Despite StarRupture's admittedly thorough base-building tutorial, you're oddly not introduced to blueprints—collectable crafting recipes hidden around the planet. Given that these restricted items periodically block progress, it's certainly an odd oversight. You're in luck, though; the Stabilizer blueprint location isn't all that far away.
Just like the Rotor and Tube blueprints to the northwest and the Stator blueprint in the north, the first few schematics are a short hike from the orbital lander where you'll have established your first base. The Stabilizer blueprint specifically is also near the best Helium location, which you'll soon need for new recipes, so I recommend checking it out while you're in the area.
Beware that there are enemies in the area, so you should at least craft the starter Reaper pistol and a few hundred bullets. Alternatively, there will be no enemies here for a short while after a Raptura event (a solar flare, basically) when the planet is scorched.
StarRupture Stabilizer blueprint location
As you can see in the video above, you'll find the Stabilizer blueprint in the CRO 'Grey Owl' outpost, also known as Claywood's Research Outpost, to the northeast of the lander where you start the game. This outpost is in the mountains, requiring you to head up into the hills and loop around to access the facility from the north side. There's a large staircase and massive pipes here, so it's hard to miss.
Once you've reached Claywood's Research Outpost, go up the stairs to the raised area on your right. You'll find the Stabilizer blueprint in a blue chest at the top of the tower at the back of the outpost, requiring a few jumps to reach. It's easy, so don't sweat it.
Grab the blueprint and return to the Recipe Station in your base to contribute the schematic to the Stabilizer recipe. You'll also need 100 Rotors, 300 Titanium Tubes, and 600 Data Points, so make sure you grab those blueprints too.
As I mentioned, this area is infested with aliens that more or less continuously spawn if you arrive during the planet's normal conditions. In this case, you'll need a gun and plenty of ammo.
However, and this is what I'd recommend doing, the outpost (and all others) will be empty during the brief window the planet is all scorched and barren after the Raptura storm. It might look more spooky, but it's much more peaceful. Or you can just run past them all like I did.
