Chapter 27: The Guardian’s Heart and Universal Gravitation

No sooner had the silver light of the teleportation array dissipated than Klein strode through the main hall of the tower.

Adèle, busy clearing mineral fragments from the experimental bench, looked up at the sound of his footsteps.

“Mentor, you’re back.”

“Where is Lia?”

“In the study on the second floor,” Adèle replied, wiping the powder from her hands. “She’s been engrossed in books about celestial motion all day.”

Klein nodded. Then, without another word, he headed straight upstairs.

Pushing open the study door, he found Lia sprawled across the desk, a thick volume titled ‘Records of Stellar Trajectory Observations’ spread before her. She didn’t even lift her head at the sound of the door opening.

“Senior Adèle, I still think there’s an issue with the decomposition temperature of malachite…”

“It’s me.”

Lia’s head snapped up, her eyes meeting Klein, who stood framed in the doorway. She instantly straightened her posture, her previous languidness vanishing without a trace.

“Mentor! You’re back.”

Klein approached her, withdrawing a small silver metal box from his robe. The box was palm-sized, its surface intricately etched with fine runes, and gleamed with a cold luster in the candlelight.

“What is this?” Lia stared at the box, a flicker of unease stirring within her.

Klein offered no direct answer. Instead, he opened the box. Inside lay a silver necklace of the same material, its pendant a fist-sized crystal, within which something appeared to pulse with a slow, internal current.

“The Guardian’s Heart,” Klein said, lifting the necklace. “Horace gave it to you.”

“Horace?” Lia blinked. “I don’t know anyone by that name.”

“The Vice-President of the Theoretical Council, a Ninth-Ring Archmage,” Klein explained, pausing. “He has reviewed your calculus manuscript.”

Lia’s heart skipped a beat.

‘Oh, no. Another formidable figure knows.’

“Is he… alright?”

“He is,” Klein reassured her, discerning her apprehension. “He greatly admires your manuscript. This pendant is his token of gratitude.”

Klein raised the necklace, gesturing for Lia to lower her head. Lia hesitated for a moment, but complied, bending her neck obediently.

As the cool silver chain settled against her neck, Lia felt a peculiar magical fluctuation emanating from the crystal, forming an almost imperceptible protective film across her skin.

“What does this thing do?”

“Upon sensing an attack, it instantly generates an Absolute Guardian Barrier,” Klein explained, withdrawing his hand. “It can withstand the full might of an Eighth-Ring Mage’s assault for ten minutes.”

Lia’s hand instinctively flew to the pendant at her chest. ‘The full might of an Eighth-Ring Mage? What did that even mean?’

“Why give this to me?” She looked up at Klein. “I’m just an apprentice; surely no one would want to kill me, right?”

Klein’s expression remained impassive, yet Lia gleaned the answer from his silence.

Someone wanted her dead.

And it was highly probable they had already begun to act.

“Because of calculus?” Lia asked.

“Because of calculus,” Klein affirmed.

A chill ran down Lia’s spine.

She had always known this day might come, but she had never anticipated it would be so soon.

“Are these people… formidable?”

“I don’t know,” Klein replied, settling into the chair opposite her. “But it is always wise to be prepared. Remember, wear it at all times, no matter where you are.”

Lia nodded. She tucked the crystal pendant beneath her clothes, feeling a persistent coolness against her skin.

“So… what should we do now? Should I hide?”

“No,” Klein’s answer was resolute. “Continue with your work as usual. Your research must not cease.”

Lia swallowed hard.

“I’ve already figured it out,” she stated, striving to keep her voice steady. “The formula that unifies heaven and earth.”

Klein’s attention was instantly captured.

“Universal gravitation,” Lia articulated the name. “A formula that explains the interaction between all objects. Whether it’s a small ball falling to the ground or stars orbiting the sun, the same principle lies behind them all.”

“Continue.”

Lia stood, and walked to the bookshelf, retrieving a thick volume titled ‘Collection of Celestial Observations’. She flipped to a page, where elliptical orbits of planets around the sun were depicted.

“The third law of stellar motion states that the square of a planet’s orbital period is directly proportional to the cube of its distance from the sun.”

She traced the orbits on the diagram with her finger. “This law, in essence, is a direct manifestation of universal gravitation.”

She turned to face Klein.

“Imagine the sun as a colossal magnet, drawing in all the stars around it. The closer an object, the stronger the attraction; the farther, the weaker.”

“However, this decrease in attractive force isn’t a simple linear relationship. Instead, it’s inversely proportional to the square of the distance.”

Klein’s brow furrowed slightly. This concept was entirely novel to him.

“Why the square?”

“That involves some complex mathematical derivations,” Lia said, a hint of diffidence in her tone. ‘Of course, she knew the derivation, but it required calculus.’ “In short, the final formula is as follows.”

She picked up a quill, and on a blank piece of parchment, she inscribed the renowned formula.

F = G × (m1 × m2) / r²

“F represents the magnitude of the gravitational force, m1 and m2 are the masses of the two objects, r is the distance between them, and G is a constant.”

Klein stared at the formula, remaining silent for a long moment.

The formula was remarkably concise.

So concise, in fact, that it scarcely seemed capable of explaining such complex phenomena.

“This G…” He pointed to the letter.

“The gravitational constant,” Lia replied. “It’s a fixed value. Its precise magnitude must be determined through experimentation.”

“And objects on the ground…”

“Also apply,” Lia confirmed with a nod. “Stones fall because they are attracted to the earth. It’s merely due to the immense size of the earth that this attractive force appears constant.”

Klein felt his worldview profoundly shaken once more.

Heaven and earth, truly, could be explained by a single, unifying formula.

“Can you prove this formula?” he inquired.

Lia’s movements stiffened momentarily.

‘Of course, but it required calculus. And calculus had only just been introduced to mages above the Sixth Ring. Though Klein had already mastered it, to derive it on the spot…’

“It will require some time,” she replied. “The derivation process is quite complex, involving advanced applications of calculus.”

“How long?”

“A month,” Lia offered a conservative estimate. “I’ll need to meticulously organize the derivation steps.”

Klein nodded. He could appreciate her prudence. After all, with theories of this magnitude, even a minor error could collapse the entire framework.

“A month, then.” He rose to his feet. “Until then, you are not to leave the tower. Conduct all your research here.”

“Yes, Mentor.”

Klein turned to depart, but paused at the doorway.

“Lia.”

“Hm?”

“If anything feels amiss, immediately activate the Guardian’s Heart. I’ve added a warning array to it; if it’s triggered, it will notify me.”

“Understood,” Lia responded. “Prioritize self-preservation, I get it.”

Klein nodded, then pushed the door open and left.

The room fell silent once more. Lia touched the pendant at her chest, feeling the coolness deepen.

She gazed at the universal gravitation formula on the desk, and a sudden realization dawned upon her.

If someone truly intended to kill her, then a month from now, when she presented the derivation of universal gravitation…

More people would likely die.