Not to go off on to much of a tangent, but the push of a button cannot run 15,000 years of advancement. That smacks of being raised on Armageddon thinking. Even a large nuclear war would not touch vast parts of human-inhabited Earth. Have you seen anyone having trouble rebuilding in or near Hiroshima and Nagasaki (much dirtier bombs, then)?
The knowledge of how to rebuild a modern Earth now lies distributed quite well around the world, on computer and backup media. Not to worry.
Even bombs jacketed with Cobalt Thorium G with a radioactive half-life of 93 years ... ?