Sentinel capital ship
Can you claim the Sentinel capital ship? No. You can fight it and destroy it, but it never surrenders, no captain offers it, and nothing in the game hands it to you.

When it comes
Fight the Sentinels in space and your wanted level climbs. At the top level, five, the Sentinels warp in a capital ship of their own, beside their usual waves of Interceptor fighters. Turrets line its hull, and four shield generators guard it.
How the fight goes
Its shield is far too strong to shoot down, and while it stands, shots do not hurt the hull. The four shield generators hold it up: round cores on the sides of the hull, two on each side, one pair just ahead of the engines and one pair just behind the bow.

- You do not need to destroy the turrets. Fourteen stand along the upper edges of the hull and at the bow; find an angle where they cannot reach you and stay there.
- Fly in under the shield and break the four shield generators, in any order. Each one you break takes a quarter of the shield away, and with all four gone the shield is down.
- From that same angle, shoot the hull for as long as it takes. It does not flee, so there is no hurry. When the ship goes down, the Interceptor fighters withdraw too.
What it gives
Destroy it and your wanted level drops to zero. A few seconds later the Sentinel ships retreat and warp out, and you get one Carrier AI Fragment. Use the fragment and it points you to Dissonance Spike Coordinates: a crashed Sentinel ship on a planet, the wreck of an Interceptor you can claim.
The big balls hanging under its hull are cargo. Shoot the balls and each one spills a small amount of trade goods.
You can also just leave. Every warp into a system sets the wanted level back to zero.
The capital ships of the sky end here. What your own freighter plugs into its slots, and who gives each module, is on freighter technology.