The model was wrong

Shen Moxin's fingers loosened around the manuscript, then tightened again. She took a deep breath, gently returned the yellowed papers to the shelf, and turned to walk around it, her footsteps light.

Lu Yuan was still sitting in that corner. His head was lowered, his fingers hovering over the open manuscript as he absently traced something in the air.

"Could you explain that in more detail?" A voice sounded from ahead and to the side.

Lu Yuan jerked back to his senses and curled his fingers. He looked up to see Shen Moxin standing a few steps away, one hand resting on the bookshelf. Her face was largely expressionless, but her eyes shone brightly behind her glasses, filled with a burning focus.

His heart tightened. He'd let something slip.

He had muttered those words very quietly, merely griping out of habit. He hadn't expected anyone on the other side of the shelf to hear him, much less this teaching assistant.

Shen Moxin didn't press him. She took two steps forward and stopped across the table, her gaze falling on the manuscript with the decay curve. "You said the model ignored the interference factor from the ambient Soul Power field," she said evenly, as though restating a fact. "You also mentioned that the decay constant would become a variable."

She tapped the tabletop lightly with her fingertip. "I'm very curious. What kind of interference did you mean? How would it change?"

Lu Yuan looked at her. There was curiosity and astonishment in her eyes, but no mockery. He had seen that look too many times-in Maple Leaf Town, at the city gate, and at the foot of the library steps. But Shen Moxin didn't have it.

He pondered briefly.

An opportunity. Or perhaps trouble.

"Simply put," Lu Yuan began, his voice steadier than usual. He pointed to the curve on the manuscript. "This record assumes that once Martial Soul energy is released, its rate of decay in the environment stays constant. So it uses an exponential decay model to fit a fixed decay constant, α."

Shen Moxin nodded. This was the basic model from the textbooks.

"But there's a problem with that assumption." Lu Yuan's finger slid down the curve. "It assumes the ambient Soul Power density is uniform and stable. But in reality..."

He paused, pulled a charcoal pencil from inside his clothes, and took out a sheet of scratch paper he had brought with him. Shen Moxin noticed that its edges were covered in densely packed small characters and symbols.

Lu Yuan drew two axes in the blank space, time on the horizontal axis and Soul Power intensity on the vertical. He first sketched a descending curve similar to the one in the manuscript.

"If the ambient Soul Power density really were constant, there'd be no problem fitting it this way." As he spoke, he drew a second, fluctuating line beside it. "But in a real environment, Soul Power density fluctuates. For example, other Soul Masters cultivating or releasing Soul Skills nearby, or even changes in the weather, can all affect it."

He marked several points on the fluctuating line. "At these points, the ambient Soul Power density suddenly rises or falls. Then the 'resistance' acting on the energy released by a Martial Soul as it decays-or rather, its 'rate of dilution'-will change."

The charcoal pencil returned to the first decay curve and paused lightly at several corresponding points. The originally smooth curve at once acquired several unnaturally steep or flat stretches.

"Look here." Lu Yuan pointed to a spot on the curve that should have transitioned smoothly but looked a little "stiff" in the manuscript. "The person who recorded it might have thought it was a measurement error. But if we introduce an interference factor β that changes with the ambient Soul Power density..."

He quickly wrote a rough equation on the scratch paper: α' = α ± k·β(t). His handwriting was messy, but the structure was clear.

"Then the decay constant α is no longer a constant, but a function α' that changes over time. If we use this corrected model to fit the data again..." He made a sweeping gesture in the air with his charcoal pencil. "These apparently contradictory data points in the manuscript can instead be connected into a more reasonable curve. The error would be much smaller."

He set down the charcoal pencil and looked at Shen Moxin.

Shen Moxin said nothing. Leaning slightly forward, she stared at the scratch paper, her gaze moving back and forth between the curves, the equation, and the manuscript. She raised a hand absentmindedly and pushed up her glasses.

The library was quiet, save for the faint sound of pages turning in the distance.

Several breaths passed.

"A two-variable influence model..." Shen Moxin said softly, as if talking to herself. She raised her head and looked at Lu Yuan with a complicated expression. "Fluctuations in ambient Soul Power density as a second variable, interfering with the core decay process... This approach of yours..."

She didn't finish, but Lu Yuan could see her shock.

The model wasn't particularly profound, but it broke away from the habitual "isolated system" thinking used in the Soul Master World's current research into energy decay. The vast majority of researchers, herself included, assumed that energy released by a Martial Soul decayed in a "vacuum," and the environment's influence was broadly lumped together as "error."

Yet the framework this shabbily dressed child had sketched out on the spot was not only logically consistent, it had even exposed several contradictions in the old manuscript's data that she too had previously found awkward, though she hadn't been able to say why.

Shen Moxin took a deep breath. "How would you determine the form of this interference factor β? And the coupling coefficient k-is it related to the type of Martial Soul?"

The questions were incisive, striking straight at the key points of the model.

Lu Yuan breathed a sigh of relief. She was thinking about it seriously, rather than rushing to dismiss it.

"The form of β would have to be worked out from measured data on fluctuations in ambient Soul Power. For now, it can only be conjecture." He chose his words carefully. "As for k... it's definitely related to the characteristics of the Martial Soul. For example, the energy of a fire-attribute Martial Soul would certainly decay at different rates in humid and dry environments. But determining that coefficient would take a large number of controlled experiments."

He was telling the truth, and that was also the difficulty. The model was only a rough framework.

Shen Moxin understood. The light in her eyes grew brighter, the excitement of meeting a worthy opponent and seeing an entirely new path. A research bottleneck that had troubled her for a long time seemed to have been pried open a crack by those few words.

She couldn't help pressing on. "If we follow your approach, then wouldn't many traditional assessments of Soul Skill power, calculations of Soul Power consumption, and even models of the energy impact when absorbing a Soul Ring all have to..."

She didn't finish.

Somewhat heavy footsteps sounded from the entrance to the reading area, drawing nearer.

Both looked up at once.

The stern-faced middle-aged librarian from before walked over, a register in his hand. He first glanced at Lu Yuan, his brows furrowing out of habit, then looked at Shen Moxin. His tone was stiff. "Assistant Shen, time's up."

He raised a hand and pointed to an inconspicuous hourglass on the wall. The fine sand inside had just run out. "Half a shichen, not a minute more."

Only then did Shen Moxin realize how much time had passed. She glanced at the manuscript open before Lu Yuan and the scratch paper covered in equations, and a strong reluctance welled up inside her.

But she knew the rules.

"All right, I understand." She nodded and began gathering the stack of materials she had brought.

The librarian didn't leave immediately, however. His gaze traveled over Lu Yuan once more, and the corners of his mouth turned down. He lowered his voice slightly. "Also, the head librarian asked me to remind you-bringing unauthorized people into the inner area to consult materials is against the rules. We'll let it go this time, but don't do it again."

He placed particular emphasis on "inner area." Only then did Lu Yuan notice that there really was a small sign at the entrance to this section of shelves. It read, "Research materials area. Restricted to teaching assistants and above."

Shen Moxin paused. She looked up at the librarian, her face largely expressionless, but her voice was clear. "He came in with me, and all the materials he consulted were within the permitted scope. The responsibility is mine. I'll explain it to the head librarian."

The librarian was momentarily taken aback, apparently not expecting Shen Moxin to take responsibility so readily. He gave a twitch of his lips, turned, and left.

In the little corner, the atmosphere grew somewhat tense.

Shen Moxin quickly jotted down the titles of several manuscripts she might need in her leather notebook, then looked at Lu Yuan and spoke faster. "You need to leave. Go out through the side door, not the main entrance."

Lu Yuan didn't say much. He immediately stood, carefully closed the manuscript, and returned it to its place. He hesitated over the scratch paper covered in equations, then crumpled it up and stuffed it inside his clothes. He put the charcoal pencil away.

His movements were brisk.

Shen Moxin watched him, and the question in her heart could no longer be suppressed. As he turned to leave, she suddenly spoke, her voice soft but more solemn than ever before:

"Wait."

Lu Yuan stopped and looked back.

Shen Moxin looked at him, her eyes behind her glasses sharp as knives. "These... these ideas about the model and the Soul Power field," she asked, enunciating every word, "who taught them to you?"

Lu Yuan was silent.

Sunlight had shifted onto the side of his face. He pressed his lips together.

Just as he was about to speak-

"Assistant Shen!" The librarian who had just left had returned. Standing several rows of shelves away, his voice was even stiffer than before. "The head librarian wants to see you now. Immediately."

Shen Moxin's expression changed slightly.

Lu Yuan glanced at her and said nothing. He merely gave the slightest nod, turned, and walked quickly toward the side door through the shadows between the shelves.

His figure soon disappeared.

Shen Moxin stood where she was, her fingers gripping the edge of her notebook tightly. The head librarian had suddenly summoned her and even sent the librarian to hurry her along... It was probably not as simple as a "reminder."

She withdrew her gaze and looked at the spot where Lu Yuan had been sitting. The tabletop was completely empty.

But that rough two-variable model, and those eyes too calm for a child's, had already been deeply etched into her mind.

She closed her notebook and turned toward the librarian. Her steps were steady.

But her heart was like a deep pool into which a stone had been thrown, ripples spreading outward in circle after circle, unable to grow calm again.