While investigating the current state of the Triglavian Collective’s invasion, I discovered The Agency interface, at the moment of my writing this query, lists the headquarters of the Triglavians as the New Eden system in Genesis.
New Eden is also the system the EVE Gate is found in.
This information is under the Invasion Info - Standing Section of The Agency, (click the Trig symbol.)
Has this headquarter’s information always been known? And is there a physical location the intrepid traveler might visit?
Like Zhi said, it’s been there since the beginning for them, and there’s nothing you’ll find there but the EVE Gate itself - but as much as it’s likely a placeholder, there are some interesting bits of older lore that make me think there might be something more to it~
In the epilogue of the “Empyrean Age” novel, we join a Jove Directorate battleship in its final moments. The last living crewmember reflects on having failed their mission, with their ship breaking apart after having apparently "passed through point genesis" - that is, the EVE Gate - "which was not at all what it seemed".
In the following novel, “Templar One”, a Jove from this ship - likely the one we followed - intercepts another important character’s ship near the EVE Gate, but in a different form. This Jove is “no longer alive”, instead appearing as a sort of AI-echo recreation of the once-living person, based on their memories.
This character has also now changed sides - we first meet this Jove in the short story “Theodicy”, where he’s fighting against the growing influence of an old and mysterious group of Jove who want to affect the direction civilization takes in New Eden. But by Templar One, he’s on their side.
There’s been a lot of speculation in regards to possible connections between this group and the Triglavians - and the form this Jove takes in Templar One seems extremely close to what we might expect one form of Triglavian life to be like - the “Navka”, specifically.
Though there’s little to support it, I like to wonder if the Abyss is in fact on the other side of the EVE gate to some degree - and was perhaps created as a result of the EVE Gate’s collapse.
So for now, there’s no reason beyond placeholding for the Trig HQ - but I think there could be something to it