe?”
“What kind of answer is that?”
“From this point on, I’m kind of lost myself...”
Frondier smiled leisurely.
“Then think about how you got lost. What led you to write that answer in the middle of that confusion.”
“How I got lost...”
Vasileo murmured softly and blinked several times.
Then he crouched down low, tracing the formula he had drawn with his finger.
“It’s certain that this formula follows theory. But it also clearly has a different form from ordinary ones. And these formulas are ones students already know. If you combine them properly, it should produce a ‘floating flame’—similar to a will-o’-the-wisp, radiating heat even without contact, a movable attack spell. But even though the same formulas are used, the shape of their combination is different. So what’s the difference? No—why does a formula combined in a different shape still not violate theory?”
Vasileo now spread out the three formulas side by side.
“Most activation failures happen due to circuit collisions. But just overlapping lines doesn’t cause collisions. That only happens when mana flows in opposite directions, or one circuit’s mana output overwhelms the other. Yet this formula shows neither.”
As he spoke, his eyes grew slightly unfocused. It was the same look he’d shown in class before.
Frondier thought,
He’s focused. He’s not explaining this for us—he’s verbalizing his thoughts so that they can progress.
Of course, that was intentional. Frondier had brought him here precisely to make him explain.
Right now, Vasileo was standing on the threshold of realization. He just didn’t know it yet.
Within Atlas, while other students laughed and chattered, excited for the upcoming vacation, it would’ve been hard for him to notice how close he was to an epiphany.
But enlightenment doesn’t come at some grand place or time. It arrives without warning—within an ordinary moment.
Reaching beyond reason and prediction—that is what intuition is.
And for a magician, intuition is a lifeline.
“So then I thought about three-dimensionality. At first, I wondered if one of these formulas was meant to be standing upright.”
Vasileo stood up.
Using his magic, he drew the formulas again in the air.
“But if you do it like this, a vertically drawn formula can’t even be written on paper, and the collisions get worse. Unless I find out why the collisions occur in the first place...”
Frondier quietly watched him.
He had already given him enough hints.
Just bringing Vasileo here and telling him to explain was the biggest hint of all.
What Vasileo lacked was confidence. Unsure whether his answer was right, he couldn’t push forward against what others said.
But now Frondier was telling him:
Up to this point—you’re right.
So don’t turn back. Take one more step.
“...Maybe it’s not that kind of three-dimensionality...?”
Vasileo murmured.
Frondier looked at Elodie.
With his lips, he mouthed: I think I won.
Elodie’s lips shaped: Not yet.
Vasileo looked over the scattered dots and lines he had spread apart.
“A collision means two opposite flows of mana crashing. But when viewed as a flat plane, all the flows here move in the same direction. Yet it still fails to manifest. Meaning—there’s an opposite flow invisible on the plane.”
So, does it appear only when seen in three dimensions?
Then, Vasileo suddenly began doing something strange.
He went beyond separating the three formulas—he started rearranging the individual dots and lines within one formula, stirring them about.
Elodie’s mouth fell open the moment she saw it.
The mana lines forming the formula are holding their positions even though he scattered them.
For most mages, the circuits within a formula last only an instant—built solely to cast a spell, not to maintain it.
For a magician, constructing a formula is like mental arithmetic—it vanishes from the mind as soon as it’s done.
But Vasileo didn’t let it vanish.
It was as if, after solving a long calculation, he still remembered the first equation.
Frondier’s eyes widened too.
If he can do that, then three-dimensional schematics would be meaningless to him.
He might not even understand them—because by holding the image in his mind without letting it fade, he’s ◆ Nоvеlіgһt ◆ (Only on Nоvеlіgһt) already performing the same function as a 3D design.
“...I understand now.”
Then Vasileo lifted his head and looked at Frondier.
Frondier said, “Show me.”
Vasileo nodded, gathered the formulas together again, and lifted them until they were at eye level. By that point, Elodie let out a quiet, astonished laugh.
This kid’s a genius.
It was Elodie herself who certified it.
Vasileo spoke.
“The opposite flows that collide, and the reason they’re invisible on the plane—it was simple once I saw it. The basic, fundamental ‘Stasis’ formula we all know...”
Vasileo spread the combined formulas before him and drew one more line and dot beneath them.
“...actually has one more circuit. A separate formula positioned at a slightly higher elevation.”
As he spoke, the completed formula took shape. The whole structure now embodied height difference: its circuits divided by vertical layers, avoiding collisions and forming new detour pathways for mana.
In other words, the truth behind the formula in Frondier’s final problem was—
“When you look at it from above, it becomes the exact shape you wrote on the exam paper!”
“──Correct.”
Frondier nodded, smiling in satisfaction.
The ‘Stasis’ formula, in truth, has one more circuit—one not visible on a flat surface, occupying the same position but at a different height.
When drawn as a perfect flat plane, using Stasis causes the circuits to overlap. That overlap reproduces the effect without needing an additional drawing.
But when viewed three-dimensionally, that higher circuit interferes unpredictably when combined with other formulas.
All magic that incorporated the ancient Stasis formula had been designed to avoid that position. Yet no one had ever understood why.
On a flat plane, no matter how they examined it, the answer never appeared. Still, as long as the spell worked by avoiding that zone, no one questioned it further.
“Then, want to try manifesting it?”
“Huh?”
“You solved the formula’s error and rewrote it yourself in three dimensions. So what kind of spell do you think that actually is?”
“Uh? Well, it should be a ‘Floating Flame,’ right?”
“Then try it.”
At Frondier’s words, Vasileo tilted his head slightly, but in any case, he infused mana into the formula.
Then—
“Ugh, w-whoa...!”
His mana drained out in chunks. That expression wasn’t even enough; nearly his entire mana reserve was sucked into that single formula.
“W-what is this...!”
Fwoosh!
And before his eyes appeared a flame.
At first glance, it looked similar to the “Floating Flame” Vasileo had just described.
But that dreadful heat, that ominous color that warned not to approach carelessly— it was so ferocious that even Vasileo, the caster himself, flinched in fear. It felt as if the flame possessed a will of its own, one that might devour him whole.
“W-what is this...?”
Vasileo started to ask, but then looked back at the flame.
He had seen it somewhere before. Or at least he thought he had. It wasn’t some trivial “Floating Flame.” It was on a completely different level— one of the very spells he had once admired and dreamed of mastering.
“Well, that is...”
Frondier, sensing the perfect moment to explain, tilted his head slightly.
“Elodie, what was that one called again?”
At his words, Elodie let out a deep sigh.
Frondier’s casual tone— addressing her without honorifics— startled Vasileo for a moment.
“Hellfire.”
Elodie explained:
“One of the two spells combined within my original technique, ‘Rise of the Vermilion Bird.’”
