The long utopia - Terry Pratchett

2045-2059. After the cataclysmic upheavals of Step Day and the Yellowstone eruption humanity is spreading further into the Long Earth, and society, on a battered Datum Earth and beyond, continues to evolve.
Now an elderly and cantankerous AI, Lobsang lives in disguise with Agnes in an exotic, far-distant world. He's convinced they're leading a normal life in New Springfield - they even adopt a child - but it seems they have been guided there for a reason. As rumours of strange sightings and hauntings proliferate, it becomes clear that something is very awry with this particular world.
Millions of steps away, Joshua is on a personal journey of discovery: learning about the father he never knew and a secret family history. But then he receives a summons from New Springfield. Lobsang now understands the enormity of what's taking place beneath the surface of his earth - a threat to all the worlds of the Long Earth.
To counter this threat will require the combined efforts of humankind, machine and the super-intelligent Next. And some must make the ultimate sacrifice . . .