Big change from the venerable T-38...

There are two curious little speed brakes that deploy below the cockpit for slow, high AOA flight.





Do these prevent uncontrollable pitch-up?
Those two "curious little speed brakes" are communications antenna.

Can’t see what speed brakes you are talking about. I see two antenna below the cockpit under the new jet. Airborne pics show no speed-brakes that I can see. The T-38 had speed brakes under the fuselage. See no such things below the new jets fuselage.
Anecdote: After landing from a T-38 solo flight, I cleared the runway and stopped short of the center runway to complete my post-landing checklist when I noticed the T-38 that landed after me was kicking up dust and “swaying” and as it topped the slight rise in the runway, I saw the jet had landed gear-up. The student deployed his speed brakes and that action ground the speed-brakes into nothing. Pretty cool to watch.
Antennas