I made a quick glance in the thread. I want to say that technically you are not really storing Bitcoin locally in your computer. It is all right there in the blockchain. But you do control the "coins" you have by having or knowing the private key to unlock them. Cloudcoin is a closer and a more appropriate name for Bitcoin if you study at it well.
This mean you can access your bitcoin thru your computer directly with the use of software like bitcoin core wallet, or other light wallet like electrum, multibitHD etc. And you can have the wallet that contain the private key and public key to that address in the blockchain. You can also back up those access keys and be able to transfer the control from one computer to another computer.
So logically you cannot store your bitcoin in your computer but can gain access and control to it thru desktop applications.
. Every Bitcoin wallet contains one or more private keys, which are saved in the wallet file.
The private keys are mathematically related to all Bitcoin addresses generated for the wallet.
https://en.bitcoin.it/wiki/Private_key