35000 nukes is overkill for *any* MAD scenario... even say the top 10 cities of any superpower (,US, China, USSR, India, etc) wiped out would be a nation ender event... thats not something any country can recover from....
Lets say MAD does happen, that is a true Great Reset and Great Equalizer event... then its matter of which side eventually builds back better, faster...
Thats where the underground stuff comes into play. Likely major powers have seeds vaults, to store not just crop seeds but other stuff like even human dna diversity to restart the race/species... and a blueprint of quickly building back from zero (stone age) to modern within say timespan of 50 years rather than 5000 years...
Things like nueral networks that take millions of dollars to train/calc can be stored in archive, like the Google Deepmind AlphaGo Zero AI network that costs $25 million on state of art data center produces just a neural net of disk size 200megabytes lol!!! It took mathematician lifetime to calculate PI to 400 digits, and first computer ENAIC was used to calculate ballistic trajectory tables that Excel does much better and faster these days
Im saying nowadays you cannot even build a CPU without using another CPU in the process, cannot make a computer without a computer, cannot code a compiler without using another compiler... but starting over again will not take as long as its possible to go from zero (stone age) to EUV 5nm within half a century timespan... We just need to leave enough tools, data, seeds, blueprints, maps and accessible format to do the bootstrapping, kinda like the voyager golden records that are universal instructions in a way even any aliens will be able to decipher and understand... we need to leave enough tools and instructions in readily accessible format for a worst case scenario post MAD situation that the Chinese civilization can start from zero and build up faster/better in record time and out compete the rest of the world... but in order for that to happen, it must be a true MAD situation and for that to be possible China needs at least 1000 deliverable nukes....
This is why US trying to trick China to sign nuke treaty, they see within decade this window will close for good