But I found others, and
while they say Norman was there, had a gun, and fought with some
students, nowhere has it been proved that he was there with the
specific intent to cause trouble.

He was there.

He had a gun.

He was picking fights with students.......

But you fail to see how that establishes he was there to cause trouble?

Norman turned his gun over to the local police, who quickly announced it had
*not* been fired. The FBI, however, was later able to establish that the gun
had been fired since it was last cleaned- although they couldnot establish that
it had been fired at the demonstration.

A good synopsis of events:

from: http://www.spectacle.org/595/kent.html

The units that responded were ill-trained and came right from riot duty
elsewhere; they hadn't had much sleep. The first day, there was some brutality;
the Guard bayonetted two men, one a disabled veteran, who had cursed or yelled
at them from cars. The following day, May 4th, the Guard, commanded with an
amazing lack of military judgment, marched down a hill, to a field in the
middle of angry demonstrators, then back up again. Seconds before they would
have passed around the corner of a large building, and out of sight of the
crowd, many of the Guardsmen wheeled and fired directly into the students,
hitting thirteen, killing four of them, pulling the trigger over and over, for
thirteen seconds. (Count out loud--one Mississippi, two Mississippi, to see how
long this is.) Guardsmen--none of whom were later punished, civilly,
administratively, or criminally--admitted firing at specific unarmed targets;
one man shot a demonstrator who was giving him the finger. The closest student
shot was fully sixty feet away; all but one were more than 100 feet away; all
but two were more than 200 feet away. One of the dead was 255 feet away; the
rest were 300 to 400 feet away. The most distant student shot was more than 700
feet from the Guardsmen.

Some rocks had been thrown, and some tear gas canisters fired by the Guard had
been hurled back, but (though some of the Guardsmen certainly must know the
truth) no-one has ever been able to establish why the Guard fired when they
were seconds away from safety around the corner of the building. None had been
injured worse than a minor bruise, no demonstrators were armed, there was
simply nothing threatening them that justified an armed and murderous response.
In addition to the demonstrators, none of whom was closer than sixty feet, the
campus was full of onlookers and students on their way to class; two of the
four dead fell in this category. Most Guardsmen later testified that they
turned and fired because everyone else was. There was an attempt to blame a
mysterious sniper, of whom no trace was ever found; there was no evidence, on
the ground, on still photographs or a film, of a shot fired by anyone but the
Guardsmen. One officer is seen in many of the photographs, out in front,
pointing a pistol; one possibility is that he fired first, causing the others,
ahead of him, to turn and fire. Or (as some witnesses testified) he or another
officer may have given an order to fire. It is indisputable that the Guardsmen
were not in any immediate physical danger when they fired; the crowd was not
pursuing them; they were seconds away from being out of sight of the
demonstration.

There was also an undercover FBI informant, Terry Norman, carrying a gun on the
field that day. Though he later turned his gun into the police, who announced
it had not been fired, later ballistic tests by the FBI showed that it had been
fired since it was last cleaned-- but by then it was too late to determine
whether it had been fired before or on May 4th.