Beyond this point, there were no names.
The town’s name, once carved into the stone pillars of the station, had been erased. But it hadn't been scraped away.
The characters were simply fading, blurring into nothingness. It wasn't the natural weathering of stone; it was as if the name itself had lost its grip and slipped through the cracks of the rock.
“This is a place where names do not take root.”
Kuon reached out and touched the pillar.
The stone was warm.
Ever since they had headed North, the very nature of stone’s coldness had shifted. In the South, the rocks had felt bone-chillingly frozen, but here, they held the warmth of something living.
“In places where the ‘Freezing of Names’ does not reach, a name cannot be fixed. Whether you carve it in stone or write it on paper, it eventually falls away. This is... a place before names.”
“Before names,” Koyoi repeated.
“Existence is possible without a name. You simply cannot call for it. And that which cannot be called cannot be recorded. That which cannot be recorded falls outside the jurisdiction of the Order.”
A single railway track stretched toward the North.
It was a lone line. In the South, there had been double tracks, but here there was only one. Silver-gray trees lined both sides of the path, their tall branches arching over the rails to form a tunnel.
Asahi peered down the line. “What’s the next station?”
“There isn't one,” Kuon said. “There are no recorded stations beyond this point. Not in the Index, not anywhere. We don't even know how far these tracks go.”
“The tracks are right there, aren't they?”
“They are. But we don't know who laid them. We don't even know if a train still runs.”
Asahi looked closer at the rails. They weren't rusted. They were being used.
There were traces of a recent passage; the surface of the rails, polished smooth by wheels, reflected a thin, pale light.
“They’re in use. Which means there’s something up ahead.”
Koyoi clutched the drawstring pouch to his chest. The droplets inside were pulsing.
They were warm.
It was a gentle but steady rhythm, possessed of a clear sense of purpose. They were pointing North.
“Let’s go,” Koyoi said, his voice catching with his breath. “These little ones remember. They know the path ahead.”
Kuon closed the Index. From here on, the road was unwritten. The golden vein of light on the book's cover continued to shine brightly, but there were no pages left for it to illuminate.
“I suppose we have no choice but to trust the pouch,” Kuon murmured. He wasn't speaking to Koyoi, but rather convincing himself.
Asahi adjusted the greatsword on his back. “Trust, doubt—it’s all too much talk. There’s a road, so we walk it. That’s all there is to it.”
Suddenly, they felt the presence of a train.
When they turned around, it was already sitting at the station. They hadn't heard it arrive. There had been no sound, no hiss of steam. It was simply there.
“We getting on?” Asahi asked, as if to confirm.
Koyoi asked the pouch. A single droplet pulsed with sudden strength.
He felt it telling him to board.
The three of them stepped onto the train. The doors slid shut. The carriage began to move.
Outside the window, the silver-gray trees began to flow past. Through the gaps in the branches, the sky was visible. In the dark expanse, the "light of names" floated—suspended in the air.
They did not fall. They did not flicker out. They simply drifted, glowing.
The train rattled North, riding over nameless tracks, illuminated by the light of names.
Koyoi pressed his forehead against the glass.
The soil beside the tracks was faintly glowing. It wasn't a reflection of the sky; the light was seeping out from within the earth itself.
One of those lights moved.
Something was rising up from beneath the dirt. Grains of ice, cradled by the warmed earth, were slowly melting away.
They were frozen names.
Tiny fragments of names belonging to no one, frozen by the Order and spilled from somewhere long ago, only to find their way to this warm soil. The thawed names rose like steam—thin, unsteady, so fragile they seemed ready to scatter at the slightest breeze.
But they were alive.
“...Did you see that?” Koyoi whispered.
Kuon nodded. Asahi, too, was staring out the window.
It was the moment Yae’s Theorem was proven.