That Algorand paper suggests a way of scaling consensus to large numbers of nodes, i.e. by running a consensus algorithm on a random sample of nodes. It doesn't address scalability with respect to transaction volume, which is what people usually mean in the context of the blockchain trilemma.

>It doesn't address scalability with respect to transaction volume.

For scalability with small transaction volume, Coda[1] is the best.

[1] https://codaprotocol.com

Thats laughable nonsense tbh. People should "mine" to compress the blockchain lol. The blockchain isnt even needed (the history). Have a look at XRPL srsly its the perfect example it has terabytes of past transactions and they are stored by some nodes but its not needed to make progress. And ofc it could be compressed but that totally destroys its purpose. If you want the transactions you want to be able to query them which you cant do efficient if its compressed.

History is very much needed to verify that the current state was arrived at by following the rules.

No, that's commonly made up thing coming form bitcoin where "balances" don't exist and the state of the ledger is defined by chain of past transactions. It is a design decision not a fundamental rule. It does not apply to the XRPL where each closed ledger has to follow all rules and contains all information to make forward progress. For example if a balance would be made up it would guaranteed violate a rule now (in the current ledger) there is no need to know the past transactions because if you add balances that would change the sum of all balances which obviously violates the rules. So form that point on each following ledger would be obviously and known in real time to be invalid. In reality ofc that cant happen because the software would simply not include a transaction that causes the invalid state. If for any reason there would actually be something considered "wrong" in the past it would not have any effect. The system is the code itself all participants agreed on running the same code and agreed on that what the code deems valid is valid and unchangeable forever. A bug can be fixed but what it caused in the past cant be. So the whole validation thing is useless it was validated already by the rules (the code) that was running back then. Validating it again with a bug fixed version of the code is useless. Just like if you would find an error in the bitcoin blockchain that validated fine with the version from that time. So what? it doesn't matter it cant be changed and if someone sends you bitcoins he only has because of a bug how does that matter if it don't change anything in the presets? You don't have to trust that no mistakes where made in the past you only need to trust that the past cant be changed to rely on the system in the presets.

Here's an example how you can validate the current state without knowing the past.

Imagine there are 100 coins made form something that does not exist beside in these coins. Someone wants to pay something to you using 2 of these coins. Do you need to know where he got them from and where the person before got them from and so on? If you know there are only 100 in total. (state is public) And no way to change that. (rules/code is known) And you know that if you take the 2 no one can force you to give it back. (transactions are irreversible) Then no, you don't need to know the past transactions at all. Maybe they where stolen in the past a thousand times also lost and found by someone else many times. Does it matter? Not at all.

The need to verify history applies to all cryptocurrencies, including account-based ones like Ethereum and XRP. You can assume the current state as valid and verify from there on, but then you're not a fully verifying node, and you risk being fooled by some peers presenting you with a made-up current state.

You just repeated yourself and you are still wrong. Maybe read my message or inform you somewhere else. There is no way for anyone to fool you with a made up state. The systems state is public remember? It's up to you from whom you get it but usually from one node and the hash from many others to verify that all have the same state) And unlike with bitcoin there cant show up a longer chain later.

You didn't even say permissionless in your post. Ripple is a company you mean the XRPL. The XRPL is permissionless in every aspect. You can insert transaction without anyones permission. You can run a node without anyones permission. You can fork and create you own version without anyones permission. You can change code and create an amendment without anyone's permission. It needs 80% favorable votes for two weeks to become active but it doesn't need anyone's permission. There is no entity that can vote against it and prevent it.