I was looking for something else when I noticed this had never been reviewed. Let me know if things go too long without getting a response!
It's been some time since the last time I read this arc, so it took a little while for the details to work their way up from memory. That's the risk of writing installments on a site like this, I suppose. Not a complaint, by the way, but if I miss something I should have remembered from the earlier bits, well, that's my excuse.
There are a few things that bother me in the collab here. It's unclear if Laermont's office is in Lupanar or just near it. Since he's an official quaestor, he wouldn't be 'allowed' to have an office within Lupanar -- the entire reason it exists is because of the unofficial truce that exists only as long as criminal elements stay in and law enforcement stays out. In order to maintain that truce, criminals who get too bold and operate outside of Lupanar, drawing too much attention to themselves, will often be dealt with by other criminals who want to keep flying under the radar. Likewise, law enforcement and investigators that get too gung-ho about chasing people or information within Lupanar may find themselves facing punishment from their superiors; better to keep most criminals bottled up in Lupanar where they mostly hurt each other, than break the truce and start an endless war on crime throughout the city.
It's corrupt on both sides, but Lupanar was set up to be this unique city-within-a-city (thus its nickname, the Little City). For Laermont to do any of his work within Lupanar, he has to be clever about it and not get caught, find or create just cause that he can hold up as an excuse, or at least hide what he is. That's world-building stuff, though, and nothing was inherently broken here. I'm just wanting to repeat myself here, because I think this is the third time it's been alluded that Laermont is ignoring the whole dynamic there.
Laermont also swaps from, 'never heard of it' to 'oh yeah, I know that but I didn't think it worked' rather quickly. Intentional forgetfulness or just something that wasn't edited before posting? On a related note, Vita brings it up first, claims that he is embarking on a new study, which he is calling Sacred Geometry. Then of course Laermont says he's never heard of it (reasonable, if Vita created the study), but later speaks as if he has heard of it before from somewhere else... and Vita seems to affirm this by saying he wants to take a closer look at, 'this Sacred Geometry, as you called it.'
Some of it is Vita's personality, but very little of the conversation here felt like two characters speaking to each other, but instead felt like two characters each talking to themselves at the same time. Only a few times do they seem to actually respond to what was said last.
The Fracture arc is one that has good potential, and I can see a lot of plot threads leading into and out of it. This installment, though, feels like it needed more revision and editing in order to put the plot forward rather than the technique. The only advice I can give for these kinds of errors is to always read through a chapter or collab from start to finish before posting. You want it to be comfortable to read so that people can pay attention to what you wrote.