First of all I must say that kladkogex communication style appears very annoying to me, almost like a textbook version of a stereotype Russian troll. This is unfortunate as the topic is super interesting IMHO. Personally I would like to see a valid counterexample to the hashgraph consensus, so I decided to get into the discussion despite the annoying communication style.

Ok, first of all we need to clarify what we want to achieve and I propose the following:

Proof that hashgraph consensus is not a byzantine fault tolerant atomic broadcast algorithm under the assumptions made in the hashgraph paper.

Do you agree? (Please no moral, hate talk, accusations bla, bla… Its hard enough to go that road with you anyway. Stay scientific, ok?)

Ok, how do we do that? BFT atomic broadcast, which hashgraph claims to be, is defined by the following four axioms:

1.) Validity: if a correct participant broadcasts a message, then all correct participants will eventually receive it.

2.) Uniform Agreement: if one correct participant receives a message, then all correct participants will eventually receive that message.

3.) Uniform Integrity: a message is received by each participant at most once, and only if it was previously broadcast.

4.) Uniform Total Order: the messages are in a total order in the mathematical sense; that is, if any correct participant receives message 1 first and message 2 second, then every other correct participant must receive message 1 before message 2.

The task is then to find a concrete counterexample to one of these axioms. This boils down to finding a time-series of concrete hashgraphs (for users A(t),B(t),C(t),…) which violates one of the previous points after we run the algorithms of the paper on it.

Now kladkogex claimed in the initial post to have found such a situation. Unfortunately his example missed the actual hashgraph. So kladkogex can you please rewrite your example into an actual series of hashgraphs for users A,B,C,…, so everyone can run the algorithms on it (by hand) and see the contradiction? After all you made very strong accusations and according to the rules of science, which you brought stubborn into the game, the burdon of proof is on you. As you accused craigdrabiktxmq as being mathematically imprecise it’s now your turn to make your also mathematically imprecise proposed counterexample precise, so we all can see that it works.

I think its enough to write the appropriate hashgraph related to your counterexample with pen&paper and then send a picture of it here for discussion.

P.S: Leemon Baird was a professor of mathematic by the time he wrote the paper. He wrote >40 other math papers. This of course does not mean, that it is correct. Personally I like the style of the hashgraph paper.

However, I’m not a fan of Hedera, not the least! I think they are like the pest for decentralized payment and I would love to see them fall. But we have to do it properly. Its David against Goliath and David can not afford to rank high on the crackpot index, if he claims any chance in this battle.