SPOILERS AHEAD (next two paragraphs)
The central mystery, is of course, the identity and purpose (if such a term were germane) of the otherworldly visitors to Arbre, content to park in orbit and observe, provoking the powers-that-be to act, apparently smug in their possession of infinitely superior armament.
While Anathem (and the avout specifically) make no assumptions about the nature of the Geometers (their moniker), it is revealed that their identities are impossibly similar to their specimens. They differ in subtle but crucial ways, such as possessing bodies of star-stuff born of different, extracosmic physics.
A generous chunk of the third act is set in space; by far the most dynamic and wonderful bits of the book. This is not your man-the-guns (pew-pew) space battle, nor is it about the chilling isolation and dread foisted upon by light-lag and the endless void; although that factors in somewhat. It’s the engineer’s space adventure, with nifty mechano space suits, space scaffolding, construction kits and camouflage, and with orbit transfers right out of a handbook of celestial mechanics. It drives home aspects of the strangeness of space that few works touch on because they are the least romantic and the hardest to describe: Maneuvering.
The end of the book contains one final twist, a denouement of a plot thread that rears its head often through the book: The Payoff, if you’ve been paying attention to the numerous diversions from before. It’s a grand tale in that the world of Arbre is irreconcilably different by the end. I would call it a thinking man’s coming-of-age, first contact story that has some social commentary, epistemology and rationalism thrown in, but that would be a colossal undersell. It’s a big-picture novel that sweats the details. It’s imaginative, funny and has a plethora of a-ha moments. It’s masterful. Go read it.