Where are the coins?

EDIT: An earlier version of this post linked to a BitcoinTalk post that speculated on the cause of BIP30 being the introduction of LevelDB. Pieter Wuille kindly informed me that LevelDB was introduced after BIP30 occured , which means that post was definitely false. The third Bitcoin halving is coming up quickly as I write this. I thought this would be a great time to write down what I learned about the amount of BTC in the UTXO set. »