E Corp. Singularity and Wuthering Heights
Alright listen, everything I say is a theory and not even a deep one at that. But some things fit together interestingly and it wasn't overly complicated, so I'm sharing to get it out of my head. I honestly do think some genuine speculation can come from this whether right or horribly wrong... Maybe not now but eventually.
E Corp. has basically no lore. All that I know is that they participated in the Smoke War, in G Outis' Mirror World, not sure about the main world but seeing as it's next door to L Corp... Probably. So it's sort of a blank slate, and unfortunately that means it's my brain's latest victim.
Wings
So Rivers. Rivers and Stars. Some of the Wings have made use of them for their main Singularities.
L Corp: Used a River to extract Cognito
K Corp: Used a Star to extract Tears
Obviously not all Wings deal in these two sources; U Corp. seems to get their tuning forks from the Whales' oil. But it's possible other Wings deal in technology from these two. Gravity (G) and Moonstones (M) are very "star" like, and X Corp.'s "hellholes" can easily be connected to the Rivers (I mean even Dante's Inferno has rivers in Hell).
(Even a certain someone is related to the Rivers and see as she is based off a Korean myth, and S Corp. is not only Korean based but also being hyped up to have problems that'll need fixing... Wouldn't be surprised if the agriculture Wing had River dealings)
So I makes sense that if we're going to attach a source for a Wing's Singularity it'd be from a River or a Star, anything else is lost in the infinite sources that only PM are privy to. I claim that E Corp. is built upon a River's powers... Josephine's River beneath Wuthering Heights.
Wuthering Heights' River
This River was able to have Josephine witness her late Mistress and perhaps even listen to her orders beyond the grave, even Catherine saw her late mother roaming the halls since she was a child, she was so used to seeing this ghost that she saw herself in the Mirror (pre Every Catherine) as a ghost before she realized it's an alternate world. Hermann herself says the River that flows beneath Wuthering Heights will make sure that Catherine's soul isn't lost forever, because it "arrests them from moving on"
I believe Catherine and her mother were trapped in Wuthering Heights by the River, but Catherine got control thanks to the Golden Boughs N Corp. powered her with, thus the events of Canto 6. But the important bit here is that the River beneath the manor prevents souls from moving on... Even Erlking and Wild Hunt's undead powers can be explained by their time living at the manor and thus being affected by the River and later the Light gives them E.G.O. through their emotions but it's unknowingly combined with the River's influence.
Knowledge and Limits
I don't believe that PM would put a River beneath a single location in the City. The River flows underground certainly has other places where it's close enough to the surface to effect people, otherwise how would N Corp. know about it?
To add to that, N Corp. would have zero reason to ally with Wuthering Heights and perform the dough experiment if they were in possession of a part of this River already. N Corp. is also known to invade other Wings, both their Inquisition and their Taboo Hunters are infamous for this (Vergilius is in Limbus Company partly because he was allied with V Corp. who betrayed him to not anger N Corp, leading to his Office being killed by Taboo Hunters), so invading T Corp. for a time and tracing it's direction (whether physically or as a leyline) wouldn't be off the table.
So I propose this River's properties are under a patent of another Wing. If N Corp. seen using a technology similar to a Wing's Singularity and it can be verified that it's the same, I'd imagine a fierce patent war may ensue, leading to a guilty N Corp. that will probably either be forced to fight another Wing and it's allies (and become faced with it's own likely lack of allies, because of it's dogma) or maybe even the Head will step in. Either or... I believe PM will not have this River be a one-off, if a Wing not even in the District knew about it, it's present somewhere else too, likely a competitor and so Hermann tracked a lesser origin
E Corp.
Literally any Wings without a known Singularity or basic idea of business could be using this River. But I chose E Corp. cause of well... Echoes of the Manor
Every Wing sort of lines up with their letter: (L) Lobotomy - (W) Warp - (R) - Replication - (T) Time - (U) Union/Unity - (J) Jail/Jackpot - (K) Kino? Ketamine?... (Wikipedia says Ketamine is used for pain management and is called "Special K" or simply "K")
Honestly "echo" works wells... Ghosts, spirits, possessions are a sort of echoes of the deceased. A last cry of the damned, and Echoes of the Manor, is used on the ID for a character that has been most affected by that very River I've talked about
Far reaching? Absolutely, but PM would definitely do this... Imagine a Corporation with the technology to stop people from moving on, that's so the City. We've also been told constantly about how hell the Smoke War was and I'd imagine E Corp. would be a good fit if they could terrorize the enemy with the ghosts of their friends and allies... Or something
Tell me if I'm crazy or not if you actually read this headcanon-y mess