"How are your studies going, Belle?"
Alia asked.
Despite the fact that it was winterbreak, Alia and Belle never neglected advance studying.
The second sester was right around the corner, and things would get harder from there on.
"I don't know. I've hit a roadblock recently."
"How so?"
Alia curiously tilted her head. It wasn't like Belle, who, for Alia, was academically smarter than her.
After all, Belle received advanced education in Milis during her middle–school years.
Which must've been why Belle's practice regarding magic was peculiar.
Each continent practiced magic differently. For Holy Britannia, they took pride in the expertise of their basics—maximizing its efficiency to the brim.
Of course, there were theories they could study on the internet.
But for Alia, it was too complex. Not in the way where she couldn't understand it, but it complicated the norm she was already used to.
"I'm having a hard ti wrapping my head around the Divergence Law."
Belle admitted.
"The Divergence Law?"
Alia blinked, finding the term unfamiliar.
Belle was always diving into complex topics that seed far removed from what they learned in class.
"Yeah, I've been trying to implent it in my wind magic."
Belle continued.
"You see, the Divergence Law focuses on the flow and dispersion of mana in three-dinsional space, particularly when applying it to elental magic like wind."
There she was again, going all nerd mode.
"For the past four months, I've been researching how the law can enhance the directional force of wind skills, but the problem is maintaining stability when increasing the divergence factor beyond a certain threshold."
"...."
Alia stared, completely lost.
"You see, when mana diverges from a central point, it creates turbulence, right? But if I could control the divergence vectors, I could theoretically amplify the wind's strength without losing control."
Belle let out an exasperated sigh.
"But I've barely scratched the surface. The calculations are…. too complex. I've spent months on it, but the correlation between divergence and velocity is... tricky."
Belle paused, finally noticing Alia's blank expression.
"Uh…. Yeah."
She had no idea at all.
"Sorry, it's just been frustrating lately."
"I get it…."
She didn't get it at all. While Alia was putting her own theories into practice, it was just the basic Carlson's Earth Attunent Law.
Sothing that all mages of the [Earth] affinity practiced.
While Alia was gifted with the [Armant] affinity, according to her father, it derived from the [Earth] affinity.
"So…. do you need help?"
"I'm glad you asked."
Belle smirked. Alia felt a sudden chill down her spine.
In fact, her head was already hurting.
"Co."
Belle dragged Alia. Before Alia realized it, blinking her eyes, they were already at the Central Library.
"Uh…."
"See this."
It was all too sudden. Alia barely had ti to think, and she was already sitting beside Belle.
Books containing laws and theories appeared on the table. Belle, donning her glasses,, a pen resting on her hand.
"So basically, this…."
Belle didn't waste a second. She flipped open her notebook, pages filled with equations, diagrams, and scribbles in the margins.
"Okay, so I've been stuck on this particular part for weeks."
She began, her pen tapping against the page.
"You see, when calculating the mana flow divergence, you have to account for the dispersal rate of mana particles. So, I started with the basic divergence equation—divergence of the mana vector field equals the mana density over ti—pretty straightforward, right?"
Alia blinked.
"Uh–huh…."
"Then, you apply the directional force to the wind current using an inverse square law to account for the expansion of the skill's radius as it propagates….."
"...."
Alia's brain had already checked out after "inverse square law."
She was nodding, but her eyes glazed over as Belle rattled on about flux density, divergence integrals, and boundary conditions.
"Integrate…. Divergence…. velocity field…. the numbers don't align….. Density…."
Belle continued scribbling furiously, drawing complex formulas that looked more suited for a math genius than a mage.
Belle pointed to a specific formula on the page.
"See, this is where it gets tricky. I tried using a Gauss theorem variation to simplify the boundary constraints, but even then, the divergence vector still doesn't align with the wind force…."
Alia stared blankly at the notebook, Belle's words barely registering.
She was so far out of her depth, it felt like she was mumbling a bunch of theoretical jargons.
But as her eyes drifted across the page, sothing caught her attention.
There was a small error in the equation—sothing simple, like a missed variable or a misplaced symbol.
Alia didn't even know what half of this ant, but she recognized that sothing wasn't right.
"Uh, Belle?"
Alia pointed at the formula.
"Hm?" Belle looked over, confused. "What is it?"
Alia hesitated.
"I think… you missed sothing here. Like, this variable should be accounted for when you're distributing the mana, right?"
Belle squinted at the page, following Alia's finger.
"Wait… oh."
She blinked, then looked back at her notes with wide eyes.
"Oh my god. You're right!"
Alia blinked, then stared at her.
"I am?"
"Yes! I completely overlooked that! That's why the flux density wasn't stabilizing! If I just modify the boundary conditions here…."
Belle grabbed her pen and began scribbling furiously, recalculating the formula.
As she worked, Alia sat back, utterly lost, but relieved that she had sohow helped.
"Alia, this is brilliant! How did I not see this? You just saved weeks of work!"
"Uh, yeah…. no problem."
She still had no idea what she'd just done.
"...."
Seeing the books scattered around her, Alia noticed it wasn't the conventional textbooks she was used to.
They were clearly Belle's evident by the scribblings, just on the cover page.
'....What the hell are these magic circles?'
Alia flipped through the pages of Belle's textbook.
These weren't the straightforward equations she was used to seeing in Holy Britannia's textbooks—these were far more advanced.
'So this is Milis magic…?'
She had heard of how fancy their practices were, but she had never realized it was to this extent.
However, she was unsure how efficient they were. It all looked like fancy magic jargon.
"Hm?"
She paused as sothing caught her eye.
"Quidell's Theorem…."
She read aloud.
Her brow furrowed. She had never heard of this theorem before.
Curious, she scanned the paragraphs that followed, trying to make sense of the dense text.
"Quidell's Theorem focuses on optimizing mana flow in [Wind] affinity magic by restructuring the magic circle to allow for faster divergence and circulation of mana within the circuit itself…."
Alia trailed off.
"The theorem suggests that if properly implented, a Wind mage could reduce casting ti by nearly 25% by rerouting the mana through auxiliary pathways…."
Alia blinked.
She wasn't a Wind affinity mage, but the theory behind it was intriguing. And if magic circuits were modifiable, maybe—
No, it was far-fetched.
Magic circuits were extrely difficult to alter, and the risks of attempting it were well–known.
But if she could succeed, she imagined how much faster she could cast her skills, even those unrelated to wind.
"Implenting Parkinson's Law alongside Quidell's Theorem results in an increase in mana velocity. This velocity compensates for the inherent instability caused by the initial divergence of mana flow…."
The page was filled with complex formulas, with terms and symbols she didn't fully understand.
"The boundary conditions for stability are set by the proportionality constant derived from the divergence formula...."
Alia felt her head spin as the words ran together.
She stared at the calculations, trying to wrap her mind around it, but it was like staring into a foreign language.
Belle, still focused on her own notes, glanced up briefly.
"Did you say sothing, Alia?"
"Uh... nothing, just... reading about this Quidell's Theorem thing."
She replied, still staring at the page. "This stuff is insane. I don't even know what half of this ans."
Belle looked up, adjusting her glasses.
"Oh, Quidell's Theorem? Yeah, it's ant for Wind affinity mages. The whole idea is to boost their casting speed, but it's tricky because the magic circle modifications are complex. And if you don't get the flux density right, you risk destabilizing the entire skill."
Alia's mind was racing, not so much at the thought of Wind magic, but the possibility of applying the principles to her own.
Her magic swords were already fast, but what if she could cut down the casting ti even more?
"Belle, could this work for soone who doesn't have Wind affinity? Like... if I tried to modify my magic circuits to use sothing like this, would it make my casting faster?"
Belle paused, raising an eyebrow.
"Well, in theory, yes. But magic circuits aren't ant to be tampered with lightly, Alia. It's not just a matter of plugging in a new formula. You'd have to completely restructure how your mana flows through your body. It's risky."
Alia's eyes glead with the potential.
"Risky…. but possible?"
Belle sighed, seeing the look of excitent in Alia's eyes.
"Yes, it's possible. But it's like surgery—you get one thing wrong, and the whole thing collapses."
"Hm…."
Her mind was already racing with possibilities.
If she could pull it off... her magic could beco faster, more efficient.
She could almost feel the speed of her magic swords in battle, slicing through the air faster than ever before.
"Wouldn't hurt to try. Here…."
Belle rummaged through her backpack and placed sothing on the table.
"I have an extra notebook. You can try formulating it there for now."
Alia blinked her eyes once more for a second.
Then a sudden determined look flashed across her features.
"Give a pen."
Finally, sothing that would take her mind off of Brandon for a while.
***
"The summit, huh?"
Bellion straightened his back, leaning on the chair.
He had just received mail—regarding Imperial Academy's invitation for the upcoming summit.
He was unsure whether to accept it.
After all, things were quite shaky between Milis at the mont.
It felt like all his efforts were put to waste, now that the truth laid bare to the world.
That the entire situation wasn't exactly what he thought it was.
The war regarding Milis.
It was nothing but a sche to ignite hostility between the two continents.
But was it actually the truth?
From the reports, there was a military–man from Milis during the auction raid.
It was odd, and sothing didn't sit right with him.
Additionally, he had a lot more problems in his hand.
The Archbishops were within their borders, most probably, scheming at the mont.
And he had no idea who they were!
His head throbbed, a sharp migraine buzzing in his head.
"Haaa…."
Too many problems.
They had just lost their greatest asset recently—Evelyn Cessna.
And now, they were supposed to accept that Milis wasn't hostile to them at all?
However, as Bellion read the contents of the mail, his brows raised.
"A eting?"
It was also an invitation for his participation—regarding a eting between nation leaders.
If…. he accepted the proposal.
Then his questions would most probably be answered.
"Haaa…. Should I?"
He was still quite reluctant.
He had attended the summit a few tis during his younger years.
All he could rember were the ridicules against Holy Britannia.
Their magic wasn't as fancy as Milis, or the other nations.
But Holy Britannia, fixated on their beliefs, knew simplicity was key.
How couldn't it be when soone like Lucian Frost and Evelyn Cessna erged from Holy Britannia itself?
It was sothing the other nations just wouldn't admit to themselves!
Even Bellion himself was confident he could wipe the floor with those mages and their fancy magic circuits!
"Ha…."
He recalled a certain mory.
It was during the tournant, where he was hailed champion, completely demolishing the opposition.
And then another mory, sending a chill down his spine.
"...."
His ntor, Jain Victoria, scolding him for the mistakes he had during his fights, embarrassing him in front of the world to see.
He was even given the nickna, "Daddy's Boy" in the past.
"...."
Yeah, he had to reject the invitation.
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