The Authority closed the case because they didn't want to spend much time finding the murderer of their traitor.
The most important work after finding out that Ulv Sylvester was a traitor was trying to figure out how much information was leaked and if any vital plan was given to him. They needed to find them and change the plan.
They had to reduce the damage done by Ulv as little as possible.
As for the murder, with their assumption that it was either Devil or Devil Contractor, they had to increase the security of the SpiritMeadow. If the Devil killed without discrimination or just came to cause trouble there, there will be many more victims for the Devil.
As soon as that happens, they will catch him and they will naturally solve the problem. But if the murderer does not show up then they know that they can't do anything. As for the victims, The Authority had to look at the bigger picture.
Anyway, it was going to be a busy day for them.
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