From TTT glossary:
Imprompta, The -- The anonymously written collection of the Warrior-Prophet's earliest sermons and aphorisms.
As for the Warrior-Prophet summoning witness, this seems to be related to a specific sermon when Kellhus counseled a nameless Conriyan knight. The knight was stricken by nightmares of a dead girl he'd seen in a nearby village. From TWP:
"But why?" [the knight] cried. "I mean, how many dead have we seen?"
"But not all seeing," Kellhus replied, "is witness."
"I don't understand..."
"Witness is the seeing that testifies, that judges so that it may be judged. You saw, and you judged. Trespass had been committed, an innocent had been murdered. You saw this."
And now to start speculating!
The idea of witness being a deeper form of seeing makes me think of a couple of things.
First, a deeper form of sight, the idea of recording a deed so it can be judged, could be related to a soul's ledger of sins committed. It might suggest that sins are only such if they are
witnessed?
Second, I can't imagine a deeper form of sight than The Judging Eye. It's suggested that Mimara not only has the ability to see the soul's ledger, but also the ability to absolve those sings.
Ordinary witness records sin, TJE witness absolves it?