Following the Doctor X path

[Soderbok]

I've started a fresh game and want to complete the Doctor X path.
I completed the first Doctor X research item.
Nothing else is appearing on that line for me to research.

Is there something I should not research to close this line?

Is there a particular mission I need to complete to get the next step on that research path?

[Delian]

You can only really start the DoctorX storyline after researching a live Academy Esper. The earliest you can obtain one is in May. Because from May on, there's a 33% chance per month that an Academy Hopper shipping (Passenger Ferrying mission) will spawn. Still need to get lucky to catch and shoot it down tho, because it's pretty fast~

[Psyentific]

You need to complete the Doctor X Prison and Gravball Thunderdome missions to progress the storyline. The former is unlocked by investigating the Academy, which is (one of?) her patron organizations. The latter is unlocked by the prison and is a random spawn some months later.
For both of these you'll need to use Castaway Gals, which are not necessarily your starting gals. Regular young uber recruits won't do, it has to be the slightly more badass variant. Sometimes these can be rescued from landed necropirates, red light brothels, distress beacons, or random events.