Tartarus and the Great Journey

As we all know, Truth gave Tartarus the Index toward the end of Halo 2 to activate Installation 05 and start the Great Journey.

My question is did Truth get word on Tartarus dying at the hands of the Arbiter?
Or did Truth think Tartarus activated Halo and began the Great Journey into Godhood since he was never heard from again?

Truth has been confronted by Johnson and Keyes. Both were prisoners of Tartarus to activate the rings.
Truth could come to the obvious conclusion that they killed him.

Or

He could think Tartarus activated the ring, went on the Great Journey, and left the humans behind considering they are “unworthy”.

I’ve never seen what Truth’s thoughts about the situation was, so I’m hoping someone can shed some light on this.

I don’t think Truth really cared.

Considering Truth knew exactly what the Halo’s do… I’m pretty sure the lack of Installation 05’s activation is evidence enough that nothing happened.