I don't know why this paper needs to introduce so much already common terminology.<p>"Corrupt" is a re-org
"stable transactions" are confirmed transactions<p>"Function maxvalid(C, C). Returns the longest chain from C ∪ {C} that does not fork from C
more than k blocks."<p>This is the recipe for partitioning consensus. All you need to do is broadcast to anyone a lower-work chain and they will be on their own fork.<p>This is easy to do during a new sync in which the node has been offline for more than k blocks, or with a little more work you could stake grind and partition the network at the tip.<p>The former problem is covered in section 3.2.<p>Generally the nothing at stake problem will result in the problem of requiring some trusted source to not lie, regardless of the implementation, see <a href="https://download.wpsoftware.net/bitcoin/pos/" rel="nofollow">https://download.wpsoftware.net/bitcoin/pos/</a>