The base had already existed when the hexarch brought Hemiola, Rhombus, and Sieve with him 280 years ago. The hexarch meant them to maintain the facility in his absence and wait upon him during his periodic visits. Like most humans, he didn’t pay attention to their individual quirks or assign them names. Then again, he had less reason than most to care. As hexarch, he had other matters on his mind.
“This individual is walking with a manform’s stride,” Rhombus was saying. “That’s got to be uncomfortable with those short legs. And didn’t Kujen say once that he was going to stick to tall bodies? The one out there is rather short.”
The figure was making good time down the stairs. Lights came on as it approached, and faded as it passed, giving the impression of a glowing snake winding its way ever deeper. Shadows ghosted along the crevasse’s walls.
“Are you sure we shouldn’t be looking to our defenses?” Rhombus asked. It gestured with two of its grippers at the descending figure’s equipment. “Not to impugn Kujen’s abilities, but does he even know how to use rappelling gear?”
“Maybe that’s a fashion statement too,” Hemiola said. “Or he’s taken up a hobby. Or he’s not sure how safe the stairs are.”
“He’s moving pretty quickly if so,” Sieve said.
Hemiola had no answer. Instead, it checked the infrared sub-display against the one for the ordinary human visual spectrum. Besides the staircase’s lights, the figure was wearing a headlamp, although it hadn’t turned it on. Preserving battery power, presumably. The stairs wound around and beneath the lip of the crevasse, taking the figure beyond sight of the sky.
“Another eight minutes and it’ll reach the outer door,” Sieve said.
“Wonderful,” Rhombus said, bobbing up and down in the air in a clear display of nerves.
“I don’t see why you’re so tense,” Hemiola said. “The calendrical lock will settle matters one way or another.”
Rhombus glowered at it in a distinctly asymmetrical pattern. “By vaporizing this moon and everything on it if that isn’t Kujen!”
“It won’t come to that,” Hemiola said.
The figure’s pace hadn’t slowed. Another three minutes before it reached the outer door.
“You’re so sanctimonious it makes my heuristics seize up,” Rhombus said.
Sanctimony had nothing to do with it. The hexarch stored notes on his top-secret projects here. He couldn’t risk them falling into his enemies’ hands. So he came here every century to deposit updates, bringing only Jedao with him. From listening in on the conversations between the two, Hemiola gathered that the hexarch had many enemies.
“There it goes,” Sieve said.
Now Sieve was bobbing up and down, too. Hemiola resisted the urge to follow suit.
The figure opened the outer door without any trouble. No surprise there; the outer door wasn’t meant to be the barrier. It stepped into the airlock. The outer door closed behind it. The figure waited for the inner door to open, then continued into the next chamber.
This one was hexagonal, with alcoves in each wall. Within each alcove rested a plaque depicting the emblem of one of the hexarchate’s six factions: the Rahal scrywolf, the Nirai voidmoth, the Shuos ninefox, the Kel ashhawk, the Andan kniferose, and the Vidona stingray. Hemiola couldn’t help a surge of affection at the sight of the voidmoth.
A terminal rose from the center of the room. Its display brightened when the figure stepped before it. The figure rested its hand against the display. A countdown flared up. Twelve minutes to open the calendrical lock, or the base would self-destruct.
The three servitors had, without the hexarch’s authorization, contrived a way to listen in on the very large number that the terminal had transmitted to the figure’s augment. (Strictly speaking, the hexarch hadn’t forbidden it.) At least scan verified that the figure did, in fact, possess an augment, or everyone would have been doomed.
Hemiola knew the principle of the calendrical lock, which the hexarch had explained to Jedao in distressingly small words.
“Look,” the hexarch had said during that first voyage to Tefos, “why don’t you take a break from playing solitaire so I can tell you about this.”
That time, the hexarch was a young man with middling dark skin and dark curls, his broad chest tapering to a slender waist. Although he affected a simple Nirai uniform, black with silver buttons, an ocean’s bounty of black pearls dripped from his ears, his wrists, his ankles.
Jedao looked up from his card game. His body was even younger than the hexarch’s, slim and unscarred, with blond hair and green eyes declaring its foreign origins. When he wasn’t playing card games, he exercised, as if by sheer effort he could overcome his thorough clumsiness. Kujen had let slip that the body had originally belonged to a Hafn prisoner of war.
“Whatever you like,” Jedao said, his face inquiring.
“How good are you at prime factorization?” the hexarch said.
“How big are the numbers,” Jedao said with unmistakable wariness, “and am I allowed to use a calculator or not?”
“You shouldn’t need a calculator for this,” the hexarch said, “unless you’re much worse at multiplication tables than I think you are. Try factoring seventy-two, just for practice.”
Jedao tapped one of the cards, frowning. “If you insist, Nirai-zho. That’s nine times eight, which becomes three times three times eight, but then you have to deal with the eight, which is four times two, which becomes two times two times two, so... three times three times two times two times two?” His fingers twitched as he counted up all the prime factors.
“You’re never going to win any prizes for speed,” the hexarch said, “but at least you got there.”
Jedao leaned back and smiled a tilted smile at him. “I thought the point of this arrangement was that you did the math bits and I did the walloping bits. Two is prime despite being even, right?”
The hexarch made a long-suffering noise. “You’re fucking with me, right?”
Jedao’s expression remained innocent.
“Saying this in a mathematical context makes me cringe, but will you take my word that with very, very large numbers, it’s very, very difficult to factor them, even using a computer?”
“Isn’t that obvious?”
“Don’t try my patience,” the hexarch said. “I’m explaining this to you so you don’t try some foxbrained scheme to get in by yourself and blow the whole archive to particles. Once you try to enter the archive, you’ll set off a timer. You have twelve minutes to not only factor the very, very large number the system presents to your augment, but to use the factors to perform a ritual that will align the local calendar in a particular manner. When the calendrical lock detects the necessary alignments, it will disarm the self-destruct and let you in.”
“Let me guess,” Jedao said. “You’re the only one fast enough to do it.”
“That’s the gamble, yes.”
“Why the additional ritual?” Jedao said. “Why not just disarm the system once the correct prime factors are regurgitated to it?”
“To prevent someone from hacking the lock remotely,” the hexarch said patiently. “It takes a human presence to affect the local calendar, so it’s an additional precaution.”
Hemiola could have added another reason, if the hexarch had ever thought of it: to prevent enemy servitors from breaking in. The three of them tried to crack the prime factorization problem out of curiosity, but they wouldn’t have dreamed of disarming it for real. In any case, even Sieve hadn’t had any luck with its factorization algorithm. It couldn’t reliably carry out the task in the necessary minutes. Even if one of them had figured it out, the fact that servitors did not generate formation effects under the high calendar meant that a fast algorithm did them no good. They couldn’t affect the lock one way or another.