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“Hm,” said Camilla neutrally, and Gideon knew immediately that she organised Palamedes’s and her socks by colour and genre.

Harrowhark and Palamedes picked their way through the mess to the tables. Palamedes was saying in his explanation voice: “It’s not as though I didn’t complete this challenge by lunchtime, though I had a distinct advantage. It was a psychometrical challenge. The main difficulty was working out what the challenge wanted in the first place: it was set up by someone with an obscure sense of humour. It was just a room with a table, a locked box, and a single molar.”

“Reconstruction?”

“Not all of us can respring a body by dint of a molar, Reverend Daughter. Anyway, I must have examined that tooth for two hours. I know every single thing there is to know about that tooth. Mandibular second, deciduous eruption, vitamin deficiency, male, died in his sixties, flossed obediently, never left the planet. Died in this selfsame tower.”

Both of them were riffling through the papers left on the desk: Palamedes left them in forensically exact piles divided by where they had been found. He adjusted his glasses and said, “Then Camilla took over because I wasn’t bloody thinking.”

Camilla grunted. She had meandered over to look at the rust-pitted crossbars of the chin-up, and Gideon had repaired to the worm mound of sleeping bags to kick them unhelpfully. Harrow said impatiently, “Get to the denouement, Sextus.”

“I had tracked the tooth. It told me nothing—no spiritual links to any part of the building. It was a black hole. It was as though the body it came from had never been alive. No ghost remnants, nothing—this is impossible, you understand, it meant the spirit had somehow been removed entirely. So I did some old-fashioned detective work.”

He peered under an abandoned clearfile. “I looked upstairs for the skeleton with the missing upper molar. He wouldn’t come down with me, but he did let me make a plaster impression of his clavicle. The clavicle! Someone was having a joke. Anyway, you can imagine my reaction when I unlocked the box with it and found it empty.”

Gideon looked up from a pasteboard box she had found: it was full of the ring tabs you got on pressurised drink cans, and jingled unmusically when she shook it. “The constructs? Like, the bone servants?”

“Second’s right, first isn’t,” said Camilla laconically.

“They’re the opposite of what Lady Septimus calls the beguiling corpse,” said Palamedes. “They seem to have most of their faculties intact. Mine was very nice, though he’s forgotten how to write. The skeletons aren’t reanimations, Ninth, they’re revenants: ghosts inhabiting a physical shell. They simply lack a true revenant’s ability to move itself along a thanergetic link. The beguiling corpse is a remnant of spirit attached to a perfect and incorruptible body—that’s the idea, anyway—where what I’ll term the hideous corpse is a fully intact spirit attached permanently to a rotting body. Not that someone hasn’t preserved those bones beautifully.”

Harrowhark slammed a ring-binder down on the bench.

“I’m a fool,” she said bitterly. “I knew they moved too well to be constructs—no matter how I tried to mimic how they’d been done. I just could have sworn—but that’s impossible. They’d need someone to control them.”

“They do—themselves,” said Palamedes. “They are autonomously powering themselves. It debunks every piece of thanergy theory I ever learned. The old fogeys back home would peel their feet for half an hour alone with one. It still doesn’t explain why there’s no energy signature on the bones, though. Anyway, this is the laboratory of the Lyctor who created them—and here’s their theory.”

Much like the one back in the other laboratory, the theorem was carved into a big stone slab pinned down in a dusty back corner and covered up with loose-leaf flimsy. Both cavaliers drifted over, and they all together stared at the carved diagrams. The laboratory was very quiet and the spotlights haloed streams of dust so thick you could lick them.

Resting on the edge of the stone set into the table, there was a tooth. Palamedes picked it up. It was a premolar, with long and horrible roots: it was brown with age. He handed it to Harrow, who gently unfolded it in the way that only a bone magician could and in the way that always made Gideon’s jaw hurt. She turned it into a long ribbon of enamel, an orange with the skin taken off and flattened, a three-dimensional object turned two-dimensional.

Written on the tooth in tiny, tiny letters was this:

FIVE HUNDRED INTO FIFTY

IT IS FINISHED!

Harrowhark took out her fat black journal and was scribbling down notes, but Palamedes had abruptly lost interest in the theory stone. He was looking at the walls instead, flipping open some of the ring-binders that she had discarded. He stopped in front of a faded pinboard, riddled thick with pins, all with bits of string attached. Gideon came to stand next to him.

“Look at this,” he said.

There were rainbow splotches of pins all over the board. There were tiny clusters, and Gideon noticed that at the centre of each cluster there was one white pin; the smallest and most numerous clusters had three pins fixed around one white pin. Some others had five or six. Then there were two other separate whorls of pins, each made up of dozens alone, and then one enormous pin-splotch: more than a hundred of them in a rainbow of colours, thickly clustered around one in white.

“The problem of necromancy,” said Palamedes, “is that the acts themselves, if understood, aren’t difficult to do. But maintaining anything … we’re glass cannons. Our military survives because we have hundreds of thousands of heavily armed men and women with big swords.”

“There’s always more thanergy to feed from, Sextus,” said Harrow distantly, flicking her eyes back and forth as she copied. “Give me a single death and I can go for ten minutes.”

“Yes, but that’s the problem, isn’t it; ten minutes, then you need more. Thanergy’s transient. A necromancer’s biggest threat is honestly themselves. My whole House for a reliable food source—”

“Warden,” said Camilla, quite suddenly.

She had opened up a ring-binder untidy with pages. Inside were an array of old flimsy lithographs, the black-and-white kind. On the very first page there was a faded note that had once been yellow, the letters still legible in a short, curt hand:

CONFIRMED INDEPENDENTLY HIGHLIGHTED BEST OPTION

ASK E.J.G.

YRS, ANASTASIA.

P.S. GIVE ME BACK MY CALIPERS I NEED THEM

Camilla flipped through the binder. The pictures were hasty, low-quality snaps of men and women from the shoulders up, squinting at the camera, eyes half-shut as though they hated the light: most of them looked very serious and solemn, as though posing for a mugshot. Some of these men and women had been crossed out. Some had a few ticks against their picture. Camilla thumbed a page over, and they all paused.

The overexposure did not disguise a head-and-shoulders photo of the man they all called Teacher, bright blue eyes a desaturated sepia, still smiling from a lifetime away. He looked not a day older or younger. And his photograph had been ringed around in a black marker pen.

“Sextus,” Harrow began, ominously.

“I couldn’t tell,” said Palamedes. For his part, he sounded almost dazed. “Ninth, I absolutely could not tell. Another beguiling corpse?”

“Then who’s controlling him? There’s nobody here but us, Sextus.”

“I’d like to hope so. Could he be independent? But how—”