Haven't read Anathem and couldn't find in any summary who the Ita are. Stephenson's story being about a post-societal collapse I fantasise that that ITA are the Information Truth Authority.
Well, if Stephenson didn't mean that, I'll just make it up, right? :) Because anyway, that's the thing we need to be mindful of and avoid in the coming years.
In some ways I see LLM-AI and DeepFakes as being the undoing of the printing press and the camera respectively.
Both inventions "liberated truth". Gutenberg's press eroded the authority of the church and kick-started the real scientific revolution. The camera changed popular conceptions of geography and history. Together they created "News" as a concept in modernity, even before electronics brought instantaneous television.
If AI undoes this, a good way to understand the worst future is to rewind to a pre-Gutenberg and pre-photographic era. A key dystopian feature would be a singular centralised truth and information authority, essentially replacing the church circa 14th century.