I called parts of it a block chain since the send/receive blocks contain a hash of the previous block and it has a one-follows-another order.  It's different than other cryptos in that one block is one transaction, a send or a receive, where others contain many transactions.

Thanks for spending the time you did looking at it, sorry about the lack of comments that's admittedly in poor style.

These differ from off-chain transactions in that each chain is replicated to all peers so all account actions are observed and validated by everyone.  Rather than packing all transactions in to a single chain, all transactions for a single account are in a single chain.

On the double spending front, since all blocks for each chain are replicated to everyone, nodes can ask and publish their view of signed Y-follows-X blocks.  If anyone instead sees a signed Z-follows-X block this is a fork and needs resolution.  Unlike monolithic blockchains, a fork in this system only affects a single account instead of everyone, again working toward scalability where we don't stall everyone because one section has an issue.

Resolution is done through a weighted vote system where losing blocks and dependents are rolled back.  Senders can be sure they're not receiving a double spend by observing votes and tallying them, if they observe no forks or a resolved fork they can safely accept the transaction in to their chain. Notice though that resolution is never needed in the normal, well-behaved case.  Forks only happen with signed, conflicting blocks; only accounts that are misbehaving by intentionally creating forks will every be put up for resolution.

Let me know if any of what I wrote doesn't make sense.