If more than one coin did the "mini-blockchain" proposal, would that make the weaker coin vulnerable?

So, I was reading this paper as a proposal to the ever growing blockchain problem. In summary, it’s security is provided without a full blockchain by having a proof chain with these fields:

  • Previous proof block hash
  • block header hash

Now this is all fine, but one problem I see is what if 2 coins were to adopt this scheme? If one chain was vastly more powerful than another, than an attacker could take the other blockchain and build fake transactions and blocks onto it and then introduce it to the weaker coin’s peers. The peers would see it as having a higher overall difficulty/length and adopt it. Other than verifying the genesis block’s hash and embedding it within the peer/wallet software, is there any other way to prevent this attack? The paper also mentions trimming extremely old proof blocks, but that doesn’t appear to be possible to securely do if the genesis block could be pruned from the proof chain.

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