Found a bug!
When the player goes outcast and still possesses territory, then purchases a home and stops being outcast, that territory is no longer accessible for Extract Arkhe projects. On the other hand, now that I'm not outcast I appear to be gaining some Arkhe each turn without any active projects.
Further information: On the random date night screen, I was informed that we couldn't go out anywhere because I didn't own any territories, even though the map shows my territory from pre-outcast days as owned. Additionally, when I'm attacked, I can select the territory as my battlefield when defending.
On an unrelated note, the skill of pottery is seriously overpowered. My character, who has the governing trait of 5, just created a piece of furniture worth 75 favors. Or, basically enough to take over generally any single lobby with a single gift. Once you know the secrets of the pottery skill, the game become more about just surviving until you can take over all the lobbies than anything else. Granted, I have nothing wrong with that, but value 75 is probably a bit excessive, since it only takes 8 Arkhe to make, and even with all the wasted attempts, its really a matter of time before the player scores enough sweet furniture to bribe enough lobbies to become Emperor. Only real obstacle is getting Renascents of proper origin (player character doesn't count) and faction affiliation (in-game descriptor of "alignment" caused me some confusion, as I thought it meant that ruthless/hedonist/philanthropist mattered...although it also doesn't say that the player can't puppet a lobby). Obstacle that I quite enjoy, although randomness makes it sometimes harder and sometimes easier.