Block headers in a multi-hash blockchain system

From a practical point of view a multi-hash blockchain means a kind of a multi-header blockchain system. For each hash pointer or each pair of hash pointers we have to save a:
- nonce for each hash pointer
- difficulty for each pair of hash pointers
- general retention policy for each pair of hash pointers
- actual retention policy for a given hash pointers

At calculating the new hash of the hash pointers, the following data should be taken into account:
- all the information that is stored in the hash pointer and was previously mentioned
- the hash values of the previous hash pointers
- merkle root of the transactions
- merkle or patricia root of the state

The block of a multi-hash system contains:
- several hash links
- the transactions
- the new state