The world held its breath. Again.

  Liu Xun stood rigid, his golden eyes burning with the glow of his so-called Yin-Yang Divine Perception. Across from him, I stood with that same light suffusing my vision, the lattice of mathematical possibility stretching out before me. The battlefield had become something else — a place where functions defined reality, where movements were no longer made, but iterated upon, anticipated, converging toward a solution before they even happened.

  It was… weird.

  The moment I so much as tensed a muscle, I saw the ripples of prediction unfold — Liu Xun’s reaction expanding outward, his counterattack forming before I had even finished thinking about my first move.

  But then, something strange happened.

  I adjusted. And he adjusted in response.

  And suddenly, he wasn’t seeing what he thought he was seeing anymore.

  Liu Xun’s brow twitched, an infinitesimal hesitation in the sharpness of his gaze. I didn’t even need to attack. The very act of thinking about attacking was already throwing off his predictions.

  Ah.

  A feedback loop.

  We were both standing still, and yet an infinite number of calculations were already happening in real-time. My body wasn’t moving, but I was expanding myself in his function, iterating over every conceivable response. He, in turn, was doing the same — seeing my possibilities before they happened, countering before I even made a choice.

  But because I saw him seeing, I made corrections before I ever moved.

  And because he saw me correcting, he had to correct his corrections.

  A strange, unnatural stillness overtook the battlefield.

  Neither of us had moved, yet we had already engaged in dozens of theoretical exchanges. It was like two chess players staring at a board, running every variation to mate without ever reaching for a piece.

  From the perspective of the peanut gallery, this must have been a scene of unparalleled tension. Two masters locked in a battle of pure perception, neither willing to move, each waiting for the other to break first.

  The truth?

  We were trapped in an infinite loop of ‘if I do this, then he does this, but then I do this, but then he does —’

  It was so, so stupid.

  Liu Xun’s jaw clenched. I could see the muscles in his neck tense.

  He had realised it too. Neither of us could trust the next step, because the moment we did, the prediction itself would change.

  This was self-referential nonsense. His Yin-Yang Divine Perception was computing me computing him computing me, and that process wasn’t converging.

  This wasn’t battle. This was a recursive function spiraling out of control.

  And the funniest part?

  I could already see that if either of us moved, we’d probably just end up in the exact same impasse again.

  Oh no.

  We were stuck.

  I bit my lip to stop from laughing. How did they never account for this? Did they just… never spar with it against each other? Or did they just assume this to be some case of an unstoppable force meets an immovable object? That this was the true culmination of the Dao?

  Liu Xun’s fingers tightened around his sword. “What is this?” he muttered, barely above a whisper.

  He was frustrated. He had never encountered this problem before. And I knew why.

  He had only ever used the technique against opponents who didn’t have it. People whose movements he could track, who couldn’t see his own actions being iterated upon at the same time. He was used to being the only function in play.

  But now?

  Now there were two.

  This wasn’t one person computing a solution. This was two functions trying to solve for each other in real time.

  And if you’ve ever tried solving a system of equations where both outputs are functions of each other…

  Well.

  Liu Xun and I were both staring at an equation that didn’t have a closed-form solution.

  My lips twitched.

  I should exploit this. I really, really should. The flaws were so obvious it was a wonder that he prided himself so much on knowing the technique.

  But first…

  I wanted to feel it out.

  Understandably, I had never used the Taylor Series in this manner before. I knew its weaknesses. I knew how to break it. But before I did that, I wanted to see how far I could push it.

  Just how much of the future could I see?

  I slowly raised my sword.

  The moment I did, I saw it. A dozen steps ahead.

  I saw Liu Xun react. I saw my blade flicker forward, a testing strike. I saw him deflect it — not when I swung, but before I even fully decided to.

  I saw the follow-up, the counterplay. If I tried to feint, he had already seen that outcome. If I tried to accelerate, he had already anticipated my acceleration.

  The future was unfolding like a series expansion. My movement was being computed into existence.

  But —

  Liu Xun flinched.

  Because I wasn’t the only one seeing a dozen steps ahead. He was too.

  Which meant he had already seen that I had already seen his counter.

  Which meant he had to adjust for that.

  Which meant I saw his adjustment.

  Which meant —

  Oh no.

  Oh no.

  This was so dumb.

  The moment either of us tried to attack, we weren’t just fighting in the present. We were fighting in every single projected iteration of the future, simultaneously.

  Liu Xun’s knuckles whitened on the hilt of his sword. His eye twitched.

  The peanut gallery was in awe.

  “What… what is happening?” one whispered.

  “Neither of them are moving…”

  “They are fighting at a level we cannot comprehend!”

  “Master Jiang is this powerful?!”

  “Yes! This is the height of divine combat! A technique beyond the mortal realm!”

  Yeah. Sure. Because an introductory calculus textbook was definitely not for mortal eyes.

  We were stuck. We were so, so stuck.

  And what made it worse?

  We both knew it.

  The moment either of us tried to break the deadlock, the other would see it happen before it even happened. It was like being stuck in a perpetual state of ‘are they bluffing or do they know that I know that they know’ but on steroids.

  I nearly started laughing again.

  Liu Xun’s nostrils flared. He was losing his patience.

  Good. Because I wanted to see what would happen first.

  And then —

  Liu Xun moved.

  He swung his sword, hard, the motion a clean, efficient arc, calculated to slice through me at the precise point where I was least able to dodge.

  But I had already seen it.

  Which meant —

  I adjusted.

  And because I adjusted —

  He adjusted.

  And because he adjusted —

  I adjusted again.

  And because I adjusted again —

  Oh no.

  We were doing it again.

  His sword flickered through the air — changing direction mid-swing. Not because he wanted to, but because I had already seen the previous trajectory.

  My own blade started to move — and I had to adjust it.

  His stance shifted — because he had to adjust for my adjustment.

  And suddenly —

  Neither of us could actually finish a single attack.

  The peanut gallery was going insane.

  “Amazing!”

  “They are feinting at a level beyond imagination!”

  “No wasted movement! They are exchanging thousands of strikes with their minds alone! They are fighting faster than the eyes can see!”

  Liu Xun’s eye twitched. “Fight me properly!” he snarled.

  I’m trying! I wanted to scream. We’re both trying!

  But we were stuck in an infinite loop of counterplay.

  A divergent series.

  Liu Xun lunged forward — but even before his foot touched the ground, he had to correct.

  I stepped back — but had to alter my step before I even landed it.

  Neither of us was fighting. We were trapped in a recursive function of infinite adjustments.

  This was it. This was our battle. This stupid, endless, self-correcting mess.

  I sighed.

  I had wanted to feel it out before exploiting the technique’s weaknesses.

  But honestly?

  This was already cruel enough.

  -x-x-x-

  Liu Xun was livid.

  He didn’t show it the way another young master might — no shouting, no irrational outbursts — but I could see it in the minute contractions of his jaw, the stiffness of his stance. His golden eyes burned brighter as he tried to refine his model of me, recalibrating after each failed prediction.

  This tale has been unlawfully lifted from Royal Road. If you spot it on Amazon, please report it.

  But there was nothing to recalibrate. He was stuck.

  I had spent the last few moments letting the Yin-Yang Divine Perception play out, letting it dictate my motion, letting it show me the ways in which it tried to approximate my existence. I had confirmed it.

  It was just a Taylor expansion. A series approximation built on lower-order terms, assuming smoothness, predictability, convergence.

  But what happens when you step outside the bounds where those assumptions hold?

  It was time to find out.

  I exhaled and attuned myself — not to motion, not to dodging, but to something deeper. To transformation.

  I let go of the simple rotations and linear shifts I had been using. Instead, I felt out the function beneath me, its curvature, its derivatives — the higher-order effects that Liu Xun’s golden glow didn’t account for.

  His approximation was limited. He was treating the world like a neatly expanding function, a smooth, well-behaved polynomial. But I was about to make things messy.

  Liu Xun moved, his sword carving a perfectly predicted arc.

  And I… stopped caring about prediction.

  Instead of stepping along an expected path, I attuned myself to curvature.

  I let my stance shift as I attuned to other functions — not just left, not just right, but in a way that forced third- and fourth-order corrections into the equation.

  Liu Xun’s golden glow flickered. His sword passed an inch from my ribs. A fraction of a second too late.

  He had predicted my motion.

  But he had not predicted that the rules of my motion had changed.

  I could almost hear the screeching sound of his mental model grinding against an equation it wasn’t built for.

  I pressed forward, my body moving in a trajectory that forced him to constantly recompute. His gaze sharpened, golden light surging as he tried to expand his perception — he saw the next movement, the one beyond, but each time he thought he had me, the higher-order terms took over, shifting the function into a space he hadn’t accounted for.

  This was no longer a battle of footwork.

  This was a battle of series expansion errors.

  His sword flickered, chasing the position I should have been in, only for his strike to overshoot — just slightly. But slightly was enough.

  Liu Xun’s breath hitched.

  The peanut gallery gasped.

  “What — what was that?!”

  “He dodged after the attack already landed?”

  “No — no, he moved before Young Master Liu even swung!”

  I moved again, curving through a transformation that wasn’t supposed to exist in Liu Xun’s mathematical model of the world.

  His sword whiffed. Again.

  Liu Xun inhaled sharply. “That’s — impossible.”

  No, it was math.

  The golden glow in his eyes wavered. I saw it now. His divine perception was struggling — not because he was slow, not because his ability was failing, but because his function was diverging from reality. It was trying to approximate my motion with a polynomial that didn’t converge in the space I was occupying.

  I wasn’t dodging his blade. I was stepping into regions where his model made for poor approximations..

  Liu Xun saw me move. He saw the trajectory form. He saw his counterplay — and then it failed. Because his sword, his strike, his entire existence had been aimed at the wrong derivative.

  He had extrapolated from the first few terms, but I had been wielding the ones he ignored.

  His technique was built on the idea that higher-order corrections don’t matter. That you could truncate the expansion at second or third degree, maybe fourth in extreme cases.

  But what happens when you push beyond that?

  What happens when the terms he discarded… take control?

  Liu Xun’s expression hardened. He stepped back, recalibrating.

  No. Trying to recalibrate.

  Because every time he tried to update his approximation, I moved again, forcing his model into yet another space where higher-order effects dominated.

  His sword lashed out — a desperate correction, his golden glow pulsing, trying to refine itself.

  But I was already beyond him.

  He was playing chess with a polynomial. I was playing chess with the remainder term.

  I shifted again, attuning myself to a transformation that demanded a fifth-order correction.

  Liu Xun’s eyes widened.

  Because this time — he didn’t even swing.

  He saw it. And he knew it wouldn’t work.

  The peanut gallery erupted.

  “Master Jiang is winning!”

  “He’s forcing Young Master Liu back!”

  “He’s making him miss! Even without moving!”

  I could see the realisation creeping into Liu Xun’s eyes. His divine perception had a horizon. A limit beyond which its predictive power fell apart. It didn’t matter how strong it was — it was still a truncated expansion. Still just a function struggling to approximate reality.

  Liu Xun’s breathing was slow and measured, but there was a tightness to his shoulders now.

  “You,” he said quietly, “are not supposed to exist.”

  I tilted my head. “And yet here I am.”

  He exhaled sharply. “Fine.”

  His stance shifted. He was preparing something.

  I could already guess what it was. If his approximation was failing, that meant he would try to compensate. Try to refine his method. Try to find a way to force me back into the space where his divine perception still held.

  I watched his golden eyes glow even brighter.

  Yes. There it was. He was pushing his function harder. Expanding it further.

  If he had been using a third-order approximation before, he was now forcing it to fifth or sixth. He was trying to bridge the gap. Trying to account for the higher-order effects. He had thought that acceleration and jerk were insufficient, and was now trying to push his technique into snap and crackle.

  He was trying to catch me.

  I almost felt bad for him. Because he still hadn’t realised the problem.

  He thought this was the limit. He thought this was the worst it could get.

  But I had seen another flaw. And when I used it…

  His technique wouldn’t just diverge.

  It would break.

  Liu Xun steadied himself, sword at the ready. His golden eyes locked onto me.

  This was it. His final attempt at convergence.

  I smiled.

  He had no idea what was coming next.

  -x-x-x-

  Liu Xun took a slow breath, his golden eyes narrowing, the light burning brighter as he pushed his perception further. He was still convinced that this was just a gap in order, a failure of resolution. That if he expanded far enough, he could pull me back into convergence.

  But that was his mistake.

  Because what happens when you reach a discontinuity? When you step beyond the radius of convergence?

  A sharp, sudden break. A function that refuses to be predicted. A step where no limit exists.

  I attuned myself — not to a smooth, well-behaved transformation, not even to the complex but continuous shifts I had been using before. No.

  I reached for a discontinuous function, and Liu Xun’s divine perception broke.

  He had been pushing further and further out in his approximation, but there was no extrapolation that could save him now.

  A finite sum of derivatives can never predict a jump discontinuity. No matter how many terms he added, the truth was always going to be different from what he expected.

  Liu Xun moved.

  I moved.

  And in that instant — his sword passed through where I should have been.

  Not where I was.

  Liu Xun stumbled. His golden eyes flashed in sheer disbelief.

  I had been there — I should have been there — and then I wasn’t. Not because I dodged, but because his model had never included my real position to begin with. Because I had simply jumped.

  A discontinuous shift. No gradual movement. No interpolation between states. A function that, for all intents and purposes, snapped from one value to another without warning.

  Liu Xun’s golden perception reeled, trying to find me again. But how do you predict something that refuses to be defined in between?

  His sword lashed out — desperate, frantic.

  But each time he predicted a path, the transformation I attuned to I had already jumped past it.There was no longer an iterative process, no refined approximations.

  Every movement I made was now a new initial condition.

  Every moment, I reset his function.

  Every moment, I broke his expectation.

  Liu Xun’s strikes became wild.

  His divine glow flickered — unstable, uncertain.

  This was the second flaw of his technique.

  He thought he could see all things, but what he actually saw was just a partial sum governed by fundamental underlying assumptions.

  I moved.

  He missed.

  Again.

  And again.

  And again.

  And then — I struck.

  The first blow landed cleanly against his ribs. The sound cracked through the air. Liu Xun’s body jerked, staggering.

  The peanut gallery erupted.

  “Master Jiang landed a hit!”

  “He’s winning — he’s actually winning!”

  Liu Xun’s head snapped toward me, stunned. His golden eyes flashed with pure indignation. He had seen the strike coming.

  But it hadn’t mattered.

  Because his function had lied to him.

  I jumped again. He swung where I should have been. I wasn’t there.

  I wasn’t anywhere he could reach.

  I brought my sword down against his shoulder. Another clean strike.

  Liu Xun gasped. His footing staggered. His golden glow flickered again.

  He had no defense. His entire technique relied on a world that didn’t exist.

  Another strike.

  Another.

  Each time, his perception predicted the wrong outcome. Each time, his function failed.

  Liu Xun was being beaten down by his own assumptions.

  His divine perception had been his greatest weapon — an all-seeing eye, a technique that had let him stand above the common martial world.

  But in this moment?

  It was useless.

  Because he wasn’t fighting an opponent anymore.

  He was fighting a discontinuity.

  The peanut gallery roared.

  “He’s unstoppable!”

  “Master Jiang is toying with him!”

  “Young Master Liu can’t hit him! He can’t even touch him!”

  Liu Xun’s breath was ragged now. His stance had lost all of its grace. His sword trembled in his hands.

  I could see the disbelief creeping in — the panic, the sheer terror of encountering something that he couldn’t even begin to comprehend.

  His entire understanding of the world had failed him.

  And I wasn’t even done yet.

  Because while a simple jump discontinuity was bad, it wasn’t the worst thing I could do.

  Oh, no, no, no.

  My friend, we were just getting started.

  If he thought this was terrifying —

  He hadn’t seen anything yet.

  -x-x-x-

  Liu Xun staggered. His sword, once a gleaming extension of his will, now hung heavy in his grip, the golden light in his eyes dimming. His mind was unraveling before my eyes — not in the way of a defeated warrior who had merely lost a battle, but in the way of a man who had glimpsed something beyond the limits of his understanding and realsed that he could never close the gap.

  I could see it in his expression: panic. Not of the body, but of the mind. His divine perception had failed him. It wasn’t just losing — it was wrong. A model that had faithfully predicted every battle he had ever fought, reduced to nonsense in my presence.

  Because I was moving in a space he did not believe existed. But reality did not care for beliefs.

  The peanut gallery had long since decided that this was the greatest martial spectacle of their lives.

  “Master Jiang is invincible!”

  “He sees through all attacks!”

  “No — he moves before the attacks even exist!”

  Liu Xun’s hands trembled. His once-pristine robes were disheveled, caked in dust. His breathing was shallow. The golden glow of his Yin-Yang Divine Perception flickered weakly, like a candle on the verge of being extinguished.

  “This… this is impossible,” he rasped, his voice hoarse.

  I tilted my head. “Is it?”

  “You —” He coughed, swallowing his pride along with whatever internal damage he had sustained. “You’re a cripple. You have no qi. How… how could you possibly…?”

  I let a pause stretch between us, as if considering his words. In truth, I was trying very hard not to say something that would give away how much of this was accidental. Honestly, I hadn’t expected the fight to be so absolutely one-sided.

  I almost felt bad… no, never mind. I didn’t. I was quite enjoying myself, in fact.

  Instead, I settled for the vague, ominous approach.

  “Not everything follows the rules you believe in, Liu Xun.”

  It was a nonsense statement, but in this context? It sounded profound.

  Liu Xun flinched as though I had struck him. I took a slow step forward. He took a half-step back before catching himself, jaw tightening. But he couldn’t hide the truth.

  He was afraid.

  I had pushed his technique past its limits. He had reached beyond his radius of convergence, trying to find a function that could still describe my movements, and in doing so, he had stepped into something even worse than divergence.

  He had stepped into chaos.

  Because now, I wasn’t going to be simply moving beyond his calculations.

  I was about to break them entirely.

  I took a breath. I peered within that profound space of all mathematical truths, attuning myself to that which I sought.

  The world sharpened, the edges of my vision turning strangely crisp for an instant, like a well-defined theorem on a perfectly white page. The noise of the peanut gallery faded, the lingering ache in my limbs dulled, and for the first time, I let go of the need to step smoothly from one state to another.

  I let go of continuity.

  And in that moment, something shattered.

  Not something visible. Not something that could be grasped by mere mortal senses. But something fundamental. A break, a fracture in the delicate lattice of expectation and intuition that bound the world together.

  Liu Xun flinched — not just in his body, but in his soul.

  He was no longer merely a cultivator locked in battle. He was a scholar before a forbidden text. A mortal before a nameless abyss. A child staring into the yawning, incomprehensible depths of something older than understanding itself.

  His Yin-Yang Divine Perception, his vaunted foresight, had seen it.

  It had seen something it was never meant to see.

  A function that should not exist.

  A function that should not be.

  And yet, it did.

  And yet, it was here.

  The peanut gallery, once a rowdy chorus of cheers and exclamations, had been silenced by an instinct deeper than thought. They did not understand what was happening. They did not need to understand.

  Their bones understood. Their flesh understood.

  Some primal whisper of their ancestors screamed at them — Do not gaze upon this. Do not comprehend.

  A single step.

  That was all I had taken.

  Yet in that step, I had abandoned continuity. I had stepped beyond the realm of well-behaved functions, past the bounds of smooth transitions, past even the last shreds of predictability.

  Liu Xun knew.

  His golden eyes, once sharp with confidence, had been emptied of certainty. His sword, once an extension of his will, now felt meaningless in his grip.

  I could feel it. The shift. The weight of the moment.

  This was the threshold.

  And beyond it lay something wrong.

  Something the world had rejected. Something that even the grandest cultivators of the Dao of mathematics of Earth had recoiled from.

  Even Hermite — surely at least a Nascent Soul, or a Dao Lord — who had peered into the unfathomable, had turned away in abject terror.

  The minds of lesser men had broken beneath its weight. Mathematicians had stared into the abyss and wept. They had begged for it to be anything else — anything that could be understood, anything that could be contained.

  But it could not be contained.

  For this was no ordinary function. No mere trick of mathematics.

  This was a monstrosity, a twisting, writhing horror that slithered between the laws of reason. A function where every point was sharp, where no derivative could tame its shape, where infinity itself coiled within every segment. It was still continuous — still moved like a river did — but this was a river of jagged glass.

  It did not flow. It churned. It lurched. It writhed.

  It should have been impossible. It was impossible.

  And yet, it had been written.

  It had been proven.

  Perhaps its discoverer had glimpsed the chaos at the heart of the universe and dared to transcribe it. Perhaps some celestial being had whispered it into his mortal mind, a test, a curse, a glimpse into something beyond comprehension.

  Or perhaps it had simply always been there, waiting for the right mind to stumble upon it.

  And now, it was here. With me. In me.

  Only the merest surface of it, yet even that was enough.

  I could feel its presence, twisting the world beneath my feet. It did not harm reality, nor did it seek to replace it. It merely refused to obey.

  I took another step. Liu Xun choked on air, his body recoiling as if struck by an invisible blow.

  He did not understand why. There was no movement to predict. There was no trajectory to follow.

  His Yin-Yang Divine Perception was grasping at mist, grasping at something that did not yield to its calculations, something that mocked the very idea of foresight.

  Because how do you track something whose motion is everywhere jagged, everywhere unknowable, everywhere shifting?

  How do you predict something that is continuous everywhere… yet analytic nowhere?

  His golden glow flickered. His fingers clenched tight around his sword, but his hands were shaking.

  His mind was still trying to comprehend. To him, every fighter, every enemy, every thing had always existed within a function — smooth, predictable, governed by the natural order of the universe.

  Cute.

  Now, that order was gone.

  His breathing had gone shallow, his stance wavering. I had not raised my sword. I had not attacked. I had not done anything.

  All I had done was align.

  A deathly silence had long seized the peanut gallery in its grasp. They must have sensed that something had changed, even if they didn’t have the eyes to see it.

  I had spent my whole past life avoiding this. Avoiding the plunge. Avoiding the depths that lay within the sea of mathematics. Avoiding what wonders and terrors alike lay within this vast sea of unfathomable ignorance.

  And yet, now, here, in this ridiculous second life where I had no proper qi, no dantian, no grand destiny —

  I had finally taken that step.

  Liu Xun shuddered. He wanted to fight it. He wanted to believe. He must have always believed that the world could be understood. That it behaved by his rules.

  But now, for the first time —

  He was gazing into the abyss, and the abyss stared back.

  I let a whisper slip from my lips.

  A name.

  A nightmare.

  A horror.

  “The Weierstrass function.”