Time seemed to stand still.
A full ten minutes passed.
Chen Zhuo opened his eyes.
Instead of heading for the blackboard, he walked over to the water cooler, filled a cup halfway with cold water, and downed it in one gulp.
The ice-cold water flowed down his throat and into his stomach, clearing his muddled mind a little.
"Senior Brother Wu."
Chen Zhuo put down the cup and turned around.
"We don’t have to cut it out."
Wu Tao looked up.
"Not cut it out? Then how do we balance the equation?"
"Why do we need to balance it?"
Chen Zhuo walked back to the blackboard and picked up a piece of chalk.
"We’re here to find the global invariant, not to solve an arithmetic problem."
"A homology group can be decomposed into a direct sum of a free abelian group and a torsion group."
Chen Zhuo wrote the formula on the blackboard.
"The torsion group represents the twisting of the space. It does exist, but it doesn’t contribute to the number of holes in the space."
"We only take its rank."
Chen Zhuo added the symbol for rank to both sides of the equation.
"For any finitely generated abelian group, the rank of the torsion group is always zero."
The chalk drew an X on the blackboard, striking out the part representing the torsion group.
"Let it stay tangled up. As long as we take the rank, it becomes mathematically invisible."
"Just the rank of the free part."
Wu Tao was stunned.
"Brilliant."
Wu Tao muttered to himself, picked his pen back up, and began working through the proof along this new line of reasoning.
「Five in the morning.」
A faint, cold gray light began to break across the Huizhou sky.
The air in the office was so stuffy it felt hard to breathe.
Li Jianming sat in the wicker chair, a thick stack of densely filled scratch paper in his hands. The old professor’s posture was still ramrod straight, but his fingers, clutching the pages, trembled slightly.
It wasn’t exhaustion. It was an involuntary physical reaction, the aftereffect of intense exhilaration.
Wu Tao was slumped in his chair, eyes staring lifelessly at the ceiling. His brain had completely shut down. If someone had asked him to calculate one plus one, it would have taken him ages just to process the question.
Before the blackboard.
Chen Zhuo was left with only a nub of chalk, too small to hold properly.
His wrist ached, and his shirt, damp with sweat, was plastered to his back.
In the bottom right corner of the blackboard,
he wrote the final equation of the entire derivation.
Through the mapping of discrete algebraic topology, the boundary oscillation term, which originally diverged infinitely in the continuous domain, was perfectly contained within a finite Betti number.
On the left side of the equation were the complex, microscopic changes within the local network.
On the right side was a concise topological invariant composed of integers.
Between them, he drew an absolute equals sign.
Chen Zhuo let go.
The piece of chalk, now too short to even hold, fell into the tray at the bottom of the blackboard.
In the office, so quiet you could hear a pin drop, the soft sound was like driving the final rivet into a magnificent structure.
’It’s done.’
Chen Zhuo took two steps back.
He looked at the entire wall of formulas, at the algebraic symbols arranged like constellations.
A vast sense of emptiness, followed by an equally immense satisfaction, washed over him like a tidal wave.
Li Jianming tapped the stack of scratch paper in his hand on the desktop, aligning the edges.
The old professor took off his reading glasses and placed them on the desk.
He didn’t look at Chen Zhuo, nor at Wu Tao. He just stared at the blackboard.
"It’s a closed loop."
Li Jianming’s voice was soft and hoarse, but it carried an indescribable weight.
"This path is open."
Sprawled in his chair, Wu Tao heard the words, and the corner of his mouth twitched. He wanted to smile, but his facial muscles were too stiff to move.
He could only close his eyes and let out a long sigh.
A fatigue that seemed to seep from the very marrow of their bones instantly overwhelmed everyone.
Chen Zhuo leaned against the wall next to the blackboard.
As the adrenaline faded, a wave of dizziness from low blood sugar rushed over him.
His face turned pale, and his stomach clenched in waves, as if a hand were wringing it from the inside.
His mental energy had been pushed to its absolute limit since his last meal—a single bite of rice in the cafeteria yesterday afternoon.
Chen Zhuo rubbed his stomach and straightened up.
He brushed the chalk dust off his clothes and looked at the professor and his senior brother, both too exhausted to move.
"Teacher Li, Senior Brother Wu."
Chen Zhuo’s voice was faint with exhaustion, but it held an unmistakable lightness, the sound of a burden released.
He pulled a meal card from his pocket and waved it.
"I don’t even have the strength to go downstairs right now."
Chen Zhuo looked at Wu Tao.
"Senior Brother, can you take this meal card to the cafeteria and get me two meat buns? And two soy milks, with sugar."

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