Seldon's trial begins. It's noted that the "[p]ress and public were excluded and it was doubtful that any significant number of outsiders even knew that a trail of Seldon was being conducted" (I.6.3). Get out your highlighters, because we'll be coming back to this.
Five members of the Commission of Public Safety stand as the judges to make for a fair and just trial—if by "fair and just" you mean "biased and corrupt."
We then get a detailed transcript of Seldon's turn on the stand with the prosecution asking the questions.
The prosecution opens by asking Seldon about the extent of his project. Seldon states he has fifty (fifty-one counting Gaal) mathematicians on his project.
Oh, you meant everyone, not just mathematicians, Mr. Prosecutor? Then the number is actually 98,572.
The two quibble about whether or not Seldon's psychohistory predictions are to be deemed disloyal to the Empire. Seldon believes mathematics to be beyond loyalty and disloyalty. His predictions are merely facts. The Prosecution, obviously, disagrees.
The prosecution suggests that maybe Seldon is raising an army to stand against the Empire, Seldon just LOLs.
Although, we might have to agree with the prosecution here. An army composed of mathematicians and scientists would actually be terrifying. All those slide rules!
When questioned whether or not the fall of the Empire can be avoided all together, Seldon says no. The mere three hundred years between the fall and the present is just too short a time. Instead, they can only minimize the effects of the collapse.
The prosecution tries to argue with Seldon that the Empire has never been stronger or more powerful.
Not according to the facts, Seldon says.
Finally, we get the gist of this trial: Seldon predicts the Dark Age following the Empire's fall will last for 30,000 years, which is a whole lot of Dark Age. But he has a plan. He can't prevent the fall, but he can lessen the Dark Age to a mere 1,000 years.
What's the plan? Seldon will save all the knowledge of the human race. The resulting product, the Encyclopedia Galactica, will allow humanity to rebuild civilization in 1,000 years.
When the questioning ends, Gaal congratulates Seldon on a job well done and asks what will happen next. Seldon says they'll adjourn the trial and follow up with a private agreement outside of court.
When asked how he knows, Seldon basically says that this time he doesn't know for certain. A little luck would definitely help.