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This was not helped by the fact that nearly every square inch was covered by flimsy: Palamedes’s scribbles were tacked up like wallpaper across every bare surface. They were taped to tables. They clustered over the mirror. Fat books lay in serried rows on the arms of every chair, stacked haphazardly, as though nobody ever sat down without bringing another one to bear. Gideon had peeked through the open door of the bedroom, into a dark nest where a huge whiteboard stared down at the ancient, wheezing four-poster bed, very neatly made. There was no question about whether or not Camilla inhabited the horrible cot attached to the end, cavalier-style. It sagged beneath assorted weapons and tins of metal polish.

“I’m not moving from my outline,” said Harrow. She and Palamedes sat on either side of a table swept hastily clear of books and notes: stray pens rolled across the surface at the least jolt. “I hold the keys. We enter together. You get an hour.”

“An hour’s not remotely sufficient—”

“You’re slow.”

“You’re paranoid.”

“I am—currently—alive,” said Harrowhark, and Gideon winced.

Palamedes had taken off his spectacles ten minutes into the argument, and he was now cleaning them on the front of his robe. This appeared to be more of an aggressive move than a defensive one: his eyes, free of glass plates, were arrestingly grey. It mainly only hurt Gideon, who was trying very badly to avoid his gaze. “So you are. The room in and of itself is of interest to me, and it ought to be of interest to you,” he said.

“You’re too forensic.”

“You lack scope. Give over, Nonagesimus. A key-for-key swap is the most logical and most elegant arrangement here. This refusal is just superstition and paranoia, cooked up with a side of—pure humbuggery.”

For a moment Gideon’s anger and remorse were overwhelmed by, Did you legit just say ‘pure humbuggery’?

The necromancers were now mirroring each other’s equally bowed postures: bony elbows on the table, hands clasped beneath their chins, staring at each other unblinking. Behind Palamedes’s chair, Camilla had the glazed expression of someone who had checked out ten minutes ago. Her arm was bandaged but not kept pinned up, and she appeared to have full range of movement with it. Gideon was lolling behind Harrow, picking at her fingernails and staring at the pieces of paper, which had handwriting that was more like cryptography. Her own necromancer settled back and said, sepulchral: “You are still convinced by your … megatheorem idea, then.”

“Yes. Aren’t you?”

“No. It’s sensational.”

“But not out of the question. Look. The tasks and challenges—the theories underpinning them—they’re really not that disparate. Neural amalgamation. Transferral of energy. As we saw in the entropy field challenge, continuous siphoning. The magical theory’s astonishing. Nobody has pushed necromantic power this far: it’s unsustainable. If the intent is to show off the sheer breadth of Lyctoral power—well, they did. I’ve seen the winnowing test, and if the self-replicating bone golem had been the only thing in it I would still be kept up at night. I don’t know how the hell they did it.”

“I do,” said Harrow, “and if my calculations are right I can replicate it. But all this is more than unsustainable, Sextus. The things they’ve shown us would be powerful—would bespeak impossible depth of necromantic ability—if they were replicable. These experiments all demand a continuous flow of thanergy. They’ve hidden that source somewhere in the facility, and that’s the true prize.”

“Ah. Your secret door theory. Very Ninth.”

She bristled. “It’s a simple understanding of area and space. Including the facility, we’ve got access to maybe thirty percent of this tower. That’s what’s called hard evidence, Warden. Your megatheorem is based on supposition and your so-called ‘instinct.’”

“Thanks! Anyway, I don’t like how many of these spells are about sheer control,” said Palamedes.

“Don’t be feeble. Necromancy is control.”

Palamedes slipped his spectacles back on. Phew. “Maybe,” he said. “I don’t know, some days. Look—Nonagesimus. These theorems are all teaching us something. I believe they’re parts of an overarching whole; like the whiteboard in the facility, remember? It is finished. You believe they’re giving us clues—prompts—toward some deeper occult understanding that’s hidden elsewhere, this power source idea. I see puzzle pieces; you see direction signs. Now, maybe you’re right and we’re meant to follow the crumbs to some master treasure. But if I’m right—if Lyctorhood is nothing more or less than the synthesis of eight individual theorems…”

Harrow did not speak. There was a long moment, and Gideon thought that Palamedes had lapsed into thought. But then he said crisply: “Then it’s wrong. There’s a flaw in the underlying logic. The whole thing is an ugly mistake.”

Now her necromancer said, “Leave the cryptic to the Ninth. What mistake, Sextus?”

“I’ll give you the relevant notes if you help me pick a lock,” said Palamedes.

This was enough to give her pause. “Give me your personal notes on all the theorems you’ve seen. What lock?”

“Throw in a copy of your map—”

“Do I have a map?” Harrowhark remarked, in general, to the air. “My goodness. That is, at the very best, a baseless assertion.”

“Not an idiot, Reverend Daughter. A Lyctoral lock—the one that matches the Sixth House key. The grey key. Which Silas Octakiseron currently holds. Hence: picking.”

“That’s impossible. How?”

“You can’t know until we do it. If it works, it gets you every single note on every theorem I’ve read, in return for yours, your cooperation, and the map. Are you in?”

There was a pregnant pause. As everyone had already known beforehand, Gideon’s necromancer was forced to admit that she was in. She rose to stand: the chair behind her teetered dangerously, and Gideon corrected it with her foot. “At least show me the door you told me about,” she commanded. “I despise this feeling that the Sixth House is taking my house for all it can get.”

“Most people would have looked upon this as a generous deal,” remarked Sextus, whose chair was being held back for him by the obliging Camilla, “but I did owe you one—for sticking by us when the Third House made its challenge. Not that we wouldn’t have won it—but we would have given more than I’m willing to give. So that’s the sticky sentiment part. Come with me for the cold hard facts.”

They all traipsed after him for the cold hard facts. When the Sixth House locked their front door, it was grimly amusing to see that as well as Palamedes’s wards they had hammered in five deadlocks, and reinforced the door so that it could not be taken off its hinges. Hearing Camilla shove all the bolts home was as good as an orchestra. The two necromancers drifted to the front—their long robes making them look like dreary grey birds—and Gideon and Camilla fell behind them, lingering beyond the mandated half step.

Camilla the Sixth’s shoulders were set. Her straight dark fringe fell out of the way as she half-turned her face to Gideon, briefly, expressionlessly, but that was all Gideon needed.

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