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I would consider what we probably want to do with Xana as goals before deciding what political statement they should make
#1 Xana being far away from anywhere else is ideal for secret projects, particularly of the Null variety. Out of the way of the astronomican, distanced from most other sectors, right at the edge of the Galaxy
#2 We therefore want to secure it for said secret projects, not just militarily but politically and securities wise. We will want to make it as impregnable to espionage and spying as we can, with as little risk to anyone just exerting their authority on it besides us and maybe Malcador who we will invite his Pariah Project on (ideally)
#3 We should achieve this in such a way while simultaneously achieving our political goals of gathering more forge worlds under our banner. Not necessarily as vassals to us directly, but to where we have enough voices in the wider mechanicum at large to give us great influence on Mars
#4 plus we also want to convince Lucius to invest its resources into Xana, given we are somewhat reliant on our good reputation and history among them and our charisma but still
Now unless I am grossly mistaken about these being our goals, we can consider which of the three options best fits said goals with the most pro's and the least con's.