If Keltham is teaching again, Broom should be there to make sure Keltham does not teach anything which is obviously going to destroy the world.

Visibly or invisibly?  Broom has been advised that Keltham does not currently have any spells that could detect Broom, and he is still within Keltham's one-day deadline for replying to Keltham's original terms.  Broom asks a great wizard about this.

If Keltham is teaching again, Broom should be there to make sure Keltham does not teach anything which is obviously going to destroy the world.

Visibly or invisibly?  Broom is still within Keltham's one-day deadline for replying to Keltham's original terms.  Do the great wizards know if Keltham will be able to detect Broom again today?  Does Cheliax want Broom to be visible regardless?  Broom goes to ask a great wizard about this.