Chapter 13. Degenerate Case
Lunch.
For all the enlightenment, the conceptual breakthroughs, and the slow, inevitable realisation that I was becoming something other than what I once was, lunch remained a universal constant.
And in some ways, that was comforting. The world of cultivation might be vast and unknowable, an endless series of nested hierarchies, but at the end of the day, even the greatest of immortals had to sit down and eat.
… actually, no, maybe not.
I frowned as I walked toward my usual dumpling stall, my mind rapidly spiraling into the kind of existential crisis that only hunger and academic curiosity could induce. If cultivators could survive on pure qi, was it analogous to photosynthesis? Did they synthesise all necessary compounds internally, or were there fundamental biochemical pathways that still required external inputs?
If a cultivator never ate, did their microbiome collapse? Did their gut bacteria ascend with them?
Wait.
I stopped in the middle of the street, considering.
Did gut bacteria cultivate?
Did I have to worry about some ungodly strain of E. coli going around?
… did they have a dantian?
I stared down at my stomach, genuinely unsettled. If qi could influence a cultivator's body, then surely it influenced their microbiome as well. And if not, then… helminth parasites? And if that was the case…
No. Stop. This was a rabbit hole I did not need to go down.
I needed lunch.
I shook my head and continued toward the dumpling stall, forcibly shoving aside the horrifying thought of a microbial golden core.
The scent of freshly steamed buns and sizzling scallion pancakes filled the air as I reached the vendor, an old woman who had long since stopped questioning why I sometimes stared into the distance like I was having an out-of-body experience. I greeted her with a polite nod, placing my order with practiced efficiency.
As I waited, I allowed myself a brief moment of self-reflection.
I was almost ready.
Four months ago, I had been barely more than a fraud — an imposter with a head full of half-remembered mathematical theorems and no real understanding of what I was doing. Now? Now, I could move with intent. I could sense the invisible structures that surrounded me. I could feel the faintest whisper of transformation when I aligned myself with the underlying symmetries of the world.
It wasn't much. Not yet. Compared to true cultivators, I was still barely a rounding error in the grand function of reality. But I was no longer just flailing blindly, hoping to brute-force my way into enlightenment through sheer academic stubbornness. I had a direction now. A method.
And most importantly — I had a plan.
Step one: Resume teaching. Probably.
Step two: Continue refining my understanding through increasingly convoluted mathematical metaphors that would make my students question the nature of existence.
Step three: Survive long enough to get to step four.
Step four: Punch a mountain apart.
I was under no delusions that step four was anytime soon. But I had started to see the outlines of the path. The first derivatives, the partial differentials that hinted at a greater underlying structure. Given enough time, enough iteration, I would reach a point where my understanding was no longer just an approximation.
And then — then we'd see what was really possible.
I allowed myself a small, satisfied nod. The wax on, wax off phase was over.
Now the good stuff began.
"Here you go," the vendor said, handing me a neatly wrapped portion of dumplings.
I accepted them with the appropriate amount of reverence. The universe was governed by certain immutable truths, and one of them was that a man who had spent the morning pondering the nature of qi transformations still needed to eat.
But before I could take a single bite, before I could even appreciate the delicate balance of soy and vinegar seeping into the perfectly pleated dough, a voice cut through the street.
"Master Jiang!"
A small figure was sprinting toward me, her breath coming in sharp, panicked gasps.
Ru Lan.
I barely had time to register the sheer desperation in her voice before she reached me, skidding to a halt with a force that suggested she had forgotten how friction worked. Her eyes were wide, wild, her hair slightly disheveled from running, and she was breathing so hard that for a moment, all she could do was stare up at me, gulping down air.
I blinked.
Well, this was new.
I knelt down slightly, setting my dumplings aside. "Ru Lan?" I said gently. "What's wrong?"
She opened her mouth, but what came out wasn't words. It was an incoherent mix of gasping and frantic gesturing, like a child who had just learned about the existence of irrational numbers and was now experiencing a personal crisis.
Huh. Was that what was happening? Had Headmaster Song been teaching them about that?
I put a steadying hand on her shoulder. "Breathe. Then explain."
She sucked in a sharp, unsteady breath, tried again. "Th-there's a cultivator —"
My mind snapped into full alertness.
A cultivator.
That single word was enough to cut through all the lingering amusement, all the idle speculation, all the deeply unsettling questions about microbial qi refinement that I had been trying to suppress. My entire body tensed instinctively — not with fear, but with the kind of acute awareness that only came from knowing you were about to be violently reminded of your own mortality.
I stayed kneeling, keeping my tone steady. "What cultivator?"
Ru Lan was still gulping air, her hands clenching and unclenching at her sides, as if trying to hold onto something solid while the world around her spun out of control. "He—he's from Longtiao City. The Liu Clan." She swallowed hard, voice barely above a whisper. "He won't leave my sister alone."
The words hit me like a cold splash of water.
Lu Clan. From Longtiao City.
I wasn't deeply versed in the politics of local cultivation sects, but even I had heard of them in passing. One of those well-established clans that owned a significant chunk of the businesses in the city and probably considered Qinghe Town to be little more than a place where their servants came from. They were not the type of people you crossed.
And if a Lu Clan cultivator had decided he was interested in someone…
I exhaled, keeping my voice calm even as my mind raced. "Where?"
Ru Lan pointed, trembling. "The market. He — he just — he —"
She didn't finish. She didn't need to. Her entire face, her entire body, told me everything.
Panic. Helplessness.
The look of someone who had already run through every possible solution in her mind and found nothing.
I had seen that look before. I had worn that look before.
It was the look of someone who had realised that, no matter how much they struggled, they were bound by constraints they could not control. That they were trapped in an equation with no real solution, and all they could do was watch as the inevitable played out.
I felt my stomach twist.
I was not a hero. I had never been. I had spent four months avoiding situations exactly like this, keeping my head down, training in quiet solitude so that when the time came — some hypothetical, far-off future that they came for me— I would be ready.
I wasn't ready.
Not really.
Yes, I had learned. Yes, I had refined my control. Yes, I had glimpsed something greater than myself.
But that didn't mean I could fight a true cultivator.
It didn't mean I could stand in front of someone from a powerful city clan and tell him to leave.
It didn't mean I wouldn't end up just like the protagonist whose body I had inherited — beaten down, discarded, powerless.
But.
But.
Ru Lan's hands were shaking.
Her breath was uneven.
She had run all the way here, past dozens of adults who would have looked away, past the rest of my students who were too young, past anyone else she might have known.
She had run to me.
I took a slow breath, forcing my own panic down.
The truth was, it didn't matter if I was ready.
Because Ru Lan hadn't come to me because she thought I was a hero. She hadn't come to me because she believed I could solve everything in one miraculous stroke.
She had come to me because I was the only one who might try.
And for that alone —
I couldn't turn away.
I let my breath out. My thoughts snapped into order, my mind aligning with a singular, unshakable decision.
"Take me there."
Ru Lan nodded frantically, already spinning on her heel.
I followed.
My lunch lay forgotten on the street behind me.
-x-x-x-
I followed Ru Lan through the winding streets of Qinghe Town, my mind racing faster than my legs could carry me.
Which was unfortunate, because if there was ever a time for my newfound mathematical cultivation insights to grant me an immediate mobility technique, this was it.
But no—better to conserve what little control I had. My qi wasn't some obedient dog that followed commands on a whim; it was more like a half-feral animal that occasionally acknowledged my presence when it felt like it. If I spent my energy now, I'd have even less to work with when I got there.
And I would need everything I had.
Because let's be real — this was exactly the kind of situation that, in every xianxia story, existed purely as a post-breakthrough face-slapping moment.
The arrogant young master shows up. He's a smug, insufferable bastard with a local backing and a handful of bootlickers. He terrorizes the common folk until the protagonist, fresh from an epiphany in seclusion, arrives to teach him a lesson.
And that was the problem.
I had not just had a breakthrough.
I was still weaker than Jiang Lingwu had been before he got trounced by Zhao Feng. If this cultivator was even close to Zhao Feng's strength, then I was already dead.
Except, of course, I couldn't think about that right now.
Ru Lan's small figure darted ahead of me, her short legs moving faster than I'd ever seen them in class. She wasn't stopping to look back—she was trusting that I was behind her, that I wouldn't hesitate.
And so I didn't.
The market came into view, and I caught my first glimpse of the situation.
Oh.
Oh, yeah.
Arrogant young master.
In the middle of the street, lounging against a silk-draped stall like he had personally invented the concept of leisure, was a man who could not have been more obviously stamped with the words face-slappable villain if he'd tried.
Expensive robes? Check. Dark green, embroidered with silver — definitely moneyed.
Elaborate hairstyle? Check. He was even holding a jade hairpin like he was deciding whether or not it was worthy of being used.
Smug expression? Oh, absolutely. The kind of smugness that came from a lifetime of never facing consequences.
And, of course — lackeys.
Two of them, standing slightly behind him with identical postures of obsequious deference. It was one of the fundamental constants of this universe. No matter where you went, arrogant young masters always came with at least two bootlickers. The optimal number for maximum synchronised laughter and unquestioning validation.
The Liu Clan cultivator was talking, his tone as lazy as his stance. "I'm being quite reasonable," he was saying. "I'm merely offering to pay for your company. Many would consider that generous."
My stomach turned.
Ru Lan's sister stood stiffly in front of him, her expression carefully neutral. Her husband was at her side, his hands balled into fists — but his entire posture screamed hesitation. Because he knew, just as I did, that if he started a fight, he would lose more than just the fight.
I took in the scene carefully, my mind snapping into the kind of brutal, analytical clarity that only absolute panic could produce.
The Liu Clan cultivator was young — maybe early twenties — but carried himself with the weight of someone who had never once questioned his own place in the world. He had that unmistakable bearing of a man who had never faced a problem that couldn't be solved by his surname, his fists, or, failing both, a sufficiently large amount of bribery.
Which presented a problem for me.
One, I had no surname worth mentioning.
Two, my fists were currently better suited for writing out proofs than throwing punches.
Three, I had about seven copper coins currently on my person, and I had just abandoned my dumplings.
Suboptimal.
Still, I needed to figure out exactly who I was dealing with. The Liu Clan was prominent in Longtiao City, but I couldn't tell if this man was an important figure in the clan or just some young master on the periphery, the kind who had just enough authority to make trouble but not enough to resolve it if things went sideways.
What was worse, I had no idea how strong he actually was.
A normal cultivator would be able to gauge an opponent's strength at a glance, sensing their qi fluctuations, measuring the density of their spiritual energy, the purity of their core.
I, on the other hand, had the keen spiritual perception of a well-trained potato. My dantian was shattered, my meridians fractured — I was fundamentally incapable of sensing qi the way normal cultivators could. For all I knew, with me and my fragmented meridians, he might just be a particularly well-dressed accountant.
Which meant I was walking into this completely blind.
All I had to go on was body language, context clues, and a deeply unhealthy level of meta-awareness about how these kinds of xianxia scenes usually played out.
I refocused on the Liu Clan cultivator.
The way he stood, the way he spoke — everything about him radiated that distinct flavor of arrogance that came from believing the universe itself had been constructed with him as the central reference frame.
And normally, I would have dismissed that as just another case of young master syndrome requiring a prescription of one hefty dose of face-slapping, PRN.
But now — after months of training, after struggling to grasp the fundamental mathematical underpinnings of reality itself — that attitude felt like a personal affront.
The arrogance was wrong. Not just in the usual 'this guy is unbearable' way, but in a deeper, more fundamental sense. It was an offense against symmetry. Against invariance. Against the very nature of mathematical truth.
Because, yes, technically, one could always perform a coordinate transformation to put oneself at the center of a system. It was a valid mathematical operation.
But doing so was not the same as being the actual center of reality.
This man, with his complete lack of self-awareness, had taken the arbitrary choice of his own existence as an absolute truth, as though he were the origin point of all things rather than just another interchangeable element in the grand equation of life.
It was offensive.
It was infuriating.
It was wrong.
And I hated that I was even having this thought because oh my god, I am going to die.
The Liu Clan cultivator turned slightly, tilting his head as he regarded Ru Lan's sister with that same unbearable, condescending smirk.
"Come now," he said, still speaking as if this were all some grand joke at everyone else's expense. "Surely you don't expect your husband to defend you?"
Her husband clenched his jaw so tightly I thought his teeth might crack. His fists were trembling at his sides — not in fear, but in sheer, helpless rage. He wanted to fight. He wanted to defend his wife. But he knew, just as everyone else in the market knew, that if he tried, he would lose.
Not just the fight. Everything.
Because that was how these things worked.
A cultivator could do what he wanted. The laws of common folk didn't apply to him. If he so much as raised a hand, the Liu Clan young master would beat him to the ground, humiliate him, cripple him, kill him — and there wouldn't be a single thing anyone could do about it.
Because power was the only thing that mattered.
My stomach twisted, a bitter taste rising in my throat.
For all the complexity of cultivation, for all the talk of enlightenment and grand cosmic principles, the reality of it was painfully simple. It was an arms race. A contest of who had the biggest, shiniest metaphysical stick. And those at the top of the hierarchy had long since decided that they were the natural center of the universe, that their power was deserved — that the suffering of others was nothing more than an acceptable error in the equation of their own superiority.
I hated it.
I hated it because it wasn't just wrong. It was sloppy.
It was bad mathematics. A false axiom accepted without proof. A system where the rules existed only to reinforce a conclusion already assumed to be true.
And in that moment, as the Liu Clan cultivator stood there, still smirking like the outcome had already been determined — because from his perspective, it had been — I felt something shift.
A redefinition of variables. A realisation of constraints.
And an undeniable certainty that I was about to do something incredibly stupid.
I exhaled slowly, stepping forward.
Not dramatically. Not heroically.
Just… moving.
The marketplace was silent as I approached. The townsfolk parted instinctively, as if afraid that proximity to me might result in some sort of collateral damage.
Liu Xun's smirk widened as I stepped into the open, his eyes lighting up like a particularly smug cat that had just cornered an exceptionally stupid mouse. He tilted his head, as though he were entertaining a brief moment of curiosity before he went back to doing whatever it was he considered important.
"And who," he drawled, "might you be?"
I clasped my hands behind my back and tilted my head in return, mirroring his condescension at a slightly off angle, as if I were adjusting a coordinate system just to be petty.
"A teacher," I said simply.
His smirk twitched. That wasn't the answer he had been expecting.
"You must be new to Qinghe Town," I continued before he could recover. "Otherwise, you'd know that anyone under the age of twelve finds me utterly terrifying."
That got a snicker from someone in the crowd. Wait. Was that Wu Liang? The lackeys, however, did not find it amusing. One of them took a step forward, hand drifting toward the hilt of his sword.
Liu Xun lifted a lazy hand, stopping him. His smirk was back in place, this time tinged with something sharper. "A teacher?" He let the word roll off his tongue like he had just been presented with an exotic insect. "And you came here thinking you could teach me something?"
I shrugged. "I didn't think it, but hope springs eternal."
That got another laugh from the crowd. Liu Xun's eyes narrowed. The amusement in his expression flickered, ever so slightly.
Then it returned, sharper than before. He tilted his head, and I caught the barest glint of calculation in his eyes. Ah. So he wasn't just all bravado — there was a working brain somewhere in there. A heavily underused one, perhaps, but functional.
"You've got quite the mouth for a cripple," he said, eyes glinting.
One of his lackeys let out a predictable, sycophantic chuckle. The other crossed his arms, clearly waiting for me to start groveling. The crowd around us was frozen in place, unwilling to speak, but I could feel their silent pleading as tangible as the humidity in the air.
I let the insult slide past me. It wasn't an inaccurate assertion. I took another step forward.
Liu Xun's eyes flickered — just briefly — to my feet.
Then he laughed. "Oh? Oh-ho! This is precious." He clasped his hands behind his back, straightening slightly. "Let me guess. You've been reading too many stories, haven't you? You think this is the part where the feeble cripple defeats the arrogant young master with hidden wisdom? Where the underdog reveals that he was secretly a peerless genius all along?"
He spread his arms. "Is that it?"
I did not respond.
He smirked wider. "Then allow me to remind you of reality."
The air shifted.
It was subtle — so subtle that I wouldn't have noticed it if not for the fact that the surrounding crowd instinctively recoiled, some of the weaker ones nearly stumbling back.
It was not power in the form of a visible explosion. It was not brute force.
It was precision. A sculpted wave of qi.
Liu Xun's smirk turned lazy. "You feel that?" he asked. "That's the difference between you and me."
Still, I did not react.
His smirk widened further.
"Since you seem confused," he continued, taking a slow step forward, "allow me to explain. I, Liu Xun, am at the sixth stage of Foundation Establishment. My mastery of the Yin-Yang Divine Perception Technique is unparalleled among my peers. With a single glance, I can see all of an opponent's movements before they even make them."
Foundation Establishment. That was a realm lower than the old Jiang Lingwu had been after his fortuitous encounter.
Yet Liu Xun's voice was measured, confident. All that he had said was not a boast. It was merely a statement of fact.
I could see it now — the way his shoulders stayed relaxed, the way his weight shifted effortlessly between each step, the way his fingers never strayed far from the hilt of his sword. He believed there was nothing I could do.
And, objectively speaking, he was probably right.
I was not at Foundation Establishment. I was not even at Qi Gathering. With my shattered dantian, I wasn't defined by the same axiomatic system as other cultivators. I was, for all intents and purposes, cultivating nothing at all.
Liu Xun glanced at his lackeys. "Jian Hong," he said lazily, as though selecting a particularly unremarkable piece from a game board. "Deal with him."
The taller of the two stepped forward. His gait was steady, but relaxed. Not aggressive. Not cautious, either. Just… dismissive.
Good.
I centered myself, feeling for the structures I had begun to understand over the past month.
Invariance. Reinforcement.
I aligned.
It was harder than I remembered. The old Jiang Lingwu had done this reflexively, without thinking, cycling his qi through his meridians. I, on the other hand, had to map the transformation manually, feel out the stress points, compensate for the inefficiencies.
But it held.
It was the identity transformation — that which left an object unchanged under its own operation. It was the zero of addition, the one of multiplication. The simplest symmetry of all, yet it was identity alone that gave all other transformations meaning. I locked into that symmetry, reinforcing my stance, my balance, my structure. The bones in my arms felt heavier, denser. My skin tightened, resisting deformation.
It was, in simpler terms, isomorphic to the tempering of the body under the action of qi.
Jian Hong sighed, drawing his blade. Still relaxed.
I moved.
Not forward. Not back.
The Knight's Tour.
A traversal of the field, avoiding linear predictability. Movements I'd been practicing for months now.
Jian Hong reacted — too slow.
His blade cut through empty space as I shifted three steps to his side. His stance wavered. Just slightly.
Good.
Five steps ahead.
I reoriented. His body twisted, correcting. His eyes narrowed.
Seven steps.
He slashed again, recalibrating, compensating for my angle. Better.
But still wrong.
Nine steps.
I was behind him before he had even finished his motion.
His mistake wasn't in speed or strength. It was in assuming my path was continuous.
I turned.
I struck.
A simple blow. No wasted energy, no theatrics. A fist, reinforced by symmetry, action under identity.
His body staggered, then crumpled.
Silence.
The marketplace, once humming with nervous whispers, now held its breath.
I straightened.
Jian Hong did not rise.
Liu Xun's smirk had not vanished, but it had changed.
He was watching now.
Liu Xun exhaled slowly through his nose. His smirk remained, but there was something new behind it — a faint, curling edge of irritation. He had been enjoying himself. Now, the amusement was wearing thin.
The sword at his waist whispered free.
The crowd scattered.
It was not a grand, dramatic movement. He did not roar, did not bellow a challenge to the heavens. He simply drew his blade, and in doing so, announced his intent more clearly than any words could.
I cursed under my breath.
His grip was relaxed, his posture easy. He didn't expect a fight — he expected a conclusion. This wasn't a battle to him. It was arithmetic. A simple equation. Me, plus his sword, equaled inevitability.
I was not part of his worldview. I was an anomaly, a rounding error that had slipped into the through unnoticed. But now, with Jian Hong lying motionless on the ground, I had upset the balance of his function. The equation had to be corrected.
He raised the tip of his sword, pointing it at me. "Crippled or not," he said, "you've made a mistake."
A familiar sensation, really.
I adjusted my stance.
Jian Hong's sword was still lying where he had fallen. That was a resource. A variable I could still manipulate. I stepped forward and nudged it with my foot, flipping it up into my grip.
My fingers curled around the hilt of the fallen sword, the unfamiliar weight settling into my palm. It wasn't much — just a basic weapon, likely forged without any grand inscriptions or ancient reforging techniques — but it was the best option available.
Liu Xun's eyes flicked down to the blade, then back up to me. His smirk had settled into something closer to irritation, as though I had just scribbled all over his neatly written proof. This was supposed to be an effortless calculation, and I had somehow introduced an unexpected remainder.
The onlookers, to their credit, had already reached the correct conclusion: that standing anywhere within the vicinity of a duel between cultivators, no matter how one-sided, was an objectively bad idea. They dispersed with the silent efficiency of people who had seen this sort of thing before — stall owners sweeping away their wares, vendors pretending they had never been present in the first place. Even the stray dogs had the good sense to vanish.
Ru Lan was behind me, gripping the sleeve of her sister's robe with small, trembling fingers. Her sister's husband stood frozen, caught between an instinct to protect his wife and the absolute certainty that any action he took would make things worse.
I exhaled slowly.
Liu Xun had drawn his sword with a casual sort of arrogance, the blade catching the afternoon light as though it had been waiting for this moment to shine. He hadn't adopted any obvious stance, hadn't made a show of his movements — because he didn't need to. He wasn't taking me seriously.
And, objectively speaking, he was correct.
He was a proper cultivator, at the sixth stage of Foundation Establishment. He had techniques, he had qi, he had experience. I had… well, a rudimentary understanding of symmetries, a month of self-taught practice, and the vague hope that Jiang Lingwu's muscle memory might kick in at a crucial moment.
So.
Not the fairest fight.
I flexed my fingers against the hilt, adjusting my grip. Jiang Lingwu had known how to use one with the swordsmanship style he practiced, and I had inherited the feel of it, if not the instincts. But wielding was different from understanding. I could stand correctly, position my feet with decent weight distribution, even shift my balance to maximise control. In the last month, I had even taken up the sword myself among my other training.
But that was only a month. Liu Xun would have trained years.
Liu Xun watched, the irritation in his gaze giving way to something else — mild curiosity, perhaps. His smirk had faded, replaced by something quieter, something more calculating.
I had upset his initial function. Now he was recomputing.
I let out another breath, deep and measured. A force through a constraint. A transformation under identity.
Align.
Reinforce.
Hold.
It was subtle. Nothing dramatic, no sudden surge of power, no explosive aura that would announce to the world that I had grasped some deeper truth. Just a shift in perception, a recalibration of internal variables. My stance locked into place with a quiet sort of finality, a structure stabilised against collapse. My grip firmed. My center of mass found its equilibrium.
It was inefficient. It was draining. It was only the first time I would be properly using it outside of a sterile training environment.
But it was something.
Liu Xun's sword tilted slightly, the edge catching a different angle of light.
His weight shifted.
I could feel the moment beginning to slip, the pause between action and consequence shortening. The function of the encounter was approaching a critical point, the limit approaching zero.
I had no idea if I could hold my own against a cultivator like him.
But I was about to find out.
Chapter 14. Roots of Unity
The world held its breath.
Liu Xun's sword gleamed in the afternoon sun, an arc of polished steel that might as well have been a guillotine. His posture was relaxed — too relaxed. He still didn't see me as a threat. To him, I was just a malformed equation, a function that hadn't resolved properly, a mistake in need of correction.
I tightened my grip on the fallen sword. It still felt wrong in my hands, an ill-defined variable, but a variable was still something I could work with.
Liu Xun exhaled through his nose, stepping forward in measured, confident strides. "I was going to let you walk away," he said, his voice carrying the exaggerated patience of a man who had never had to wait for anything in his life. "But you had to interfere."
He lifted his blade, tilting it just slightly, as if appraising me under a new lens. "Jian Hong was careless. I won't be."
I wasn't sure what was worse — the arrogance or the fact that, objectively speaking, he was probably right.
Still, an equation wasn't solved by praying and hoping the variables randomly canceled out. It required method. Structure.
Transformation.
I took a slow breath and centered myself. The battlefield was a complex plane. Every movement an operation, every step a rotation about some unseen origin.
Liu Xun moved.
It was fast. Not the overwhelming, world-splitting speed of some grandmaster tearing the heavens asunder, but fast enough that he blurred at the edges. A linear trajectory, a vector cutting through space with no deviation. The shortest path between two points.
An efficient function.
I rotated, summoning the rudimentary style of swordsmanship I had been developing over the last month in my downtime.
The Roots of Unity.
eiπ/3, a sixty-degree shift — a primitive sixth root of unity. Not a mere sidestep, but a transformation of my position entirely, shifting my entire reference frame. His blade passed through the empty space I had just vacated.
Liu Xun's brows furrowed. He adjusted instantly, bringing his sword back in a tight arc, pivoting to face me once more.
But I was already moving.
eiπ/4 , a quarter-turn rotation. Another axis, another transformation. From his perspective, I was simply vanishing from where he expected me to be, my movement not following any predictable Euclidean path.
He slashed again.
eiπ/6. Smaller now, a fine-tuned shift. The blade grazed past my shoulder, missing by fractions of an inch. Another change in basis, another reformulation of the problem.
I wasn't dodging.
I was iterating.
Liu Xun's expression shifted from idle amusement to mild annoyance. "You're fast," he admitted, though the words were more of a begrudging observation than praise. "But movement alone won't win you this fight."
That was the problem with people who saw the world as a fixed system. To them, movement was just displacement, a function that changed position but not substance.
But I wasn't just shifting.
I was composing functions.
Liu Xun lunged, his blade moving in a broad, cleaving stroke.
I composed two transformations — eiπ/3 followed by eiπ/4 — rotating through arguments, stacking one transformation atop another. A new function, the product of rotations, shifting my reference frame yet again.
His blade whistled through another empty point in space.
Liu Xun's irritation deepened. He withdrew half a step, studying me. The arrogance hadn't faded — he still saw me as a lesser function, an unoptimised algorithm — but now, I had become an edge case. A problem that needed solving.
I adjusted my grip. My breathing was steady, my stance balanced.
The battle wasn't about sword against sword.
It was transformations against transformations.
A duel of x versus y.
Liu Xun exhaled, shifting his weight, recalibrating. "Alright," he muttered, rolling his shoulders. "Let's see how long you can keep that up."
The world did not still. It rotated.
Somewhere, in some distant place, the stars wheeled along their celestial orbits, unbothered by the trivialities of men and their swords. But here, in this moment, the world pivoted on a different kind of axis — one traced by footwork and steel, by rotations and reflections.
I could feel it now, the lattice of possibility stretching out around me. A sea of transformations, an infinite domain of mappings waiting to be applied. Many of them were beyond me, unreachable, just as an undefined function collapses when evaluated at the wrong input. But the simpler truths — the ones I had spent a month internalising —those lay within my grasp.
Liu Xun, of course, felt none of this.
From his perspective, I was an irritating insect that refused to die on schedule. His stance was still loose, his blade held with casual confidence. The way his lip curled was telling — he believed himself engaged in the most tedious form of combat: the one where the opponent thought they stood a chance.
I adjusted my grip. This sword still didn't feel like an extension of myself, but a clumsy approximation. No matter. I wasn't wielding a sword.
I was wielding a function.
Liu Xun moved.
A fast, efficient strike, a perfect minimisation of distance and effort. No unnecessary flourishes, no wasted arcs. A simple, linear approach.
Predictable.
I applied a sixth root of unity — sixty degrees counterclockwise. Not a dodge, not a step, but a full transformation of my spatial reference. His blade passed harmlessly through where I had been, intersecting empty space.
Liu Xun didn't falter. His wrist turned, adjusting the angle in an immediate counterstrike.
I rotated again — forty-five degrees this time, a composition of eighth roots.
His blade found nothing.
His eyes narrowed.
Interesting. Had I finally entered the phase where I was no longer a nuisance but an actual equation that needed solving?
"Not bad," Liu Xun admitted, straightening slightly. His smirk returned, sharp and condescending. "But movement alone —"
"— won't win me this fight," I finished for him. "Yes, yes. I understand that."
His grip tightened.
Excellent.
He lunged again, this time cutting horizontally. I stepped not backward, not sideways, but perpendicular to the entire engagement — an orthogonal step, a shift into a dimension of motion he had not accounted for.
I lifted off the ground.
Not jumping. This wasn't a mere vertical displacement.
Gauss had once argued that i, the so-called imaginary unit, should have been named the lateral unit instead. A misunderstanding of its nature had led to its unfortunate branding as something unreal when, in truth, it was a fundamental expansion of movement, of perspective.
I applied it.
A leap, not just up but laterally — an operation into a space where Liu Xun's strike could not follow, where his swing had no meaningful projection. A transformation along an unseen axis, a perpendicular movement to reality as he understood it.
Liu Xun's blade passed below me.
The world felt lighter, clearer. My position was no longer constrained to the Euclidean battlefield he had mapped in his mind. I could feel the rotations, the symmetries, the elegant simplicity of it all. The way transformations could be stacked, iterated upon, building one upon another in an endless recursive sequence.
A cycle.
The moment stretched. Liu Xun's sword was rising, recalibrating.
I completed my descent. A controlled vector.
I landed behind him, my foot touching the ground at the exact moment his blade finished its arc.
Liu Xun stiffened. The crowd murmured.
The function had been executed successfully.
I straightened, tilting my head at an angle. "You were saying?"
Liu Xun inhaled sharply through his nose. "You're starting to annoy me."
That was fine. I had spent a good fraction of the last month annoying myself with partial differential equations, so this was an improvement.
I could feel it now. Not just possibility, but inevitability.
I could win.
Liu Xun lunged.
This time, there was no pretense of restraint, no calculated measure of arrogance. His sword carved through the air in a wild arc, its trajectory aggressive and unchecked. This was no longer the footwork of a cultivator playing at refinement — this was frustration, an algorithm that had lost convergence, desperately iterating toward a solution it could no longer define.
I stepped.
Another sixty-degree rotation — one-sixth of a full revolution, another primitive root of unity. The world adjusted. Not a dodge, but a transformation. My position in the fight was no longer a continuous function of time but a discrete mapping, each step a point along a lattice of movement.
His blade found empty space.
Liu Xun did not stop. His grip shifted, pivoting mid-motion, forcing another slash along a perpendicular axis.
Ah. He was trying to bracket me, reducing my degrees of freedom. Smart.
I rotated again, stacking more transformations, an eighth-root of unity compounding over the sixth. A finer correction, a higher resolution shift in the complex plane. Again, he missed.
A flicker of irritation crossed his face.
"Stop running," he snapped, twisting his stance to cut downward in a vicious arc.
I didn't run.
I iterated.
Another orthogonal step, one whose principles be still didn't seem to understand. Upward and lateral, perpendicular not just to him but to the entire structure of the fight as he understood it. A transition into a space that he hadn't mapped, hadn't parameterised. I lifted from the plane of engagement, stepping into a higher-dimensional motion he had no answer for.
Again, his blade passed beneath me.
For a moment, neither of us moved. The silence stretched.
Liu Xun's breath was measured, but his shoulders were tense. His expression hadn't changed, but his grip had tightened, fingers flexing slightly around the hilt of his sword.
"I see," he said, voice low. "Some kind of movement technique."
Ah, there it was. The reclassification.
I was no longer just an irritant. No longer just a lucky commoner who had somehow avoided the first few strikes.
Now, I was a phenomenon. A function that needed to be solved.
Liu Xun exhaled and pivoted sharply, stepping forward as he slashed — not wildly this time, but deliberately, aiming to collapse my solution space.
I sidestepped, but he had already accounted for it. The next strike came immediately, cutting off my expected angle of rotation.
I adjusted. An eighth-root transformation, a fine shift along the lattice.
He adjusted. A diagonal cut, fast, sharp, closing my escape.
I was running out of variables.
So I rewrote the equation.
I stepped, but not in the way he expected. Not into an evasion, not into another Orthogonal Step.
I stepped forward.
Into the attack.
For the first time, Liu Xun hesitated. His sword arced toward me, a function executing exactly as intended.
I reached.
Not for him. For the pattern. The rhythm of his strikes. The implicit structure underlying his form.
The Knight's Tour.
And I disrupted it.
A shift — not an avoidance, but a counterterm, a calculated error introduced to his perfect solution. A perturbation that forced him to adjust, to recalculate.
And in that moment —
I struck.
A clean, direct motion, my sword slamming into his midsection.
A sharp crackle of qi burst between us — Liu Xun had reinforced his body at the last second, a defensive layer hastily applied.
But hasty was not the same as perfect. The force of the impact sent him staggering back.
Silence.
Liu Xun's gaze flickered down, his free hand brushing against the point of impact. He wasn't injured. Not really. But the fact remained —
I had touched him.
And in the perfectly well-ordered worldview of xianxia young masters that had them as the supremum of the set, that was unacceptable.
His eyes snapped back up to mine. Something in the air shifted.
I inhaled slowly.
Liu Xun's expression was still composed, but the arrogance had changed. It was no longer presumed victory.
It was certainty.
"You," he said quietly, "are going to regret that."
The parameters of the fight had changed.
Liu Xun had recognized me as a problem. And a problem, once recognized, needed to be solved.
Liu Xun straightened, his breathing slow and measured. The golden glow in his eyes pulsed, faint at first, then growing brighter, suffusing his gaze with an unnatural radiance. It was not the overwhelming aura of a grandmaster, nor the suffocating presence of an elder unleashing his cultivation, but something else—a sharpening of perception, a refinement of prediction.
I knew that glow.
Oh no.
This was it. The inevitable young master power-up.
There was a predictable rhythm to these things. First, the arrogant opponent underestimates the protagonist. Then, the protagonist surprises them, scoring an unexpected hit. And just as hope begins to bloom, the opponent smirks, wipes the blood from their lip, and unveils their true power.
It was practically a conservation law in xianxia physics: for every moment of protagonist triumph, there exists an equal and opposite moment of young master escalation.
And, sure enough —
"Hmph." Liu Xun rolled his shoulders, the light in his eyes intensifying. "I suppose I should commend you. Not many can touch me in combat. You should consider it an honor."
I exhaled slowly. Ah, yes. The classic 'I acknowledge your existence now' phase. How generous of him.
"But don't think that means anything," Liu Xun continued, voice brimming with the absolute certainty of a man who had never once considered the possibility of losing. "What you fail to realise is that you've already lost."
Oh good, the 'you are already defeated' phase. We were moving through the checklist at an efficient pace.
"My Yin-Yang Divine Perception has now fully activated," Liu Xun declared, and with those words, the very air around us seemed to shift. "A lesser opponent may evade a few strikes through tricks and deception, but I see through all things. Your feints, your rotations, your little footwork tricks — they are nothing before my sight."
He lifted his sword, pointing it at me.
"Move," he said. "Try whatever technique you like. It won't matter."
I hesitated.
And then I moved.
A sixteenth-root transformation, the finest resolution shift I could manage. My foot touched the ground at an adjusted argument, my stance shifting seamlessly.
Liu Xun's blade was already there.
I barely twisted in time, the sword's edge whispering past my ribs. Too close. I pivoted, adjusting the function, shifting through a second transformation.
He adjusted faster.
I barely had time to block, the force of his strike rattling up my arm.
Oh.
Oh no.
He really was reading me.
The battle that had once felt like an elegant, flowing composition had suddenly become a brutal, desperate defense. My footwork, my transformations, my carefully structured mappings — Liu Xun intercepted them all. Where before he had swung into empty space, now his blade met me. Not always perfectly, not yet, but with enough accuracy that I was forced onto the defensive.
It wasn't luck. It wasn't coincidence.
It was something far worse.
He was computing me.
Liu Xun pressed forward, his sword carving through the air in precise, measured arcs. His form was sharp, but it was his perception that was suffocating. He was striking into my future, his blade arriving at the solution before I had even computed it myself.
I dodged, barely.
Then again.
Again.
Each escape was thinner, closer. Each step a desperate correction, a perturbation to his model that only barely delayed the inevitable.
He was iterating faster than I could escape.
Liu Xun's smirk widened as he advanced. "So much for your clever footwork," he sneered. "What good is movement if I always know where you will be?"
I gritted my teeth. This was bad.
This was very bad.
For the first time since I had started training, my system of movement failed. Not because I had miscalculated, not because my understanding was flawed, but because Liu Xun had solved for me. I was no longer an unknown function. I was a fully defined variable, a closed-form solution sitting neatly in his perception.
I needed to escape.
I needed a new function.
A diagonal slash came at me, faster than I could counter. I threw myself back, barely avoiding the edge. My chest heaved as I tried to recalibrate, to find some new symmetry that he hadn't yet accounted for.
Nothing.
Everything I could apply, he could predict.
I was trapped.
Liu Xun paused, as if sensing my growing frustration. He exhaled softly, the golden glow in his eyes steady and unwavering.
"I told you," he murmured. "I see through all things."
The arrogance was unbearable.
And yet, this time, I couldn't deny it.
I adjusted my grip, my stance, my breath. The sea of transformations around me, the endless lattice of possibility — it was still there.
But he was standing inside it.
He wasn't just reacting. He was anticipating. Every movement, every shift, every mapping I attempted — Liu Xun's blade was already there.
He had computed my function before I had.
And that meant —
I was already in his domain of definition.
A shiver crawled down my spine. This wasn't just prediction. This wasn't just fast reaction time. He had formed an approximation of me. A predictive model. A function that mapped my inputs to my outputs before I even had time to decide them myself.
Liu Xun's blade carved through the space between us in perfect arcs, no longer the careless swings of a young master toying with an insect, but the efficient, calculated strokes of someone who had solved for all variables.
I barely twisted out of the way, my function perturbing just enough to escape, but it was getting harder. He was refining his approximation with every iteration.
The crowd gasped.
"He's toying with him now."
"That teacher had tricks, but the moment Young Master Liu got serious, it was over."
"No! Master Jiang, don't give up!"
Another voice, breathless with reverence: "They say it's like seeing into the future."
I gritted my teeth as I staggered back, deflecting another blow at an awkward angle. Future, huh?
Liu Xun tilted his head, golden light flickering before his eyes. "This is the difference between a talentless cripple like you and a true genius. From the moment you so much as twitch, I already know where you'll move." He took a single, deliberate step forward. "Every footstep. Every swing. Every evasion. I see through all of it."
The murmurs swelled.
"Impossible…"
"He's not even reacting? He's attacking where the teacher will be before he moves?"
"This is the power of the Liu Clan's techniques?"
Liu Xun's lips curled into a smirk as he raised his sword again. "You should feel honored. The Yin-Yang Divine Perception is among my clan's greatest techniques, one that only the most talented can awaken." He exhaled slowly. "You think your crude tricks — your amateurish movement techniques — can escape my sight?"
I barely had time to move before he struck again.
I dodged — or tried to.
My step was too slow. Or rather — his cut had already arrived.
Steel met flesh.
A thin line of pain traced across my arm. The wound wasn't deep, but the meaning was clear.
He wasn't missing anymore.
My breath came hard and fast. Sweat clung to my back. Ru Lan, standing at the edge of the battlefield, had both hands clenched into fists, her lips pressed together as though she wanted to speak but couldn't.
Liu Xun laughed softly.
"Struggling?"
My grip on the sword tightened.
I was running out of space. Running out of angles. Running out of mappings I could take that he wouldn't already have a solution for.
He had a function. He had defined me. He was converging.
And I…
… I was a problem about to be solved.
Liu Xun stepped forward again. His golden eyes gleamed. "What's wrong? Where's that confidence from before?"
I panted, wiping the sweat from my brow. Damn it. Damn it. Damn it.
I had known it. I had known this would happen.
This was the law of young master escalation. They always had a trump card. A bloodline power. A hidden domain. An invincible technique that suddenly activated when the protagonist got too confident.
I had nothing.
I wasn't a secret young master of a fallen clan. I didn't have a divine-grade martial soul lurking in my dantian. I had no lost inheritance, no golden finger, no hidden master to swoop in and save me.
All I had was my little understanding of math.
And math wasn't working.
Liu Xun's blade flicked up. "If you're out of tricks, I'll end this now."
I raised my sword again, breath still heavy. My legs burned. My mind spun through possibilities, through solutions, through anything that could turn this around.
He was predicting me. Seeing into my future.
I needed something he hadn't accounted for.
I needed —
"Enough playing," Liu Xun muttered. "It's time you learned the gap between heaven and earth."
His golden eyes pulsed.
The moment I moved, he would already know.
He would see my first step — no, even before it was taken — he would expand the function, extrapolate my movement, and converge onto the correct answer before I had even finished computing it myself.
My stomach twisted.
Liu Xun exhaled, his golden irises burning with light.
"I can see everything. I predict all your moves. I alone see the flow of the river of fate. Before your sword even moves, I already know where it will be."
I froze.
A single thought slammed through my mind like a hammer.
Wait.
Wait.
Seeing everything? Predicting my movements? The moment I move, he already knows? The flow of the river of fate?
My mind latched onto the words. Stared at them. Examined them from every possible axis.
Prediction.
Approximation.
Convergence.
Expanding —
My breath caught.
Wait.
No.
No.
It couldn't be.
…surely not?
Liu Xun's golden gaze narrowed. "Your stance is faltering. Have you realised it? Have you accepted it yet?"
My heart pounded in my chest.
Was it…?
I squinted, peering at the truths visible only to me.
It was.
It absolutely, unequivocally was.
This wasn't some mystical divine technique.
This wasn't fate-defying combat precognition.
This —
…wasn't this just the Taylor Series?
-x-x-x-
I stared at Liu Xun.
I stared at his glowing, golden eyes, his smug, self-assured smirk, his whole holier-than-thou posture as he declared his absolute victory.
Then I focused again, reaching outward, seeing not with my eyes but my mind.
I stared at that grand world of mathematical truths that Hermite spoke of. I pored over the shimmering field of possibility that surrounded him — the pulsing operators, the ghostly specters of approximations and differentials trailing behind his every motion, his entire form suffused with the recursive glow of infinite series expansion.
This — this was it?
This was the grand, divine, bloodline-exclusive technique of one of the young masters of Longtiao City? This was the sacred art that was going to crush me beneath the weight of inevitable fate?
This was just the Taylor Series?
I almost dropped my sword.
I mean, sure, the Taylor Series was important. Revolutionary, even. A cornerstone of modern analysis, an infinite sum that let you approximate smooth functions locally with nothing but derivatives evaluated at a single point. You probably couldn't do any analysis without it. Hell, to even be analytic was literally defined on the Taylor Series.
But this was their supreme technique? The one passed down through generations, accessible only to the most talented?
I hadn't even studied math formally and I knew this!
I felt a laugh bubble up in my chest. I tried to suppress it. I really did. But the absurdity was too much.
A month ago, I had been staring at a world of incomprehensible cultivation techniques, qi-based movement arts, footwork that defied classical physics. I had spent weeks developing a mathematical framework just to understand the smallest sliver of possibility. My table had a dent in the shape of my forehead from my frustration at trying to recreate complex analysis, just so I could figure out what Riemann had done to provide the foundation for his famed hypothesis.
And now?
Now it turned out they had been using basic calculus all along.
I burst out laughing.
Liu Xun froze mid-step.
The peanut gallery whispered in hushed tones.
"Master Jiang is laughing?"
"Has he lost his mind?"
"This is too cruel…"
"Perhaps he's simply broken under the pressure. Young Master Liu's divine perception is beyond mortal comprehension!"
Beyond mortal comprehension, my ass! Any random high schooler could do this!
Liu Xun scowled. "What are you laughing at?"
I shook my head, still chuckling. Oh, this was perfect.
How could I have been so blind? I had been standing in the midst of a sea of mathematical truth, clawing for understanding, while these young masters had been unknowingly wielding basic mathematical concepts as divine arts.
It was almost cruel.
Almost.
Because now, I understood it, too.
Liu Xun's golden eyes flickered, his frown deepening. "You've finally gone insane. Accept it. No matter what trick you play, no matter how fast you try to move — I already know where you'll be."
He stepped forward, slow and deliberate, each movement layered with that shimmering prediction, an expansion of my function before I could even compute it myself.
I wiped the corner of my eye, still grinning. "Oh, I see it now."
Liu Xun tensed.
"I was struggling so much," I murmured. "Trying to find a way past your perception. Trying to disrupt your function. But I was thinking about it all wrong."
I exhaled, centering myself, and let go.
The world shifted.
I had been so focused on transformations, on rotations and mappings, on evading within a fixed system. But that was the wrong perspective.
Because if Liu Xun was expanding me into a series —
Then I could expand, too.
I reached into the sea of possibility, into the shimmering field of mathematical truth that had always been there, and I aligned myself with it.
The first derivative — velocity.
The second — acceleration.
The third — jerk.
The fourth — snap.
The approximations unfolded before me in infinite layers, each term cascading into the next, recursive, iterative, inevitable.
Liu Xun flinched.
For the first time, he hesitated. The golden glow in his eyes trembled.
I wasn't just an input into his function anymore. I was the function.
The world exploded into possibility.
A gasp rippled through the crowd. The murmurs turned to shouts.
"He — his eyes! They're glowing!"
"It's the same golden light!"
"Impossible! Master Jiang is using the Yin-Yang Divine Perception as well?!"
"He is a hidden master! I win the bet!"
Liu Xun flinched. His stance shifted, not in preparation for an attack, but in uncertainty. Then his smirk returned, but it was thinner now, stretched too tight.
"A trick," he spat. "A pale imitation. You don't even know what you're wielding."
I tilted my head, watching him. No, I wouldn't explain. I wouldn't waste my breath giving him a lecture on Taylor expansions and how his so-called perception was just a glorified polynomial fit. How the weaknesses of it were so glaring, it was almost laughable.
That would be too cruel.
No, I had other ways to demonstrate.
"Tell me," I said, voice quiet, steady. "How confident are you in your calculations?"
Liu Xun scoffed. "The Yin-Yang Divine Perception is absolute. Your every movement is already known to me."
I smiled.
"Good. Then —" I lifted my sword. "Prepare for a lesson."