So... Back to talking about the Labs?

That's agreeable to the Fifth. Though honestly, Abigail got distracted speaking with Teacher and then chasing down references in the library and they haven't made it to the Facility yet.

Well, the background reading might be of use. 

Are the others willing to share their insights and notes on the Labs (or parts of labs) they've done?

Palamedes and Angerona were working on Lab Six. A table with a locked box and a single tooth, molar, human. Male, late sixties, good flosser, never left the First a day in his life and the tooth had never departed afterwards. Literally nothing at all to do with the box, though. Nor any other part of Canaan House. Absolutely zero resonance to anything. Which should be flatly impossible, everything here is original to the construction.

So...?

So. They went looking for a body with a missing tooth. Eventually tracked down one of the servitors who had a matching hole, and through a series of charades, were rewarded with the opportunity to make a cast of its clavicle. Which proved to be the key to open the box, if you like puns.

" - But where's the necromantic challenge? I could've done that one on my own."

"It's the constructs."

"But they're not constructs, that's the trick. They think, they react in real time, they can communicate. They're more like revenants, but tied to one physical body."

"Oh," says Abigail Pent.

"We knew their natural language processing was too good for constructs - are you sure they're being controlled individually as a kind of bound revenant, versus some kind of centralized control via something like Lab Two's theorems?"

"They're not controlled at all, or to put it another way, they're controlling themselves, individually and respectively."

Interested nod! "I'm tempted to skip ahead there," Gideon tells Ellyn. To Palamedes: "Do you mind sharing your key from the lab?"

"We didn't get a key. The box was empty when we unlocked it."

"So there's only one key per lab - but who else has even been down there?"

"The Second haven't. I'm pretty sure they don't even know it exists."

"Eighth or Seventh, then."

"And the Eighth definitely isn't going to cooperate with us."

"Seventh won't be better."

"...We need to get to the other keys before they do."

"I think we're close on Lab 7," Phoe volunteers.

"Ellyn and I were planning to start Lab 4 tomorrow morning."

"So that leaves, what, Lab 5 and Lab 8?"

"Lab 5 might be auspicious for us," the Fifth necro says.

"Can't say I'm any more eager than the Third to take a crack at 8."