Extra's Descent

"How are your studies going, Belle?"

Amelia asked.

Despite the fact that it was winterbreak, Amelia and Belle never neglected advance studying.

The second semester 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?"

Amelia curiously tilted her head. It wasn't like Belle, who, for Amelia, 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 Amelia, 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 time wrapping my head around the Divergence Law."

Belle admitted.

"The Divergence Law?"

Amelia blinked, finding the term unfamiliar.

Belle was always diving into complex topics that seemed far removed from what they learned in class.

"Yeah, I've been trying to implement it in my wind magic."

Belle continued.

"You see, the Divergence Law focuses on the flow and dispersion of mana in three-dimensional space, particularly when applying it to elemental 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."

"...."

Amelia 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 Amelia'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 Amelia was putting her own theories into practice, it was just the basic Carlson's Earth Attunement Law.

Something that all mages of the [Earth] affinity practiced.

While Amelia was gifted with the [Armament] affinity, according to her father, it derived from the [Earth] affinity.

"So…. do you need help?"

"I'm glad you asked."

Belle smirked. Amelia felt a sudden chill down her spine.

In fact, her head was already hurting.

"Come."

Belle dragged Amelia. Before Amelia realized it, blinking her eyes, they were already at the Central Library.

"Uh…."

"See this."

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It was all too sudden. Amelia barely had time 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 time—pretty straightforward, right?"

Amelia 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….."

"...."

Amelia'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…."

Amelia 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, something caught her attention.

There was a small error in the equation—something simple, like a missed variable or a misplaced symbol.

Amelia didn't even know what half of this meant, but she recognized that something wasn't right.

"Uh, Belle?"

Amelia pointed at the formula.

"Hm?" Belle looked over, confused. "What is it?"

Amelia hesitated.

"I think… you missed something here. Like, this variable should be accounted for when you're distributing the mana, right?"

Belle squinted at the page, following Amelia's finger.

"Wait… oh."

She blinked, then looked back at her notes with wide eyes.

"Oh my god. You're right!"

Amelia 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, Amelia sat back, utterly lost, but relieved that she had somehow helped.

"Amelia, this is brilliant! How did I not see this? You just saved me weeks of work!"

"Uh, yeah…. no problem."

She still had no idea what she'd just done.

"...."

Seeing the books scattered around her, Amelia 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?'

Amelia 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 something 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…."

Amelia trailed off.

"The theorem suggests that if properly implemented, a Wind mage could reduce casting time by nearly 25% by rerouting the mana through auxiliary pathways…."

Amelia 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 extremely 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.

"Implementing 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...."

Amelia 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 something, Amelia?"

"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 means."

Belle looked up, adjusting her glasses.

"Oh, Quidell's Theorem? Yeah, it's meant 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."

Amelia'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 time even more?

"Belle, could this work for someone who doesn't have Wind affinity? Like... if I tried to modify my magic circuits to use something like this, would it make my casting faster?"

Belle paused, raising an eyebrow.

"Well, in theory, yes. But magic circuits aren't meant to be tampered with lightly, Amelia. 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."

Amelia's eyes gleamed with the potential.

"Risky…. but possible?"

Belle sighed, seeing the look of excitement in Amelia'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 become 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 something on the table.

"I have an extra notebook. You can try formulating it there for now."

Amelia blinked her eyes once more for a second.

Then a sudden determined look flashed across her features.

"Give me a pen."

Finally, something 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 moment.

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 scheme 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 something 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 moment.

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 meeting?"

It was also an invitation for his participation—regarding a meeting 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 times during his younger years.

All he could remember 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 someone like Lucian Frost and Evelyn Cessna emerged from Holy Britannia itself?

It was something 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 memory.

It was during the tournament, where he was hailed champion, completely demolishing the opposition.

And then another memory, sending a chill down his spine.

"...."

His mentor, 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 nickname, "Daddy's Boy" in the past.

"...."

Yeah, he had to reject the invitation.