The forest was silent.

Tall trees stretched into the night sky, their leaves shifting slightly in the breeze. The moon cast a pale glow over the landscape, illuminating the still lake ahead of me.

I stood at the water's edge, watching the surface ripple slightly under the wind's influence.

Water walking.

It was a technique that required a different approach than simple wall walking. While wall walking demanded a constant and controlled flow of chakra to one's feet, water walking was dynamic. The surface was unstable, requiring constant adjustments in chakra output.

I had understood the theory for years. Now, I would test it.

I stepped forward, allowing my foot to hover just above the water's surface.

A controlled release of chakra, spread evenly across my sole. I lowered my foot.

Failure.

The moment my weight shifted forward, the water caved, and my foot sank in. I pulled back before it could fully submerge.

Not enough chakra output.

I adjusted. A slightly stronger flow. A shift in distribution.

Another step forward.

The foot held for a brief second before the water collapsed beneath me once more.

I withdrew again, analyzing the issue.

Too much chakra at the point of contact, but not enough distributed around the foot. The balance was off.

The reason for failure was clear.

Unlike walls, which provided a solid surface for chakra to adhere to, water was constantly shifting. Applying chakra only to the sole of my foot created a localized pressure point, which was immediately destabilized by the liquid's movement.

A proper shinobi instinctively adjusted chakra output to counteract this instability.

I did not have instincts. I had logic.

I adjusted again.

This time, I visualized the process. Chakra, spread evenly across my entire foot. A constant feedback loop-detecting the water's shift, counteracting the instability before it could collapse.

I stepped forward.

The surface held.

The water trembled slightly under my weight, but I did not sink.

I took another step. Then another.

I was standing on the lake.

The surface shifted beneath me, unstable but manageable. I adjusted instinctively, maintaining a steady flow of chakra, adapting to each movement.

I walked further.

Each step was precise, controlled. The lake's surface rippled with my movements, but I no longer sank.

------

The night was still.

The lake behind me reflected the moonlight, a perfect mirror of the sky above. I stood at the water's edge, my mind no longer concerned with the mechanics of water walking. That problem had been solved. Now, it was time to move forward.

The Chakra Encoding System.

Shinobi relied on instinct. Their training was based on repetition, drilling the same sequences into their bodies until muscle memory dictated their movements. Hand signs were a language-one learned through experience rather than understanding.

That was inefficient.

I would redefine jutsu into something precise. A mathematical language.

A hand sign, in itself, was meaningless. It was only in sequence that it carried purpose. A set of movements that shaped chakra into something usable. But why?

The answer lay in the structure.

Each hand sign was not just a symbol-it was an instruction. A shift in chakra's composition, a command issued through the body. That meant it could be measured, analyzed, and reconstructed.

I reached into my pouch, pulling out a small notebook and a pencil.

This was the foundation. If I could break down each hand sign into quantifiable data, I could control them at will. I could remove redundancy. I could refine jutsu to their purest form.

I needed a framework.

The three fundamental components of chakra were:

Physical chakra - The energy derived from stamina and raw bodily force.

Spiritual chakra - The energy generated by the mind, refined through experience and willpower.

Natural chakra - The external force present in the environment.

These could be represented in a three-dimensional model. A hand sign was no longer just a motion-it was a vector.

Each hand sign could be assigned a set of coordinates in a three-dimensional space:

X-axis (Physical Chakra) - Represents raw stamina consumption and bodily strain.

Y-axis (Spiritual Chakra) - Represents mental focus and chakra control.

Z-axis (Natural Chakra Influence) - Represents nature energy's impact on the jutsu.

I assigned values based on observed patterns in jutsu execution:

Tiger - (1,3,-1)

Ox - (2,2,0)

Boar - (3,1,1)

Rat - (-1,3,2)

Dragon - (2,-1,3)

Monkey - (-2,-1,0)

Rooster - (1,2,-2)

Dog - (-1,2,-1)

Horse - (2,-1,-2)

Ram - (1,1,1)

Snake - (0,3,-1)

Rabbit - (-2,0,2)

Each sign carried specific chakra properties, and their combinations formed jutsu.

I flipped to the next page and wrote down an example.

A jutsu was not just a collection of hand signs-it was a structured formula. A matrix.

I analyzed the Fireball Jutsu sequence:

Snake → Ram → Monkey → Boar → Horse → Tiger

Now rewritten as a matrix:

Summing the vectors:

A clear pattern emerged. Each jutsu had a unique signature based on its matrix composition.

Jutsu could be optimized. By rearranging vectors, I could minimize redundancy and reduce the number of required hand signs.

Jutsu could be executed with one hand. If each hand sign carried a specific vector, then pre-training my body to replicate the frequencies could remove the need for symmetrical gestures.

Jutsu could be cast with no hand signs at all. If my body could be trained to instinctively produce the correct chakra frequency, physical gestures would become unnecessary.

If jutsu was structured as vectors, chakra output must follow a frequency-based model.

Every shinobi adjusted their chakra flow instinctively to match a jutsu's required output. I would do so deliberately.

The formula:

Where:

F is the required chakra frequency (Hz)

X, Y, Z are the summed chakra components

n is the number of hand signs

For the Fireball Jutsu:

Lightning Release - High-speed jutsu require a frequency above 2 Hz.

Earth Release - Stable jutsu require a frequency below 1 Hz.

Fire Release, Wind Release, Water Release - Moderate control, typically between 1-2 Hz.

If I could learn to modulate chakra frequency manually, I could replicate any jutsu-even those I hadn't learned.

The implications were clear.

Shinobi relied on tradition. I would rewrite the system from the ground up.

I closed the notebook and looked up at the sky. The stars were still, distant.

----

It was time for my appointment with Naruto.

I arrived at the designated meeting spot a few minutes early. Naruto wasn't here yet, which was unsurprising given his lack of discipline. I leaned against a wooden fence, observing the village. The late afternoon sun casts long shadows on the dirt roads, and the streets bustled with people finishing their daily routines. Vendors shouted their offers, shinobi trainees ran errands, and somewhere in the distance, a dog barked at nothing in particular.

I didn't have to wait long.

"There you are, Kiyotaka!" Naruto's loud, excited voice cut through the air before he even reached me. He was grinning, his orange jacket slightly unzipped, revealing the white t-shirt underneath. "I thought you wouldn't come!"

I tilted my head slightly, calculating my response. "You asked me to come, and I agreed."

Naruto blinked, then laughed. "You talk kinda weird, y'know that?"

I merely shrugged.

We started walking aimlessly through the streets. Naruto was the type to fill silences, so I let him talk. He rambled about his dream to become Hokage, about how everyone ignored him, how the villagers treated him like he didn't belong. I responded only when necessary, keeping my words simple and direct, subtly guiding the conversation.

After a while, I decided it was time to deepen his trust. "I get it." My voice was quieter, more thoughtful.

Naruto tilted his head. "Huh?"

"The way people look at you. How they avoid you. How it feels like no one really sees you."

Naruto slowed his steps. "Yeah..."

"I've never had parents either," I continued, voice steady. "I don't have friends. I don't belong anywhere."

Naruto's eyes widened. The emotional reaction I expected. "You too?"

I nodded. "That's why I don't talk much. There's no point in talking when no one listens."

Naruto clenched his fists. "Yeah, exactly! I always try so hard, but people still treat me like I'm nobody."

I sighed, as if exhausted by the topic. "It doesn't matter. People like us, we survive on our own."

That did it. I could see it in his eyes. He now saw me as someone who truly understood him. Not just someone who pitied him-someone who lived through the same pain.

Before he could respond, his eyes flickered toward something in the distance. I followed his gaze.

An ice cream cart.

Naruto immediately checked his pockets, face twisting in disappointment as he came up empty. Then he looked at me.

I slowly shook my head and patted my pockets, mimicking his earlier motion. No money.

Naruto groaned. "Man, I was gonna buy us some!"

I was about to suggest we move along when Naruto suddenly grabbed my wrist. "Come on!"

Something was off. His grip was too firm, too determined. I frowned. "What are you doing?"

He didn't answer. Instead, he pulled me forward, rushing toward the cart with reckless enthusiasm. My mind caught up instantly. This idiot plans to steal it.

I quickly analyzed the situation. The vendor was an elderly man with thick glasses, currently occupied with a small group of children buying ice cream. The surrounding area had moderate foot traffic-not too crowded, but enough potential witnesses. If Naruto tried to snatch the ice cream and run, the likelihood of getting caught was high. At best, we'd get yelled at. At worst, someone would report us to the shinobi in charge of the village.

Unacceptable.

I yanked my arm free just before we reached the cart. "That's a bad plan."

Naruto turned, confused. "Huh? But-"

I exhaled through my nose. I didn't want trouble, but... my eyes flickered toward the colorful ice cream display. Cold, sweet, melting against my tongue-

Sigh.

I quickly suppressed the thought. But another thought surfaced. A better plan.

"If you're going to steal," I said flatly, "do it correctly."

Naruto's eyes lit up. "You got a plan?"

I nodded. "I'll distract the vendor. You take two ice creams and walk away normally."

Naruto grinned. "You're pretty smart, Kiyotaka!"

I didn't respond. We moved into position.

I approached the vendor, maintaining a neutral expression. "Excuse me," I said, voice calm and polite. "I have a question about your ice cream."

The old man turned to me with a smile. "Of course, young man! What would you like to know?"

I gestured at the different flavors. "Which of these melts the slowest?"

The vendor blinked. "Ah, well... that depends on the ingredients. The chocolate and vanilla hold their shape longer, but the fruit-based ones-"

As he started his explanation, I kept nodding attentively, pretending to be deeply invested. Behind him, Naruto moved swiftly. He grabbed two ice creams and slipped away without a sound.

I gave the vendor one final nod. "Thank you. That was helpful."

Then I walked away, unhurried.

Naruto was waiting around the corner, grinning like an idiot. "We did it!" He handed me one of the stolen ice creams. "Here you go, partner-in-crime."

I took the ice cream without a word. The cold sensation spread through my fingers. I took a bite. The sweetness melted on my tongue.

This reminds me of the first time i ate ice cream with my old Ayanokoji group from my past world.

Naruto laughed. "You like it?"

I didn't answer. But I took another bite.

We sat on the steps of an empty shop, eating in silence.

Naruto leaned back, grinning up at the sky. "Y'know, I never had someone to share food with before. It's nice."

I continued eating, analyzing his words. "Share" implied ownership. But neither of us owned this ice cream. It was stolen. And yet, he framed it as an act of generosity. His perspective was fascinating.

Naruto suddenly looked at me. "Hey, Kiyotaka."

I glanced at him.

He grinned. "We're friends now, right?"

I chewed slowly, pretending to consider it.

"Yes. We are friends."

I swallowed. "This was a one-time thing."

Naruto laughed. "Yeah, yeah. That's what you say now."

I took another bite, letting the cold sweetness linger.

Author's notes:

What do you think about the Chakra Encoding System? Too much math?