Mini-Blockchain proposal: How is the proof-chain secured against injections?
Block data is not necessary to check proof of work, or to check that past block headers has not been altered. This is because for a block to pass proof of work check, the hash of its header must be less than a certain value. So, the header (which is just 80 bytes in Bitcoin) has enough information to check proof of work. Also, each header includes the hash of header of the previous block. So, assuming that the hash function is collision-resistant, it is impossible to modify any of the previous headers without changing the hash of the last header, and it is impossible to change any header while keeping proof of any work done after the corresponding block. The only way to "fake" a mini-blockchain is to outrun the honest miners, which requires an attacker to have comparable amount of hash power.