Each of you has accepted work from The Verge for your own reasons (see player secrets for more details) and it won't be a simple task they ask of you. In essence, they need a large power core. Some of you might know more about this than others, but essentially it is a rare and valuable Artifact used to restore power to Numenera that has drained its own supply. Apparently it is needed to whatever they've found in the dig site, but they aren't saying more… yet. This is NOT an easy job, so they'll be grateful for your services. Plus you've already bargained for your reward.
The starting point given to you is that the Morradinites in New Morradin have several "extra" power cores. So off you go to haggle, bribe, steal, or cheat your way into getting one (or more?). Two sources in New Morradin are known; their "gift", an impressive piece of Numenera the town was built around, or their secret stash. There are probably other cores currently stockpiled by one Faction or another, but New Morradin is certainly the closest. It is worth noting that the Morradinites aren't terribly friendly towards The Verge despite pretending to be, and thus you're being sent NOT as agents of The Verge and won't be publicly admitted to if caught, tortured, blackmailed, or tricked into saying or doing something stupid.