Dealing with many versions of history:

In the approach described in the above posts, you can never be sure which version of history is the right one, in fact, it's not meaningful to talk about a "right" version of history, only different versions of history that you have different confidence about. It may turn out that one version of history preferred by H right now may not extend to the version preferred by H in the next block. For the most part, that's ok, because most versions will be identical except for small differences due to transactions not reaching the deciders/dropped. So you just request to add your events to your most preferred versions of history as determined by H, and stick to just the most preferred resulting versions of history.

To avoid dealing with an exponentially growing tree of histories and save computing resources, you can discard the least preferred versions of history. e.g. if H is the lowest sum of HIT/EFFECTIVE_STAKEs, you can know the probability distribution of the lowest HIT/EFFECTIVE_STAKE during each block by sampling previous blocks. If you know that the difference between the lowest HIT/EFFECTIVE_STAKE and say the 10th lowest HIT/EFFECTIVE_STAKE has never been greater than e and will likely almost never be greater than e, then you can just keep the history with the lowest sum SUM of HIT/EFFECTIVE_STAKEs in memory, along with just those histories whose sum are less than SUM + e and discard the rest. In the unlikely event that the versions of history that the rest of the network prefers are built on an old version that you discarded, then you end up on a fork, and you'll have to deal with it manually by redownloading the histories from somewhere you trust.

This is when all the actors are honest. When there are dishonest actors, then large differences from deliberate actions by them can occur. So the problem is how to discover who they are, and consequently blacklist them and reject their versions of history. This could be done outside the network of actors and events, through e.g. RL investigation. It could also be done within the network. e.g. if the versions of history broadcast by a certain actor frequently don't include the events involving you that are sent to them while other versions of history do, that suggests that actor is not being honest with you. You may want to prefer other versions of history that did include your events (or if you think it's not a big deal just try to include that event again later based on the same history, when it is a different decider's turn), and you may want to increase their blacklist weight, and announce the discrepancy to other actors so they can likewise increase their blacklist weights.