Nice! I haven't read Axiomatic yet, but this has been my "Greg Egan year". I have read Permutation City and Diaspora: maybe the two most stimulating scifi novels I have ever read.
Read Diaspora last year w/o knowing anything about it. Easily one of my favorite sci-do books to date—I can’t believe it was there waiting for me the entire time. Permutation City is one of my next 3 reads.
+1 for permutation city.
The core concept is so well established in the book.
I also highly recommend _Distress_ as it continues some cosmology ideas from Permutation City.
There are also several novels which kind of similar to Diaspora: Schild's Ladder, Incandescence, and stories in the Incandescence universe: Ride a crocodile, Hot rock, Glory.